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blog(leetcode): add matrix sort
Signed-off-by: Matej Focko <mfocko@redhat.com>
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blog/leetcode/sort-matrix-diagonally.md
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blog/leetcode/sort-matrix-diagonally.md
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---
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title: Sort the matrix diagonally
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description: Compiler assisted development.
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date: 2023-03-04T23:15
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slug: leetcode/sort-diagonally
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authors:
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- name: Matej Focko
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title: "a.k.a. @mf"
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url: https://gitlab.com/mfocko
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image_url: https://github.com/mfocko.png
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tags:
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- cpp
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- leetcode
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- iterators
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hide_table_of_contents: false
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---
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Let's try to solve one of the LeetCode challenges in easy and hard mode at the
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same time.
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<!--truncate-->
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* Link to the problem: https://leetcode.com/problems/sort-the-matrix-diagonally/
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## Problem description
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A **matrix diagonal** is a diagonal line of cells starting from some cell in
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either the topmost row or leftmost column and going in the bottom-right direction
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until reaching the matrix's end. For example, the **matrix diagonal** starting
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from `mat[2][0]`, where `mat` is a `6 x 3` matrix, includes cells `mat[2][0]`,
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`mat[3][1]`, and `mat[4][2]`.
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Given an `m x n` matrix `mat` of integers, sort each matrix diagonal in ascending
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order and return the resulting matrix.
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### Example
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![Image describing the problem](https://assets.leetcode.com/uploads/2020/01/21/1482_example_1_2.png)
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## Skeleton and initial adjustments
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We are given the following skeleton for the C++ and the given challenge:
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```cpp
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class Solution {
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public:
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vector<vector<int>> diagonalSort(vector<vector<int>>& mat) {
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}
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};
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```
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The task is to sort the passed matrix diagonally and then return it. First of all,
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I don't like to solve this in a web browser, so we'll need to adjust it accordingly
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for running it locally. We'll start by including the `vector` header and using
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fully-qualified namespaces[^1] and also adding few tests:
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```cpp
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#include <cassert>
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#include <vector>
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using matrix = std::vector<std::vector<int>>;
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class Solution {
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public:
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matrix diagonalSort(matrix& mat)
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{
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}
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};
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static void test_case_1()
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{
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// Input: mat = [[3,3,1,1],[2,2,1,2],[1,1,1,2]]
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// Output: [[1,1,1,1],[1,2,2,2],[1,2,3,3]]
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Solution s;
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assert((s.diagonalSort(std::vector { std::vector { 3, 3, 1, 1 },
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std::vector { 2, 2, 1, 2 },
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std::vector { 1, 1, 1, 2 } })
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== std::vector { std::vector { 1, 1, 1, 1 },
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std::vector { 1, 2, 2, 2 },
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std::vector { 1, 2, 3, 3 } }));
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}
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static void test_case_2()
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{
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// Input: mat =
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// [[11,25,66,1,69,7],[23,55,17,45,15,52],[75,31,36,44,58,8],[22,27,33,25,68,4],[84,28,14,11,5,50]]
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// Output:
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// [[5,17,4,1,52,7],[11,11,25,45,8,69],[14,23,25,44,58,15],[22,27,31,36,50,66],[84,28,75,33,55,68]]
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Solution s;
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assert((s.diagonalSort(std::vector { std::vector { 11, 25, 66, 1, 69, 7 },
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std::vector { 23, 55, 17, 45, 15, 52 },
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std::vector { 75, 31, 36, 44, 58, 8 },
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std::vector { 22, 27, 33, 25, 68, 4 },
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std::vector { 84, 28, 14, 11, 5, 50 } })
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== std::vector { std::vector { 5, 17, 4, 1, 52, 7 },
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std::vector { 11, 11, 25, 45, 8, 69 },
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std::vector { 14, 23, 25, 44, 58, 15 },
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std::vector { 22, 27, 31, 36, 50, 66 },
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std::vector { 84, 28, 75, 33, 55, 68 } }));
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}
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int main()
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{
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test_case_1();
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test_case_2();
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return 0;
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}
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```
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We need to return the matrix, but we're given a reference to the input matrix. We
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can easily abuse the C++ here and just switch the reference to value, this way
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the matrix will be copied when passed to the function, we can sort the copy and
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just return it back. And we also get yelled by the compiler for the fact that the
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method doesn't return anything yet, so to make it “shut up” we will just return
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the input for now:
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```diff
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- matrix diagonalSort(matrix& mat)
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+ matrix diagonalSort(matrix mat)
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{
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+ return mat;
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}
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```
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Now, we get the copy and we're good to go.
