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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">A. Beautiful Matrix</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>You've got a <span class="tex-span">5 × 5</span> matrix, consisting of <span class="tex-span">24</span> zeroes and a single number one. Let's index the matrix rows by numbers from <span class="tex-span">1</span> to <span class="tex-span">5</span> from top to bottom, let's index the matrix columns by numbers from <span class="tex-span">1</span> to <span class="tex-span">5</span> from left to right. In one move, you are allowed to apply one of the two following transformations to the matrix:</p><ol> <li> Swap two neighboring matrix rows, that is, rows with indexes <span class="tex-span"><i>i</i></span> and <span class="tex-span"><i>i</i> + 1</span> for some integer <span class="tex-span"><i>i</i></span> <span class="tex-span">(1 ≤ <i>i</i> < 5)</span>. </li><li> Swap two neighboring matrix columns, that is, columns with indexes <span class="tex-span"><i>j</i></span> and <span class="tex-span"><i>j</i> + 1</span> for some integer <span class="tex-span"><i>j</i></span> <span class="tex-span">(1 ≤ <i>j</i> < 5)</span>. </li></ol><p>You think that a matrix looks <span class="tex-font-style-it">beautiful</span>, if the single number one of the matrix is located in its middle (in the cell that is on the intersection of the third row and the third column). Count the minimum number of moves needed to make the matrix beautiful.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The input consists of five lines, each line contains five integers: the <span class="tex-span"><i>j</i></span>-th integer in the <span class="tex-span"><i>i</i></span>-th line of the input represents the element of the matrix that is located on the intersection of the <span class="tex-span"><i>i</i></span>-th row and the <span class="tex-span"><i>j</i></span>-th column. It is guaranteed that the matrix consists of <span class="tex-span">24</span> zeroes and a single number one.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print a single integer — the minimum number of moves needed to make the matrix beautiful.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>0 0 0 0 0<br />0 0 0 0 1<br />0 0 0 0 0<br />0 0 0 0 0<br />0 0 0 0 0<br /></pre></div><div class="output"><div class="title">Output</div><pre>3<br /></pre></div><div class="input"><div class="title">Input</div><pre>0 0 0 0 0<br />0 0 0 0 0<br />0 1 0 0 0<br />0 0 0 0 0<br />0 0 0 0 0<br /></pre></div><div class="output"><div class="title">Output</div><pre>1<br /></pre></div></div></div></div></div>
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">B. Squares</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>Vasya has found a piece of paper with a coordinate system written on it. There are <span class="tex-span"><i>n</i></span> distinct squares drawn in this coordinate system. Let's number the squares with integers from 1 to <span class="tex-span"><i>n</i></span>. It turned out that points with coordinates <span class="tex-span">(0, 0)</span> and <span class="tex-span">(<i>a</i><sub class="lower-index"><i>i</i></sub>, <i>a</i><sub class="lower-index"><i>i</i></sub>)</span> are the opposite corners of the <span class="tex-span"><i>i</i></span>-th square.</p><p>Vasya wants to find such integer point (with integer coordinates) of the plane, that belongs to exactly <span class="tex-span"><i>k</i></span> drawn squares. We'll say that a point belongs to a square, if the point is located either inside the square, or on its boundary. </p><p>Help Vasya find a point that would meet the described limits.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains two space-separated integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>k</i></span> <span class="tex-span">(1 ≤ <i>n</i>, <i>k</i> ≤ 50)</span>. The second line contains space-separated integers <span class="tex-span"><i>a</i><sub class="lower-index">1</sub>, <i>a</i><sub class="lower-index">2</sub>, ..., <i>a</i><sub class="lower-index"><i>n</i></sub></span> <span class="tex-span">(1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub> ≤ 10<sup class="upper-index">9</sup>)</span>.