2780. Minimum Index of a Valid Split

Description

An element x of an integer array arr of length m is dominant if more than half the elements of arr have a value of x.

You are given a 0-indexed integer array nums of length n with one dominant element.

You can split nums at an index i into two arrays nums[0, ..., i] and nums[i + 1, ..., n - 1], but the split is only valid if:

• 0 <= i < n - 1
• nums[0, ..., i], and nums[i + 1, ..., n - 1] have the same dominant element.

Here, nums[i, ..., j] denotes the subarray of nums starting at index i and ending at index j, both ends being inclusive. Particularly, if j < i then nums[i, ..., j] denotes an empty subarray.

Return the minimum index of a valid split. If no valid split exists, return -1.

 

Example 1:

Input: nums = [1,2,2,2]
Output: 2
Explanation: We can split the array at index 2 to obtain arrays [1,2,2] and [2]. 
In array [1,2,2], element 2 is dominant since it occurs twice in the array and 2 * 2 > 3. 
In array [2], element 2 is dominant since it occurs once in the array and 1 * 2 > 1.
Both [1,2,2] and [2] have the same dominant element as nums, so this is a valid split. 
It can be shown that index 2 is the minimum index of a valid split. 

Example 2:

Input: nums = [2,1,3,1,1,1,7,1,2,1]
Output: 4
Explanation: We can split the array at index 4 to obtain arrays [2,1,3,1,1] and [1,7,1,2,1].
In array [2,1,3,1,1], element 1 is dominant since it occurs thrice in the array and 3 * 2 > 5.
In array [1,7,1,2,1], element 1 is dominant since it occurs thrice in the array and 3 * 2 > 5.
Both [2,1,3,1,1] and [1,7,1,2,1] have the same dominant element as nums, so this is a valid split.
It can be shown that index 4 is the minimum index of a valid split.

Example 3:

Input: nums = [3,3,3,3,7,2,2]
Output: -1
Explanation: It can be shown that there is no valid split.

 

Constraints:

• 1 <= nums.length <= 105
• 1 <= nums[i] <= 109
• nums has exactly one dominant element.

 

Solutions

Solution: Hash Map

• Time complexity: O(n)
• Space complexity: O(n)

 

JavaScript

/**
 * @param {number[]} nums
 * @return {number}
 */
const minimumIndex = function (nums) {
  const n = nums.length;
  const countMap = new Map();
  let dominant = -1;
  let maxCount = 0;

  for (const num of nums) {
    const count = countMap.get(num) ?? 0;

    countMap.set(num, count + 1);
  }

  for (const [num, count] of countMap) {
    if (count <= maxCount) continue;

    dominant = num;
    maxCount = count;
  }
  let count = 0;

  for (let index = 0; index < n; index++) {
    const num = nums[index];

    if (num === dominant) count += 1;
    if (count * 2 > index + 1 && (maxCount - count) * 2 > n - index - 1) {
      return index;
    }
  }

  return -1;
};