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## Naïve solution
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As you may know, C++ offers a plethora of functions that can be used to your
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advantage, given that you know how to “bend” the data structures accordingly.
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What does that mean for us? Well, we have an `std::sort`, we can use it, right?
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Let's have a look at it:
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```cpp
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template< class RandomIt >
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void sort( RandomIt first, RandomIt last );
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```
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This overload is more than we need. What does it do? It just sorts the elements
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in the range `[first, last)` using `operator<` on them. We can't sort the whole
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matrix using this, but… we can sort just »one« diagonal without doing much work
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on our end.
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What is the `RandomIt` type though? If we look more into the documentation, we
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can easily find the requirements for it and also learn that it's a _random access_
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_iterator_ and allows swapping its values at the same time.
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:::tip Random access iterator
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What is the _random access iterator_ though? We can find it in a documentation
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and see the following description:
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> A **LegacyRandomAccessIterator** is a [LegacyBidirectionalIterator](https://en.cppreference.com/w/cpp/named_req/BidirectionalIterator)
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> that can be moved to point to any element in constant time.
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After that we can see all the requirements for it being listed. I don't feel like
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reading them right now, so we will just use it and see where the compilation blows
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up, i.e. “_compiler-assisted development_”[^2] if you will ;)
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:::
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Now we know that we can use `std::sort` to sort the diagonal itself, but we also
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need to get the diagonals somehow. I'm rather lazy, so I'll just delegate it to
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someone else[^3]. And that way we get
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```cpp
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matrix diagonalSort(matrix mat)
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{
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// we iterate over the diagonals
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for (auto d : diagonals(mat)) {
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// and we sort each diagonal
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std::sort(d.begin(), d.end());
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}
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// we take the matrix by copy, so we can sort in-situ and return the copy
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// that we sorted
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return mat;
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}
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```
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This solution looks very simple, doesn't it? Well, cause it is.
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Let's try compiling it:
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```
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matrix-sort.cpp:11:23: error: use of undeclared identifier 'diagonals' [clang-diagnostic-error]
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for (auto d : diagonals(mat)) {
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^
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Found compiler error(s).
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make: *** [makefile:14: tidy] Error 1
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```
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OK, seems about right. We haven't implemented the `diagonals` yet. And based on
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what we've written so far, we need a function or a class `diagonals` that will
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give us the diagonals we need.
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## Implementing the `diagonals`
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Cool, so we need the function that will let us go through each and every diagonal
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in our matrix. We use the _for-range_ loop, so whatever we get back from the
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`diagonals` must support `.begin()` and `.end()`. Since I am a masochist, we will
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do such functionality for a matrix of any type, not just the `int` from the challenge.
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As I said, we need to be able to
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* construct the object
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* get the beginning
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* get the end (the “sentinel”)
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```cpp
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template <typename T>
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class diagonals {
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using matrix_t = std::vector<std::vector<T>>;
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matrix_t& _matrix;
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public:
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diagonals(matrix_t& m)
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: _matrix(m)
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{
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}
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diagonals_iter begin()
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{
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/* TODO */
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}
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diagonals_iter end()
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{
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/* TODO */
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}
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};
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```
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Now we have a `diagonals` that we can use to go through the diagonals. We haven't
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implemented the core of it yet. Let's go through what we have for now.
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We have a templated class with templated `T` that is used as a placeholder for any
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type we would store in the matrix. Because I'm lazy, I have defined the `matrix_t`
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type that is a “shortcut” for `std::vector<std::vector<T>>`, so I don't have to
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type it out all the time. Of course, we need to store the matrix, we are given,
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as a private attribute. And then just have the constructor and the 2 methods we
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need for the _for-range_.
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### Iterating over diagonals
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Now that we have an object that will allow us to iterate through the diagonals,
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we need to implement the iterating itself. We need to go through all of them, so
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we have multiple options how to do so. I have decided to start from the “main”
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diagonal that starts at `(0, 0)` index and then proceed with the diagonals starting
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in the first row, followed by the rest of the diagonals in the first column.
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We need to be able to tell that we've iterated through all of them, and also we
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need to know which diagonal is next. For that purpose we will pass the indices
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of the first cell on the diagonal. That way we can always tell how to move forward.
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We will start by updating the `begin` and `end` to reflect our choice accordingly.
