Can I Win problem solved

Author: hasibulislam999

Game Theory/464_can-i-win.js

@@ -0,0 +1,47 @@
+/**
+ * Title: Can I Win
+ * Description: In the "100 game" two players take turns adding, to a running total, any integer from 1 to 10. The player who first causes the running total to reach or exceed 100 wins.
+ * Author: Hasibul Islam
+ * Date: 06/05/2023
+ */
+
+/**
+ * @param {number} maxChoosableInteger
+ * @param {number} desiredTotal
+ * @return {boolean}
+ */
+function canIWin(maxChoosableInteger, desiredTotal) {
+  if (desiredTotal === 0) return true;
+  if ((maxChoosableInteger * (maxChoosableInteger + 1)) / 2 < desiredTotal)
+    return false;
+
+  const initialChoices = Math.pow(2, maxChoosableInteger) - 1;
+
+  const dp = [];
+
+  function DP(choices, total) {
+    if (total <= 0) return false;
+
+    if (dp[choices] !== undefined) {
+      return dp[choices];
+    }
+
+    let pow = 0;
+    let choicesCopy = choices;
+
+    dp[choices] = false;
+
+    while (choicesCopy > 0) {
+      if (choicesCopy % 2 && !DP(choices - (1 << pow), total - pow - 1)) {
+        dp[choices] = true;
+        break;
+      }
+      choicesCopy >>= 1;
+      pow++;
+    }
+
+    return dp[choices];
+  }
+
+  return DP(initialChoices, desiredTotal);
+}