</p><p>It is guaranteed that all given squares are distinct.</p></div><div class="output-specification"><div class="section-title">Output</div><p>In a single line print two space-separated integers <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span> <span class="tex-span">(0 ≤ <i>x</i>, <i>y</i> ≤ 10<sup class="upper-index">9</sup>)</span> — the coordinates of the point that belongs to exactly <span class="tex-span"><i>k</i></span> squares. If there are multiple answers, you are allowed to print any of them. </p><p>If there is no answer, print "<span class="tex-font-style-tt">-1</span>" (without the quotes).</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 3<br />5 1 3 4<br /></pre></div><div class="output"><div class="title">Output</div><pre>2 1<br /></pre></div><div class="input"><div class="title">Input</div><pre>3 1<br />2 4 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>4 0<br /></pre></div><div class="input"><div class="title">Input</div><pre>4 50<br />5 1 10 2<br /></pre></div><div class="output"><div class="title">Output</div><pre>-1<br /></pre></div></div></div></div></div>
|
|||
|
|
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|
|||
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|
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">C. Circle of Numbers</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>One day Vasya came up to the blackboard and wrote out <span class="tex-span"><i>n</i></span> distinct integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> in some order in a circle. Then he drew arcs to join the pairs of integers <span class="tex-span">(<i>a</i>, <i>b</i>)</span> <span class="tex-span">(<i>a</i> ≠ <i>b</i>)</span>, that are either each other's immediate neighbors in the circle, or there is number <span class="tex-span"><i>c</i></span>, such that <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>с</i></span> are immediate neighbors, and <span class="tex-span"><i>b</i></span> and <span class="tex-span"><i>c</i></span> are immediate neighbors. As you can easily deduce, in the end Vasya drew <span class="tex-span">2·<i>n</i></span> arcs.</p><p>For example, if the numbers are written in the circle in the order <span class="tex-span">1, 2, 3, 4, 5</span> (in the clockwise direction), then the arcs will join pairs of integers <span class="tex-span">(1, 2)</span>, <span class="tex-span">(2, 3)</span>, <span class="tex-span">(3, 4)</span>, <span class="tex-span">(4, 5)</span>, <span class="tex-span">(5, 1)</span>, <span class="tex-span">(1, 3)</span>, <span class="tex-span">(2, 4)</span>, <span class="tex-span">(3, 5)</span>, <span class="tex-span">(4, 1)</span> and <span class="tex-span">(5, 2)</span>.</p><p>Much time has passed ever since, the numbers we wiped off the blackboard long ago, but recently Vasya has found a piece of paper with <span class="tex-span">2·<i>n</i></span> written pairs of integers that were joined with the arcs on the board. Vasya asks you to find the order of numbers in the circle by these pairs.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line of the input contains a single integer <span class="tex-span"><i>n</i></span> (<span class="tex-span">5 ≤ <i>n</i> ≤ 10<sup class="upper-index">5</sup></span>) that shows, how many numbers were written on the board. Next <span class="tex-span">2·<i>n</i></span> lines contain pairs of integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> (<span class="tex-span">1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub>, <i>b</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i></span>, <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub> ≠ <i>b</i><sub class="lower-index"><i>i</i></sub></span>) — the numbers that were connected by the arcs.</p><p>It is guaranteed that no pair of integers, connected by a arc, occurs in the input more than once. The pairs of numbers and the numbers in the pairs are given in the arbitrary order.</p></div><div class="output-specification"><div class="section-title">Output</div><p>If Vasya made a mistake somewhere and there isn't any way to place numbers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span> on the circle according to the statement, then print a single number "-1" (without the quotes). Otherwise, print any suitable sequence of <span class="tex-span"><i>n</i></span> distinct integers from <span class="tex-span">1</span> to <span class="tex-span"><i>n</i></span>. </p><p>If there are multiple solutions, you are allowed to print any of them. Specifically, it doesn't matter which number you write first to describe the sequence of the order. It also doesn't matter whether you write out