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```cpp
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diagonals_iter begin() { return diagonals_iter { _matrix, 0, 0 }; }
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diagonals_iter end() { return diagonals_iter { _matrix, 0, _matrix.size() }; }
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```
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For the `begin` we return the first diagonal that starts at `(0, 0)`. And because
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we have decided to do the diagonals in the first column at the end, the first
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diagonal that is not a valid one is the one at `(0, height)`. Apart from the
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indices, we also need to pass reference to the matrix itself.
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:::note
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You may have noticed that we also include the diagonals that have length 1,
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specifically the ones at `(0, height - 1)` and `(width - 1, 0)`. We are implementing
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an iterator that **should not** care about the way it's being used. Therefore, we
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don't care about the fact they don't need to be sorted.
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:::
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Cool, let's leave the iterator itself to someone else, right?[^4]
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### Implementing the iterator over diagonals
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We can start with a simple skeleton based on the information that we pass from
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the `diagonals`. Also to utilize the `matrix_t` and also contain implementation
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details hidden away, we will put this code into the `diagonals` class.
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```cpp
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class diagonals_iter {
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matrix_t& m;
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std::size_t x;
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std::size_t y;
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public:
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diagonals_iter(matrix_t& matrix, std::size_t x, std::size_t y)
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: m(matrix)
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, x(x)
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, y(y)
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{
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}
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};
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```
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In this case we will be implementing a “simple” forward iterator, so we don't
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need to implement a lot. Notably it will be:
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* inequality operator (we need to know when we reach the end and have nothing to
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iterate over)
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* preincrementation operator (we need to be able to move around the iterable)
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* dereference operator (we need to be able to retrieve the objects we iterate
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over)
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```cpp
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class diagonals_iter {
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matrix_t& m;
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std::size_t x;
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std::size_t y;
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public:
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diagonals_iter(matrix_t& matrix, std::size_t x, std::size_t y)
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: m(matrix)
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, x(x)
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, y(y)
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{
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}
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bool operator!=(const diagonals_iter& rhs) const
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{
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// iterators are not equal if they reference different matrices, or
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// their positions differ
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return m != rhs.m || x != rhs.x || y != rhs.y;
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}
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diagonals_iter& operator++()
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{
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if (y != 0) {
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// iterating through diagonals down the first column
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y++;
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return *this;
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}
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// iterating the diagonals along the first row
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x++;
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if (x == m.front().size()) {
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// switching to diagonals in the first column
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x = 0;
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y++;
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}
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return *this;
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}
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diagonal<T> operator*() const { return diagonal { m, x, y }; }
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};
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```
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Let's go one-by-one. Inequality operator is rather simple, just compare iterator's
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attributes field-by-field. If you think about it, checking inequality of two 2D
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vectors may be a bit inefficient, therefore, we can swap around and check it as
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a last thing.
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```diff
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- return m != rhs.m || x != rhs.x || y != rhs.y;
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+ return x != rhs.x || y != rhs.y || m != rhs.m;
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```
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Preincrementation is where the magic happens. If you have a better look, you can
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see two branches of this operation:
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1. When `y != 0` (we're iterating over the diagonals in the first column)
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In this case, we just bump the row and we're done.
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2. When `y == 0` (we're iterating over the diagonals in the first row)
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In this case, we bump the column and check if we haven't gotten out of bounds,
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i.e. the end of the first row. If we get out of the bounds, we're continuing
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with the second diagonal in the first column.
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Dereferencing the iterator must “yield” something. In our case it will be the
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diagonal that we want to sort. For sorting we need just the iterators that can
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move around said diagonal. The simplest thing, we can do, is to delegate it to
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something else. In our case it will be a class called `diagonal`.
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## Implementing the `diagonal` itself
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After implementing the iterator over diagonals, we know that all we need to describe
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a diagonal is the matrix itself and the “start” of the diagonal (row and column).
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And we also know that the diagonal must provide some iterators for the `std::sort`
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function. We can start with the following skeleton:
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```cpp
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template <typename T>
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class diagonal {
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using matrix_t = std::vector<std::vector<T>>;
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matrix_t& matrix;
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std::size_t x;
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std::size_t y;
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public:
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diagonal(matrix_t& matrix, std::size_t x, std::size_t y)
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: matrix(matrix)
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, x(x)
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, y(y)
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{
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}
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diagonal_iter begin() const { return diagonal_iter { matrix, x, y }; }
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diagonal_iter end() const
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{
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auto max_x = matrix[y].size();
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auto max_y = matrix.size();
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// we need to find the distance in which we get out of bounds (either in
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// column or row)
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auto steps = std::min(max_x - x, max_y - y);
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return diagonal_iter { matrix, x + steps, y + steps };
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}
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};
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```
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Initialization is rather simple, we just “keep” the stuff we get, `begin` is the
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simplest, we just delegate.
