Cat and Mouse II problem solved

Author: hasibulislam999

Game Theory/1728_cat-and-mouse-ii.js

@@ -0,0 +1,110 @@
+/**
+ * Title: Cat and Mouse II
+ * Description: Given a rows x cols matrix grid and two integers catJump and mouseJump, return true if Mouse can win the game if both Cat and Mouse play optimally, otherwise return false.
+ * Author: Hasibul Islam
+ * Date: 06/05/2023
+ */
+
+/**
+ * @param {string[]} grid
+ * @param {number} catJump
+ * @param {number} mouseJump
+ * @return {boolean}
+ */
+function canMouseWin(grid, catJump, mouseJump) {
+  const dirs = [
+    [1, 0],
+    [-1, 0],
+    [0, 1],
+    [0, -1],
+  ];
+  const m = grid.length;
+  const n = grid[0].length;
+  let mouse_pos = null;
+  let cat_pos = null;
+  let available = 0; // available steps for mouse and cat
+
+  // Search the start pos of mouse and cat
+  for (let i = 0; i < m; i++) {
+    for (let j = 0; j < n; j++) {
+      if (grid[i][j] !== "#") {
+        available++;
+      }
+      if (grid[i][j] === "M") {
+        mouse_pos = [i, j];
+      } else if (grid[i][j] === "C") {
+        cat_pos = [i, j];
+      }
+    }
+  }
+
+  const dp = function (turn, mouse_pos, cat_pos) {
+    // if (turn === m * n * 2) {
+    // We already search the whole grid (9372 ms 74.3 MB)
+    if (turn === available * 2) {
+      // We already search the whole touchable grid (5200 ms 57.5 MB)
+      return false;
+    }
+    if (turn % 2 === 0) {
+      // Mouse
+      const [i, j] = mouse_pos;
+      for (let [di, dj] of dirs) {
+        for (let jump = 0; jump <= mouseJump; jump++) {
+          // Note that we want to do range(mouseJump + 1) instead of range(1, mouseJump + 1)
+          // considering the case that we can stay at the same position for next turn.
+          const new_i = i + di * jump;
+          const new_j = j + dj * jump;
+          if (
+            0 <= new_i &&
+            new_i < m &&
+            0 <= new_j &&
+            new_j < n &&
+            grid[new_i][new_j] !== "#"
+          ) {
+            // Valid pos
+            if (
+              dp(turn + 1, [new_i, new_j], cat_pos) ||
+              grid[new_i][new_j] === "F"
+            ) {
+              return true;
+            }
+          } else {
+            // Stop extending the jump since we cannot go further
+            break;
+          }
+        }
+      }
+      return false;
+    } else {
+      // Cat
+      const [i, j] = cat_pos;
+      for (let [di, dj] of dirs) {
+        for (let jump = 0; jump <= catJump; jump++) {
+          const new_i = i + di * jump;
+          const new_j = j + dj * jump;
+          if (
+            0 <= new_i &&
+            new_i < m &&
+            0 <= new_j &&
+            new_j < n &&
+            grid[new_i][new_j] !== "#"
+          ) {
+            if (
+              !dp(turn + 1, mouse_pos, [new_i, new_j]) ||
+              (new_i === mouse_pos[0] && new_j === mouse_pos[1]) ||
+              grid[new_i][new_j] === "F"
+            ) {
+              // This condition will also handle the case that the cat cannot jump through the mouse
+              return false;
+            }
+          } else {
+            break;
+          }
+        }
+      }
+      return true;
+    }
+  };
+
+  return dp(0, mouse_pos, cat_pos);
+}