#823 - Binary Trees With Factors

Medium • View on LeetCode • View on GitHub

Array Hash Table Dynamic Programming Sorting

Problem Description

Given an array of unique integers, arr, where each integer arr[i] is strictly greater than 1.

We make a binary tree using these integers, and each number may be used for any number of times.

Each non-leaf node's value should be equal to the product of the values of its children.

Return the number of binary trees we can make. The answer may be too large so return the answer modulo 109 + 7.

Solution

/**
 * @param {number[]} arr
 * @return {number}
 */
var numFactoredBinaryTrees = function(arr) {
  const MOD = 1e9 + 7;
  const dp = {};
  const numMap = new Map();

  arr.sort((a, b) => a - b);
  for (let i = 0; i < arr.length; i++) {
    numMap.set(arr[i], i);
  }

  let result = 0;
  for (let i = 0; i < arr.length; i++) {
    dp[arr[i]] = 1;
    for (let j = 0; j < i; j++) {
      if (arr[i] % arr[j] === 0) {
        const complement = arr[i] / arr[j];
        if (numMap.has(complement)) {
          dp[arr[i]] = (dp[arr[i]] + dp[arr[j]] * dp[complement]) % MOD;
        }
      }
    }
    result = (result + dp[arr[i]]) % MOD;
  }

  return result;
};