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In case of the `end`, it gets more complicated. We need to know where is the “end”
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of the diagonal. Since `end` should point to the first element “after” the iterable,
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we know that it's the first position of the iterator where either `y` becomes
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`matrix.size()` or `x` becomes `matrix[y].size()`. Also we are moving along diagonal,
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duh, therefore we can deduce the first “position” afterwards by minimal amount of
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steps to get out of the any column or row, hence `std::min(max_x - x, max_y - y)`.
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Final position is then computed simply by adding the steps to the beginning of
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the diagonal.
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Now we just need to finish the iterator for the diagonal itself and we're done.
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### Implementing `diagonal_iter`
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This part is the hardest from all we need to do. It's because of the requirements
|
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of the `std::sort` that requires us to implement a _random access iterator_. I have
|
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briefly described it above, and “in a nutshell” it means that we need to implement
|
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an iterator that can move in constant time along the diagonal in any amount of
|
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steps.
|
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|
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Let's go through all of the functionality that our iterator needs to support to
|
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be used in `std::sort`. We need the usual operations like:
|
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|
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* equality/inequality
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* incrementation
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* dereferencing
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|
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We will also add all the types that our iterator uses with the category of the
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iterator, i.e. what interface it supports:
|
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```cpp
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class diagonal_iter {
|
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// we need to keep reference to the matrix itself
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matrix_t& m;
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|
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// we need to be able to tell our current position
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std::size_t x;
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std::size_t y;
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|
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public:
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using difference_type = std::ptrdiff_t;
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using value_type = T;
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using pointer = T*;
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using reference = T&;
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using iterator_category = std::random_access_iterator_tag;
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|
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diagonal_iter(matrix_t& matrix,
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std::size_t x,
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std::size_t y)
|
||||
: m(matrix)
|
||||
, x(x)
|
||||
, y(y)
|
||||
{
|
||||
}
|
||||
|
||||
bool operator==(const diagonal_iter& rhs) const
|
||||
{
|
||||
return x == rhs.x && y == rhs.y && m == rhs.m;
|
||||
}
|
||||
|
||||
diagonal_iter& operator++()
|
||||
{
|
||||
// we are moving along the diagonal, so we increment both ‹x› and ‹y› at
|
||||
// the same time
|
||||
x++;
|
||||
y++;
|
||||
return *this;
|
||||
}
|
||||
|
||||
reference operator*() const { return m[y][x]; }
|
||||
};
|
||||
```
|
||||
|
||||
