Cat and Mouse problem solved

Author: hasibulislam999

Game Theory/913_cat-and-mouse.js

@@ -0,0 +1,78 @@
+/**
+ * Title: Cat and Mouse
+ * Description: A game on an undirected graph is played by two players, Mouse and Cat, who alternate turns.
+ * Author: Hasibul Islam
+ * Date: 06/05/2023
+ */
+
+/**
+ * @param {number[][]} graph
+ * @return {number}
+ */
+var catMouseGame = function (graph) {
+  const n = graph.length;
+  //using anything less than n * 5 won't pass the 89 test cases since the June 2022. As test cases get harder will need to increase this value or fix this algorithm
+  const state = new Array(n * 5)
+    .fill(0)
+    .map((el, i) => new Array(n).fill(0).map((el, i) => new Array(n).fill(-1)));
+
+  function updateState(step, cat, mouse, value) {
+    state[step][cat][mouse] = value;
+    return state[step][cat][mouse];
+  }
+
+  function dfs(step, cat, mouse) {
+    if (step >= state.length) return 0;
+    if (state[step][cat][mouse] !== -1) {
+      return state[step][cat][mouse];
+    }
+    let finalResult = -1;
+    if (step & 1) {
+      //cat's turn
+      if (graph[cat].includes(mouse)) {
+        return (state[step][cat][mouse] = 2);
+      }
+      for (const node of graph[cat]) {
+        if (node !== 0) {
+          let nextResult = dfs(step + 1, node, mouse, 0);
+          if (nextResult === 2) {
+            return (state[step][cat][mouse] = 2);
+          } else if (nextResult === 1) {
+            if (finalResult === -1) {
+              finalResult = 1;
+            }
+          } else if (nextResult === 0) {
+            finalResult = 0;
+          }
+        }
+      }
+      if (finalResult === -1) {
+        finalResult = 1;
+      }
+    } else {
+      //mouse's turn
+      if (graph[mouse].includes(0)) {
+        return (state[step][cat][mouse] = 1);
+      }
+      for (const node of graph[mouse]) {
+        if (node !== cat && !graph[node].includes(cat)) {
+          let nextResult = dfs(step + 1, cat, node, 1);
+          if (nextResult === 1) {
+            return (state[step][cat][mouse] = 1);
+          } else if (nextResult === 2) {
+            if (finalResult === -1) {
+              finalResult = 2;
+            }
+          } else if (nextResult === 0) {
+            finalResult = 0;
+          }
+        }
+      }
+      if (finalResult === -1) {
+        finalResult = 2;
+      }
+    }
+    return (state[step][cat][mouse] = finalResult);
+  }
+  return dfs(0, 2, 1);
+};