|
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">D. Cycle in Graph</div><div class="time-limit"><div class="property-title">time limit per test</div>2 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>You've got a undirected graph <span class="tex-span"><i>G</i></span>, consisting of <span class="tex-span"><i>n</i></span> nodes. We will consider the nodes of the graph indexed by integers from 1 to <span class="tex-span"><i>n</i></span>. We know that each node of graph <span class="tex-span"><i>G</i></span> is connected by edges with at least <span class="tex-span"><i>k</i></span> other nodes of this graph. Your task is to find in the given graph a simple cycle of length of at least <span class="tex-span"><i>k</i> + 1</span>.</p><p>A <span class="tex-font-style-it">simple cycle</span> of length <span class="tex-span"><i>d</i></span> <span class="tex-span">(<i>d</i> > 1)</span> in graph <span class="tex-span"><i>G</i></span> is a sequence of distinct graph nodes <span class="tex-span"><i>v</i><sub class="lower-index">1</sub>, <i>v</i><sub class="lower-index">2</sub>, ..., <i>v</i><sub class="lower-index"><i>d</i></sub></span> such, that nodes <span class="tex-span"><i>v</i><sub class="lower-index">1</sub></span> and <span class="tex-span"><i>v</i><sub class="lower-index"><i>d</i></sub></span> are connected by an edge of the graph, also for any integer <span class="tex-span"><i>i</i></span> <span class="tex-span">(1 ≤ <i>i</i> < <i>d</i>)</span> nodes <span class="tex-span"><i>v</i><sub class="lower-index"><i>i</i></sub></span> and <span class="tex-span"><i>v</i><sub class="lower-index"><i>i</i> + 1</sub></span> are connected by an edge of the graph.</p></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span>, <span class="tex-span"><i>k</i></span> <span class="tex-span">(3 ≤ <i>n</i>, <i>m</i> ≤ 10<sup class="upper-index">5</sup>; 2 ≤ <i>k</i> ≤ <i>n</i> - 1)</span> — the number of the nodes of the graph, the number of the graph's edges and the lower limit on the degree of the graph node. Next <span class="tex-span"><i>m</i></span> lines contain pairs of integers. The <span class="tex-span"><i>i</i></span>-th line contains integers <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i></sub></span>, <span class="tex-span"><i>b</i><sub class="lower-index"><i>i</i></sub></span> <span class="tex-span">(1 ≤ <i>a</i><sub class="lower-index"><i>i</i></sub>, <i>b</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i>; <i>a</i><sub class="lower-index"><i>i</i></sub> ≠ <i>b</i><sub class="lower-index"><i>i</i></sub>)</span> — the indexes of the graph nodes that are connected by the <span class="tex-span"><i>i</i></span>-th edge. </p><p>It is guaranteed that the given graph doesn't contain any multiple edges or self-loops. It is guaranteed that each node of the graph is connected by the edges with at least <span class="tex-span"><i>k</i></span> other nodes of the graph.</p></div><div class="output-specification"><div class="section-title">Output</div><p>In the first line print integer <span class="tex-span"><i>r</i></span> <span class="tex-span">(<i>r</i> ≥ <i>k</i> + 1)</span> — the length of the found cycle. In the next line print <span class="tex-span"><i>r</i></span> distinct integers <span class="tex-span"><i>v</i><sub class="lower-index">1</sub>, <i>v</i><sub class="lower-index">2</sub>, ..., <i>v</i><sub class="lower-index"><i>r</i></sub></span> <span class="tex-span">(1 ≤ <i>v</i><sub class="lower-index"><i>i</i></sub> ≤ <i>n</i>)</span> — the found simple cycle.