This is pretty similar to the previous iterator, but now we need to implement the
|
||||
remaining requirements of the _random access iterator_. Let's see what those are:
|
||||
|
||||
* decrementation - cause we need to be able to move backwards too, since _random _
|
||||
_access iterator_ extends the interface of _bidirectional iterator_
|
||||
* moving the iterator in either direction by steps given as an integer
|
||||
* being able to tell the distance between two iterators
|
||||
* define an ordering on the iterators
|
||||
|
||||
Let's fill them in:
|
||||
```cpp
|
||||
class diagonal_iter {
|
||||
// we need to keep reference to the matrix itself
|
||||
matrix_t& m;
|
||||
|
||||
// we need to be able to tell our current position
|
||||
std::size_t x;
|
||||
std::size_t y;
|
||||
|
||||
public:
|
||||
using difference_type = std::ptrdiff_t;
|
||||
using value_type = T;
|
||||
using pointer = T*;
|
||||
using reference = T&;
|
||||
using iterator_category = std::random_access_iterator_tag;
|
||||
|
||||
diagonal_iter(matrix_t& matrix,
|
||||
std::size_t x,
|
||||
std::size_t y)
|
||||
: m(matrix)
|
||||
, x(x)
|
||||
, y(y)
|
||||
{
|
||||
}
|
||||
|
||||
bool operator==(const diagonal_iter& rhs) const
|
||||
{
|
||||
return x == rhs.x && y == rhs.y && m == rhs.m;
|
||||
}
|
||||
|
||||
diagonal_iter& operator++()
|
||||
{
|
||||
// we are moving along the diagonal, so we increment both ‹x› and ‹y› at
|
||||
// the same time
|
||||
x++;
|
||||
y++;
|
||||
return *this;
|
||||
}
|
||||
|
||||
reference operator*() const { return m[y][x]; }
|
||||
|
||||
// exactly opposite to the incrementation
|
||||
diagonal_iter operator--()
|
||||
{
|
||||
x--;
|
||||
y--;
|
||||
return *this;
|
||||
}
|
||||
|
||||
// moving ‹n› steps back is same as calling decrementation ‹n›-times, so we
|
||||
// can just return a new iterator and subtract ‹n› from both coordinates in
|
||||
// the matrix
|
||||
diagonal_iter operator-(difference_type n) const
|
||||
{
|
||||
return diagonal_iter { m, x - n, y - n };
|
||||
}
|
||||
|
||||
// here we assume that we are given two iterators on the same diagonal
|
||||
difference_type operator-(const diagonal_iter& rhs) const
|
||||
{
|
||||
assert(m == rhs.m);
|
||||
return x - rhs.x;
|
||||
}
|
||||
|
||||
// counterpart of moving ‹n› steps backwards
|
||||
diagonal_iter operator+(difference_type n) const
|
||||
{
|
||||
return diagonal_iter { m, x + n, y + n };
|
||||
}
|
||||
|
||||
// we compare the coordinates, and also assume that those 2 iterators are
|
||||
// lying on the same diagonal
|
||||
bool operator<(const diagonal_iter& rhs) const
|
||||
{
|
||||
assert(m == rhs.m);
|
||||
return x < rhs.x && y < rhs.y;
|
||||
}
|
||||
};
|
||||
```
|
||||
|
||||
At this point we could probably try and compile it, right? If we do so, we will
|
||||
get yelled at by a compiler for the following reasons:
|
||||
```
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1792:11: error: object of type 'diagonal<int>::diagonal_iter' cannot be assigned because its copy assignment operator is implicitly deleted [clang-diagnostic-error]
|
||||
__last = __next;
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1817:11: note: in instantiation of function template specialization 'std::__unguarded_linear_insert<diagonal<int>::diagonal_iter, __gnu_cxx::__ops::_Val_less_iter>' requested here
|
||||
std::__unguarded_linear_insert(__i,
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1849:9: note: in instantiation of function template specialization 'std::__insertion_sort<diagonal<int>::diagonal_iter, __gnu_cxx::__ops::_Iter_less_iter>' requested here
|
||||
std::__insertion_sort(__first, __first + int(_S_threshold), __comp);
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1940:9: note: in instantiation of function template specialization 'std::__final_insertion_sort<diagonal<int>::diagonal_iter, __gnu_cxx::__ops::_Iter_less_iter>' requested here
|
||||
std::__final_insertion_sort(__first, __last, __comp);
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:4820:12: note: in instantiation of function template specialization 'std::__sort<diagonal<int>::diagonal_iter, __gnu_cxx::__ops::_Iter_less_iter>' requested here
|
||||
std::__sort(__first, __last, __gnu_cxx::__ops::__iter_less_iter());
|
||||
^
|
||||
matrix-sort.cpp:161:18: note: in instantiation of function template specialization 'std::sort<diagonal<int>::diagonal_iter>' requested here
|
||||
std::sort(d.begin(), d.end());
|
||||
^
|
||||
matrix-sort.cpp:17:19: note: copy assignment operator of 'diagonal_iter' is implicitly deleted because field 'm' is of reference type 'diagonal<int>::matrix_t &' (aka 'vector<std::vector<int>> &')
