Prefix Sum III: The Definition of Prefix Sum

Another typical prefix sum problem (O(n)-time, O(n)-space). Code is down below, cheers, ACC.

Number of Ways to Split Array - LeetCode

2270. Number of Ways to Split Array

Medium

You are given a 0-indexed integer array nums of length n.

nums contains a valid split at index i if the following are true:

• The sum of the first i + 1 elements is greater than or equal to the sum of the last n - i - 1 elements.
• There is at least one element to the right of i. That is, 0 <= i < n - 1.

Return the number of valid splits in nums.

 

Example 1:

Input: nums = [10,4,-8,7]
Output: 2
Explanation: 
There are three ways of splitting nums into two non-empty parts:
- Split nums at index 0. Then, the first part is [10], and its sum is 10. The second part is [4,-8,7], and its sum is 3. Since 10 >= 3, i = 0 is a valid split.
- Split nums at index 1. Then, the first part is [10,4], and its sum is 14. The second part is [-8,7], and its sum is -1. Since 14 >= -1, i = 1 is a valid split.
- Split nums at index 2. Then, the first part is [10,4,-8], and its sum is 6. The second part is [7], and its sum is 7. Since 6 < 7, i = 2 is not a valid split.
Thus, the number of valid splits in nums is 2.

Example 2:

Input: nums = [2,3,1,0]
Output: 2
Explanation: 
There are two valid splits in nums:
- Split nums at index 1. Then, the first part is [2,3], and its sum is 5. The second part is [1,0], and its sum is 1. Since 5 >= 1, i = 1 is a valid split. 
- Split nums at index 2. Then, the first part is [2,3,1], and its sum is 6. The second part is [0], and its sum is 0. Since 6 >= 0, i = 2 is a valid split.

 

Constraints:

• 2 <= nums.length <= 105
• -105 <= nums[i] <= 105

public int WaysToSplitArray(int[] nums)
{
    long[] prefixSum = new long[nums.Length];

    prefixSum[0] = nums[0];
    for (int i = 1; i < nums.Length; i++) prefixSum[i] = nums[i] + prefixSum[i - 1];

    int nWays = 0;
    for (int i = 0; i < nums.Length - 1; i++)
    {
        if (prefixSum[i] >= prefixSum[prefixSum.Length - 1] - prefixSum[i]) nWays++;
    }

    return nWays;
}