#805 - Split Array With Same Average

Hard • View on LeetCode • View on GitHub

Array Dynamic Programming Math Bit Manipulation Bitmask

Problem Description

You are given an integer array nums.

You should move each element of nums into one of the two arrays A and B such that A and B are non-empty, and average(A) == average(B).

Return true if it is possible to achieve that and false otherwise.

Note that for an array arr, average(arr) is the sum of all the elements of arr over the length of arr.

Solution

/**
 * @param {number[]} nums
 * @return {boolean}
 */
var splitArraySameAverage = function(nums) {
  if (nums.length <= 1) return false;
  const sum = nums.reduce((acc, num) => acc + num, 0);
  const dp = Array(Math.floor(nums.length / 2) + 1).fill().map(() => new Set());
  dp[0].add(0);

  for (const num of nums) {
    for (let size = Math.min(Math.floor(nums.length / 2), dp.length - 1); size > 0; size--) {
      for (const prevSum of dp[size - 1]) {
        dp[size].add(prevSum + num);
      }
    }
  }

  for (let size = 1; size <= Math.floor(nums.length / 2); size++) {
    const targetSum = sum * size / nums.length;

    if (targetSum % 1 === 0 && dp[size].has(targetSum)) {
      return true;
    }
  }

  return false;
};