|
||||
matrix_t& m;
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1830:2: error: no matching function for call to '__unguarded_linear_insert' [clang-diagnostic-error]
|
||||
std::__unguarded_linear_insert(__i,
|
||||
^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1850:9: note: in instantiation of function template specialization 'std::__unguarded_insertion_sort<diagonal<int>::diagonal_iter, __gnu_cxx::__ops::_Iter_less_iter>' requested here
|
||||
std::__unguarded_insertion_sort(__first + int(_S_threshold), __last,
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1940:9: note: in instantiation of function template specialization 'std::__final_insertion_sort<diagonal<int>::diagonal_iter, __gnu_cxx::__ops::_Iter_less_iter>' requested here
|
||||
std::__final_insertion_sort(__first, __last, __comp);
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:4820:12: note: in instantiation of function template specialization 'std::__sort<diagonal<int>::diagonal_iter, __gnu_cxx::__ops::_Iter_less_iter>' requested here
|
||||
std::__sort(__first, __last, __gnu_cxx::__ops::__iter_less_iter());
|
||||
^
|
||||
matrix-sort.cpp:161:18: note: in instantiation of function template specialization 'std::sort<diagonal<int>::diagonal_iter>' requested here
|
||||
std::sort(d.begin(), d.end());
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1782:5: note: candidate template ignored: substitution failure [with _RandomAccessIterator = diagonal<int>::diagonal_iter, _Compare = __gnu_cxx::__ops::_Val_less_iter]
|
||||
__unguarded_linear_insert(_RandomAccessIterator __last,
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1923:11: error: object of type 'diagonal<int>::diagonal_iter' cannot be assigned because its copy assignment operator is implicitly deleted [clang-diagnostic-error]
|
||||
__last = __cut;
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1937:9: note: in instantiation of function template specialization 'std::__introsort_loop<diagonal<int>::diagonal_iter, long, __gnu_cxx::__ops::_Iter_less_iter>' requested here
|
||||
std::__introsort_loop(__first, __last,
|
||||
^
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:4820:12: note: in instantiation of function template specialization 'std::__sort<diagonal<int>::diagonal_iter, __gnu_cxx::__ops::_Iter_less_iter>' requested here
|
||||
std::__sort(__first, __last, __gnu_cxx::__ops::__iter_less_iter());
|
||||
^
|
||||
matrix-sort.cpp:161:18: note: in instantiation of function template specialization 'std::sort<diagonal<int>::diagonal_iter>' requested here
|
||||
std::sort(d.begin(), d.end());
|
||||
^
|
||||
matrix-sort.cpp:17:19: note: copy assignment operator of 'diagonal_iter' is implicitly deleted because field 'm' is of reference type 'diagonal<int>::matrix_t &' (aka 'vector<std::vector<int>> &')
|
||||
matrix_t& m;
|
||||
^
|
||||
```
|
||||
|
||||
That's a lot of noise, isn't it? Let's focus on the important parts:
|
||||
```
|
||||
/usr/bin/../lib/gcc/x86_64-redhat-linux/12/../../../../include/c++/12/bits/stl_algo.h:1792:11: error: object of type 'diagonal<int>::diagonal_iter' cannot be assigned because its copy assignment operator is implicitly deleted [clang-diagnostic-error]
|
||||
…
|
||||
matrix-sort.cpp:17:19: note: copy assignment operator of 'diagonal_iter' is implicitly deleted because field 'm' is of reference type 'diagonal<int>::matrix_t &' (aka 'vector<std::vector<int>> &')
|
||||
matrix_t& m;
|
||||
^
|
||||
```
|
||||
|
||||
Ah! We have a reference in our iterator, and this prevents us from having a copy
|
||||
assignment operator (that is used “somewhere” in the sorting algorithm). Well…
|
||||
Let's just wrap it!
|
||||
```diff
|
||||
# we need to keep a different type than reference
|
||||
- matrix_t& m;
|
||||
+ std::reference_wrapper<matrix_t> m;
|
||||
|
||||
# in comparison we need to get the reference out of the wrapper first
|
||||
- return x == rhs.x && y == rhs.y && m == rhs.m;
|
||||
+ return x == rhs.x && y == rhs.y && m.get() == rhs.m.get();
|
||||
|
||||
# same when we return a reference to the “cell” in the matrix
|
||||
- reference operator*() const { return m[y][x]; }
|
||||
+ reference operator*() const { return m.get()[y][x]; }
|
||||
|
||||
# and finally in the assertions that we set for the “distance” and “less than”
|
||||
- assert(m == rhs.m);
|
||||
+ assert(m.get() == rhs.m.get());
|
||||
```
|
||||
|
||||
We're done now! We have written an iterator over diagonals for a 2D `vector`. You can have a look at the final result [here](pathname:///files/blog/leetcode/sort-matrix-diagonally/matrix-sort.cpp).