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<div class="ttypography"><div class="problem-statement"><div class="header"><div class="title">E. Rhombus</div><div class="time-limit"><div class="property-title">time limit per test</div>3 seconds</div><div class="memory-limit"><div class="property-title">memory limit per test</div>256 megabytes</div><div class="input-file"><div class="property-title">input</div>standard input</div><div class="output-file"><div class="property-title">output</div>standard output</div></div><div><p>You've got a table of size <span class="tex-span"><i>n</i> × <i>m</i></span>. On the intersection of the <span class="tex-span"><i>i</i></span>-th row (<span class="tex-span">1 ≤ <i>i</i> ≤ <i>n</i></span>) and the <span class="tex-span"><i>j</i></span>-th column (<span class="tex-span">1 ≤ <i>j</i> ≤ <i>m</i></span>) there is a non-negative integer <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i>, <i>j</i></sub></span>. Besides, you've got a non-negative integer <span class="tex-span"><i>k</i></span>.</p><p>Your task is to find such pair of integers <span class="tex-span">(<i>a</i>, <i>b</i>)</span> that meets these conditions: </p><ul> <li> <span class="tex-span"><i>k</i> ≤ <i>a</i> ≤ <i>n</i> - <i>k</i> + 1</span>; </li><li> <span class="tex-span"><i>k</i> ≤ <i>b</i> ≤ <i>m</i> - <i>k</i> + 1</span>; </li><li> let's denote the maximum of the function <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/74b071ff624618e510fc76a44202edfacb3aeeb0.png" style="max-width: 100.0%;max-height: 100.0%;" /> among all integers <span class="tex-span"><i>x</i></span> and <span class="tex-span"><i>y</i></span>, that satisfy the inequalities <span class="tex-span"><i>k</i> ≤ <i>x</i> ≤ <i>n</i> - <i>k</i> + 1</span> and <span class="tex-span"><i>k</i> ≤ <i>y</i> ≤ <i>m</i> - <i>k</i> + 1</span>, as <span class="tex-span"><i>mval</i></span>; for the required pair of numbers the following equation must hold <span class="tex-span"><i>f</i>(<i>a</i>, <i>b</i>) = <i>mval</i></span>. </li></ul></div><div class="input-specification"><div class="section-title">Input</div><p>The first line contains three space-separated integers <span class="tex-span"><i>n</i></span>, <span class="tex-span"><i>m</i></span> and <span class="tex-span"><i>k</i></span> (<span class="tex-span">1 ≤ <i>n</i>, <i>m</i> ≤ 1000</span>, <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/596a06314f9d523a5aa986f3b618cd141adfde30.png" style="max-width: 100.0%;max-height: 100.0%;" />). Next <span class="tex-span"><i>n</i></span> lines each contains <span class="tex-span"><i>m</i></span> integers: the <span class="tex-span"><i>j</i></span>-th number on the <span class="tex-span"><i>i</i></span>-th line equals <span class="tex-span"><i>a</i><sub class="lower-index"><i>i</i>, <i>j</i></sub></span> (<span class="tex-span">0 ≤ <i>a</i><sub class="lower-index"><i>i</i>, <i>j</i></sub> ≤ 10<sup class="upper-index">6</sup></span>).</p><p>The numbers in the lines are separated by spaces.</p></div><div class="output-specification"><div class="section-title">Output</div><p>Print the required pair of integers <span class="tex-span"><i>a</i></span> and <span class="tex-span"><i>b</i></span>. Separate the numbers by a space.</p><p>If there are multiple correct answers, you are allowed to print any of them.</p></div><div class="sample-tests"><div class="section-title">Examples</div><div class="sample-test"><div class="input"><div class="title">Input</div><pre>4 4 2<br />1 2 3 4<br />1 1 1 1<br />2 2 2 2<br />4 3 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>3 2<br /></pre></div><div class="input"><div class="title">Input</div><pre>5 7 3<br />8 2 3 4 2 3 3<br />3 4 6 2 3 4 6<br />8 7 6 8 4 5 7<br />1 2 3 2 1 3 2<br />4 5 3 2 1 2 1<br /></pre></div><div class="output"><div class="title">Output</div><pre>3 3<br /></pre></div></div></div></div></div>
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