805. Split Array With Same Average

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.

 

Example 1:

Input: nums = [1,2,3,4,5,6,7,8]
Output: true
Explanation: We can split the array into [1,4,5,8] and [2,3,6,7], and both of them have an average of 4.5.

Example 2:

Input: nums = [3,1]
Output: false

 

Constraints:

• 1 <= nums.length <= 30
• 0 <= nums[i] <= 104

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(n²*2ⁿ)
• Space complexity: O(n*2ⁿ)

 

JavaScript

/**
 * @param {number[]} nums
 * @return {boolean}
 */
const splitArraySameAverage = function (nums) {
  const n = nums.length;
  const sum = nums.reduce((result, num) => result + num);

  /* 
        sum / n === sum1 / count1 === sum2 / (n - count1)

        => sum1 = sum * count1 / n
        => sum * count1 % n === 0
    **/

  const sums = new Array(n)
    .fill('')
    .map(_ => new Set());

  sums[0].add(0);

  for (const num of nums) {
    for (let count = n - 1; count > 0; count--) {
      const target = (sum * count) / n;

      for (const previous of sums[count - 1]) {
        const current = previous + num;

        sums[count].add(current);
        if ((sum * count) % n !== 0) continue;
        if (current === target) return true;
      }
    }
  }
  return false;
};