|
||||
|
||||
[^1]: just because I'm used to it and don't care about your opinion ;)
|
||||
[^2]: exercise at your own risk
|
||||
[^3]: me in 5 minutes in fact, but don't make me scared
|
||||
[^4]: me in the next section…
|
16
static/files/blog/leetcode/sort-matrix-diagonally/makefile
Normal file
16
static/files/blog/leetcode/sort-matrix-diagonally/makefile
Normal file
|
@ -0,0 +1,16 @@
|
|||
CXX=clang++
|
||||
CXXFLAGS=-std=c++20 -Wall -Wextra -Werror -g -pedantic
|
||||
|
||||
test: matrix-sort
|
||||
./matrix-sort
|
||||
|
||||
matrix-sort: format tidy
|
||||
$(CXX) $(CXXFLAGS) matrix-sort.cpp -o matrix-sort
|
||||
|
||||
format:
|
||||
clang-format -i -style=webkit *.cpp
|
||||
|
||||
tidy:
|
||||
clang-tidy *.cpp -- $(CXXFLAGS)
|
||||
|
||||
.PHONY: matrix-sort format tidy
|
|
@ -0,0 +1,229 @@
|
|||
#include <algorithm>
|
||||
#include <cassert>
|
||||
#include <vector>
|
||||
|
||||
using matrix = std::vector<std::vector<int>>;
|
||||
|
||||
template <typename T>
|
||||
class diagonal {
|
||||
using matrix_t = std::vector<std::vector<T>>;
|
||||
|
||||
matrix_t& matrix;
|
||||
std::size_t x;
|
||||
std::size_t y;
|
||||
|
||||
class diagonal_iter {
|
||||
// we need to keep reference to the matrix itself
|
||||
std::reference_wrapper<matrix_t> m;
|
||||
|
||||
// we need to be able to tell our current position
|
||||
std::size_t x;
|
||||
std::size_t y;
|
||||
|
||||
public:
|
||||
using difference_type = std::ptrdiff_t;
|
||||
using value_type = T;
|
||||
using pointer = T*;
|
||||
using reference = T&;
|
||||
using iterator_category = std::random_access_iterator_tag;
|
||||
|
||||
diagonal_iter(matrix_t& matrix,
|
||||
std::size_t x,
|
||||
std::size_t y)
|
||||
: m(matrix)
|
||||
, x(x)
|
||||
, y(y)
|
||||
{
|
||||
}
|
||||
|
||||
bool operator==(const diagonal_iter& rhs) const
|
||||
{
|
||||
return x == rhs.x && y == rhs.y && m.get() == rhs.m.get();
|
||||
}
|
||||
|
||||
diagonal_iter& operator++()
|
||||
{
|
||||
// we are moving along the diagonal, so we increment both ‹x› and ‹y›
|
||||
// at the same time
|
||||
x++;
|
||||
y++;
|
||||
return *this;
|
||||
}
|
||||
|
||||
reference operator*() const { return m.get()[y][x]; }
|
||||
|
||||
// exactly opposite to the incrementation
|
||||
diagonal_iter operator--()
|
||||
{
|
||||
x--;
|
||||
y--;
|
||||
return *this;
|
||||
}
|
||||
|
||||
// moving ‹n› steps back is same as calling decrementation ‹n›-times, so
|
||||
// we can just return a new iterator and subtract ‹n› from both
|
||||
// coordinates in the matrix
|
||||
diagonal_iter operator-(difference_type n) const
|
||||
{
|
||||
return diagonal_iter { m, x - n, y - n };
|
||||
}
|
||||
|
||||
// here we assume that we are given two iterators on the same diagonal
|
||||
difference_type operator-(const diagonal_iter& rhs) const
|
||||
{
|
||||
assert(m.get() == rhs.m.get());
|
||||
return x - rhs.x;
|
||||
}
|
||||
|
||||
// counterpart of moving ‹n› steps backwards
|
||||
diagonal_iter operator+(difference_type n) const
|
||||
{
|
||||
return diagonal_iter { m, x + n, y + n };
|
||||
}
|
||||
|
||||
// we compare the coordinates, and also assume that those 2 iterators are
|
||||
// lying on the same diagonal
|
||||
bool operator<(const diagonal_iter& rhs) const
|
||||
{
|
||||
assert(m.get() == rhs.m.get());
|
||||
return x < rhs.x && y < rhs.y;
|
||||
}
|
||||
};
|
||||
|
||||
public:
|
||||
diagonal(matrix_t& matrix, std::size_t x, std::size_t y)
|
||||
: matrix(matrix)
|
||||
, x(x)
|
||||
, y(y)
|
||||
{
|
||||
}
|
||||
|
||||
diagonal_iter begin() const { return diagonal_iter { matrix, x, y }; }
|
||||
|
||||
diagonal_iter end() const
|
||||
{
|
||||
auto max_x = matrix[y].size();
|
||||
