Guess Number Higher or Lower II

README.md

@@ -297,6 +297,7 @@ A collection of JavaScript problems and solutions for studying algorithms.
 - [Subset Sum Problem](src/dynamic-programming/subset-sum-problem.js)
 - [Matrix Chain Multiplication](src/dynamic-programming/matrix-chain-multiplication.js)
 - [Burst Balloons](src/dynamic-programming/burst-balloons.js)
+- [Guess Number Higher or Lower II](src/dynamic-programming/guess-number-higher-or-lower-ii.js)
 
 ### Greedy
 

src/dynamic-programming/guess-number-higher-or-lower-ii.js

@@ -0,0 +1,80 @@
+/**
+ * Guess Number Higher or Lower II
+ *
+ * We are playing the Guess Game. The game is as follows:
+ *
+ * I pick a number from 1 to n. You have to guess which number I picked.
+ *
+ * Every time you guess wrong, I'll tell you whether the number I picked is higher or lower.
+ *
+ * However, when you guess a particular number x, and you guess wrong, you pay $x.
+ * You win the game when you guess the  * number I picked.
+ *
+ * Example:
+ *
+ * n = 10, I pick 8.
+ *
+ * First round:  You guess 5, I tell you that it's higher. You pay $5.
+ * Second round: You guess 7, I tell you that it's higher. You pay $7.
+ * Third round:  You guess 9, I tell you that it's lower. You pay $9.
+ *
+ * Game over. 8 is the number I picked.
+ *
+ * You end up paying $5 + $7 + $9 = $21.
+ *
+ * Given a particular n ≥ 1, find out how much money you need to have to guarantee a win.
+ */
+
+/**
+ * Recursion
+ *
+ * @param {number} n
+ * @return {number}
+ */
+const getMoneyAmountR = n => {
+  return helper(1, n);
+};
+
+const helper = (start, end) => {
+  if (start >= end) {
+    return 0;
+  }
+
+  let min = Number.MAX_SAFE_INTEGER;
+
+  for (let i = start; i <= end; i++) {
+    const val = i + Math.max(helper(start, i - 1), helper(i + 1, end));
+    min = Math.min(min, val);
+  }
+
+  return min;
+};
+
+/**
+ * Dynamic Programming
+ *
+ * @param {number} n
+ * @return {number}
+ */
+const getMoneyAmount = n => {
+  const dp = Array(n + 2)
+    .fill()
+    .map(() => Array(n + 2).fill(0));
+
+  for (let len = 2; len <= n; len++) {
+    for (let start = 1; start + len - 1 <= n; start++) {
+      const end = start + len - 1;
+
+      dp[start][end] = Number.MAX_SAFE_INTEGER;
+
+      for (let i = start; i <= end; i++) {
+        const val = i + Math.max(dp[start][i - 1], dp[i + 1][end]);
+        dp[start][end] = Math.min(dp[start][end], val);
+      }
+    }
+  }
+
+  return dp[1][n];
+};
+
+export { getMoneyAmountR, getMoneyAmount };