2270. Number of Ways to Split Array

2270. Number of Ways to Split Array

Difficulty: Medium

Topics: Array, Prefix Sum

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

Hint:

1. For any index i, how can we find the sum of the first (i+1) elements from the sum of the first i elements?


2. If the total sum of the array is known, how can we check if the sum of the first (i+1) elements greater than or equal to the remaining elements?

Solution:

We can approach it using the following steps:

Approach:

1. 
   Prefix Sum: First, we compute the cumulative sum of the array from the left, which helps in checking the sum of the first i+1 elements.


2. 
   Total Sum: Compute the total sum of the array, which is useful in checking if the sum of the remaining elements is less than or equal to the sum of the first i+1 elements.


3. 
   Iterate over the array: For each valid index i (where 0 <= i < n-1), we check if the sum of the first i+1 elements is greater than or equal to the sum of the last n-i-1 elements.


4. 
   Efficiency: Instead of recalculating the sums repeatedly, use the prefix sum and the total sum for efficient comparisons.

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