From d1e2d4a9cf6eb830d521a94d0eb6e906b054e012 Mon Sep 17 00:00:00 2001
From: Matej Focko <matej.focko@outlook.com>
Date: Mon, 18 Jul 2022 17:40:53 +0000
Subject: [PATCH] problems: add out of boundary paths

---
 problems/out-of-boundary-paths.cpp | 62 ++++++++++++++++++++++++++++++
 1 file changed, 62 insertions(+)
 create mode 100644 problems/out-of-boundary-paths.cpp

diff --git a/problems/out-of-boundary-paths.cpp b/problems/out-of-boundary-paths.cpp
new file mode 100644
index 0000000..d731fd8
--- /dev/null
+++ b/problems/out-of-boundary-paths.cpp
@@ -0,0 +1,62 @@
+class Solution {
+private:
+    const static unsigned CAP = 1000000007;
+
+    class dp {
+        const int rows;
+        const int cols;
+        const int maxMove;
+
+        std::vector<std::vector<std::map<int, unsigned>>> paths;
+
+        int
+        dfs(int y, int x, int moves)
+        {
+            if (y < 0 || y >= rows || x < 0 || x >= cols) {
+                // BASE: we got out of the bounds
+                return 1;
+            }
+
+            if (moves <= 0) {
+                // BASE: all moves were used or there are no moves left
+                return 0;
+            }
+
+            if (paths[y][x].count(moves)) {
+                // BASE(dynamic): already evaluated
+                return paths[y][x][moves];
+            }
+
+            int options = 0;
+            for (auto& [dx, dy] : std::vector<std::pair<int, int>> {
+                     { 0, 1 }, { 1, 0 }, { 0, -1 }, { -1, 0 } }) {
+                options = (options + dfs(y + dy, x + dx, moves - 1)) % CAP;
+            }
+            paths[y][x][moves] = options;
+
+            return options;
+        }
+
+    public:
+        dp(int rows, int cols, int maxMove)
+            : rows(rows)
+            , cols(cols)
+            , maxMove(maxMove)
+            , paths(rows, std::vector<std::map<int, unsigned>>(cols))
+        {
+        }
+
+        int
+        get(int row, int col)
+        {
+            return dfs(row, col, maxMove);
+        }
+    };
+
+public:
+    int
+    findPaths(int m, int n, int maxMove, int startRow, int startColumn) const
+    {
+        return dp(m, n, maxMove).get(startRow, startColumn);
+    }
+};