auto max_y = matrix.size();
|
||||
|
||||
// we need to find the distance in which we get out of bounds (either in
|
||||
// column or row)
|
||||
auto steps = std::min(max_x - x, max_y - y);
|
||||
|
||||
return diagonal_iter { matrix, x + steps, y + steps };
|
||||
}
|
||||
};
|
||||
|
||||
template <typename T>
|
||||
class diagonals {
|
||||
using matrix_t = std::vector<std::vector<T>>;
|
||||
|
||||
class diagonals_iter {
|
||||
matrix_t& m;
|
||||
std::size_t x;
|
||||
std::size_t y;
|
||||
|
||||
public:
|
||||
diagonals_iter(matrix_t& matrix, std::size_t x, std::size_t y)
|
||||
: m(matrix)
|
||||
, x(x)
|
||||
, y(y)
|
||||
{
|
||||
}
|
||||
|
||||
bool operator!=(const diagonals_iter& rhs) const
|
||||
{
|
||||
// iterators are not equal if they reference different matrices, or
|
||||
// their positions differ
|
||||
return x != rhs.x || y != rhs.y || m != rhs.m;
|
||||
}
|
||||
|
||||
diagonals_iter& operator++()
|
||||
{
|
||||
if (y != 0) {
|
||||
// iterating through diagonals down the first column
|
||||
y++;
|
||||
return *this;
|
||||
}
|
||||
|
||||
// iterating the diagonals along the first row
|
||||
x++;
|
||||
if (x == m.front().size()) {
|
||||
// switching to diagonals in the first column
|
||||
x = 0;
|
||||
y++;
|
||||
}
|
||||
|
||||
return *this;
|
||||
}
|
||||
|
||||
diagonal<T> operator*() const { return diagonal { m, x, y }; }
|
||||
};
|
||||
|
||||
matrix_t& _matrix;
|
||||
|
||||
public:
|
||||
diagonals(matrix_t& m)
|
||||
: _matrix(m)
|
||||
{
|
||||
}
|
||||
diagonals_iter begin() { return diagonals_iter { _matrix, 0, 0 }; }
|
||||
diagonals_iter end() { return diagonals_iter { _matrix, 0, _matrix.size() }; }
|
||||
};
|
||||
|
||||
class Solution {
|
||||
public:
|
||||
matrix diagonalSort(matrix mat)
|
||||
{
|
||||
// we iterate over the diagonals
|
||||
for (auto d : diagonals(mat)) {
|
||||
// and we sort each diagonal
|
||||
std::sort(d.begin(), d.end());
|
||||
}
|
||||
|
||||
// we take the matrix by copy, so we can sort in-situ and return the copy
|
||||
// that we sorted
|
||||
return mat;
|
||||
}
|
||||
};
|
||||
|
||||
static void test_case_1()
|
||||
{
|
||||
// Input: mat = [[3,3,1,1],[2,2,1,2],[1,1,1,2]]
|
||||
// Output: [[1,1,1,1],[1,2,2,2],[1,2,3,3]]
|
||||
|
||||
Solution s;
|
||||
assert((s.diagonalSort(std::vector { std::vector { 3, 3, 1, 1 },
|
||||
std::vector { 2, 2, 1, 2 },
|
||||
std::vector { 1, 1, 1, 2 } })
|
||||
== std::vector { std::vector { 1, 1, 1, 1 },
|
||||
std::vector { 1, 2, 2, 2 },
|
||||
std::vector { 1, 2, 3, 3 } }));
|
||||
}
|
||||
|
||||
static void test_case_2()
|
||||
{
|
||||
// Input: mat =
|
||||
// [[11,25,66,1,69,7],[23,55,17,45,15,52],[75,31,36,44,58,8],[22,27,33,25,68,4],[84,28,14,11,5,50]]
|
||||
// Output:
|
||||
// [[5,17,4,1,52,7],[11,11,25,45,8,69],[14,23,25,44,58,15],[22,27,31,36,50,66],[84,28,75,33,55,68]]
|
||||
|
||||
Solution s;
|
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assert((s.diagonalSort(std::vector { std::vector { 11, 25, 66, 1, 69, 7 },
|
||||
std::vector { 23, 55, 17, 45, 15, 52 },
|
||||
std::vector { 75, 31, 36, 44, 58, 8 },
|
||||
std::vector { 22, 27, 33, 25, 68, 4 },
|
||||
std::vector { 84, 28, 14, 11, 5, 50 } })
|
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== std::vector { std::vector { 5, 17, 4, 1, 52, 7 },
|
||||
std::vector { 11, 11, 25, 45, 8, 69 },
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||||
std::vector { 14, 23, 25, 44, 58, 15 },
|
||||
std::vector { 22, 27, 31, 36, 50, 66 },
|
||||
std::vector { 84, 28, 75, 33, 55, 68 } }));
|
||||
}
|
||||
|
||||
int main()
|
||||
{
|
||||
test_case_1();
|
||||
test_case_2();
|
||||
|
||||
return 0;
|
||||
}
|
Loading…
Reference in a new issue