split-array-with-equal-sum.js

/**
 * Split Array with Equal Sum
 *
 * Given an array with n integers, you need to find if there are triplets (i, j, k) which satisfies
 * following conditions:
 *
 * 0 < i, i + 1 < j, j + 1 < k < n - 1
 *
 * Sum of subarrays (0, i - 1), (i + 1, j - 1), (j + 1, k - 1) and (k + 1, n - 1) should be equal.
 * where we define that subarray (L, R) represents a slice of the original array starting from the element
 * indexed L to the element indexed R.
 *
 * Example:
 *
 * Input: [1,2,1,2,1,2,1]
 * Output: True
 *
 * Explanation:
 *
 * i = 1, j = 3, k = 5.
 * sum(0, i - 1) = sum(0, 0) = 1
 * sum(i + 1, j - 1) = sum(2, 2) = 1
 * sum(j + 1, k - 1) = sum(4, 4) = 1
 * sum(k + 1, n - 1) = sum(6, 6) = 1
 *
 * Note:
 * 1 <= n <= 2000.
 * Elements in the given array will be in range [-1,000,000, 1,000,000].
 */

/**
 * @param {number[]} nums
 * @return {boolean}
 */
const splitArray = nums => {
  if (nums.length < 7) {
    return false;
  }

  // Step 1. Calculate the prefix sum
  const sum = Array(nums.length).fill(0);
  sum[0] = nums[0];
  for (let i = 1; i < nums.length; i++) {
    sum[i] = sum[i - 1] + nums[i];
  }

  // Here j is used for middle cut, i for left cut and k for right cut.
  // Iterate middle cuts and then find left cuts which divides the first
  // half into two equal quarters, store that quarter sums in the hashset.
  // Then find right cuts which divides the second half into two equal
  // quarters and check if quarter sum is present in the hashset.
  // If yes return true.
  for (let j = 3; j < nums.length - 3; j++) {
    const set = new Set();

    for (let i = 1; i < j - 1; i++) {
      if (sum[i - 1] == sum[j - 1] - sum[i]) {
        set.add(sum[i - 1]);
      }
    }

    for (let k = j + 2; k < nums.length - 1; k++) {
      if (sum[nums.length - 1] - sum[k] == sum[k - 1] - sum[j] && set.has(sum[k - 1] - sum[j])) {
        return true;
      }
    }
  }

  return false;
};

export { splitArray };