Add solution #1420

Author: JoshCrozier

README.md

@@ -1,4 +1,4 @@
-# 1,295 LeetCode solutions in JavaScript
+# 1,296 LeetCode solutions in JavaScript
 
 [https://leetcodejavascript.com](https://leetcodejavascript.com)
 
@@ -1086,6 +1086,7 @@
 1417|[Reformat The String](./solutions/1417-reformat-the-string.js)|Easy|
 1418|[Display Table of Food Orders in a Restaurant](./solutions/1418-display-table-of-food-orders-in-a-restaurant.js)|Medium|
 1419|[Minimum Number of Frogs Croaking](./solutions/1419-minimum-number-of-frogs-croaking.js)|Medium|
+1420|[Build Array Where You Can Find The Maximum Exactly K Comparisons](./solutions/1420-build-array-where-you-can-find-the-maximum-exactly-k-comparisons.js)|Hard|
 1422|[Maximum Score After Splitting a String](./solutions/1422-maximum-score-after-splitting-a-string.js)|Easy|
 1431|[Kids With the Greatest Number of Candies](./solutions/1431-kids-with-the-greatest-number-of-candies.js)|Easy|
 1436|[Destination City](./solutions/1436-destination-city.js)|Easy|

solutions/1420-build-array-where-you-can-find-the-maximum-exactly-k-comparisons.js

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+/**
+ * 1420. Build Array Where You Can Find The Maximum Exactly K Comparisons
+ * https://leetcode.com/problems/build-array-where-you-can-find-the-maximum-exactly-k-comparisons/
+ * Difficulty: Hard
+ *
+ * You are given three integers n, m and k. Consider the following algorithm to find the maximum
+ * element of an array of positive integers.
+ *
+ * You should build the array arr which has the following properties:
+ * - arr has exactly n integers.
+ * - 1 <= arr[i] <= m where (0 <= i < n).
+ * - After applying the mentioned algorithm to arr, the value search_cost is equal to k.
+ *
+ * Return the number of ways to build the array arr under the mentioned conditions. As the answer
+ * may grow large, the answer must be computed modulo 109 + 7.
+ */
+
+/**
+ * @param {number} n
+ * @param {number} m
+ * @param {number} k
+ * @return {number}
+ */
+function numOfArrays(length, maxValue, searchCost) {
+  const MOD = 1e9 + 7;
+  const cache = Array.from({ length: length + 1 }, () =>
+    Array.from({ length: maxValue + 1 }, () =>
+      Array(searchCost + 1).fill(-1)
+    )
+  );
+
+  function computeArrays(pos, currentMax, remainingCost) {
+    if (pos === length) return remainingCost === 0 ? 1 : 0;
+    if (remainingCost < 0) return 0;
+    if (cache[pos][currentMax][remainingCost] !== -1) {
+      return cache[pos][currentMax][remainingCost];
+    }
+
+    let total = 0;
+    for (let value = 1; value <= currentMax; value++) {
+      total = (total + computeArrays(pos + 1, currentMax, remainingCost)) % MOD;
+    }
+
+    if (remainingCost > 0) {
+      for (let value = currentMax + 1; value <= maxValue; value++) {
+        total = (total + computeArrays(pos + 1, value, remainingCost - 1)) % MOD;
+      }
+    }
+
+    return cache[pos][currentMax][remainingCost] = total;
+  }
+
+  let result = 0;
+  for (let value = 1; value <= maxValue; value++) {
+    result = (result + computeArrays(1, value, searchCost - 1)) % MOD;
+  }
+
+  return result;
+}