1712. Ways to Split Array Into Three Subarrays

A split of an integer array is good if:

  • The array is split into three non-empty contiguous subarrays - named left, mid, right respectively from left to right.
  • The sum of the elements in left is less than or equal to the sum of the elements in mid, and the sum of the elements in mid is less than or equal to the sum of the elements in right.

Given nums, an array of non-negative integers, return the number of good ways to split nums. As the number may be too large, return it modulo 109 + 7.

 

Example 1:

Input: nums = [1,1,1]
Output: 1
Explanation: The only good way to split nums is [1] [1] [1].

Example 2:

Input: nums = [1,2,2,2,5,0]
Output: 3
Explanation: There are three good ways of splitting nums:
[1] [2] [2,2,5,0]
[1] [2,2] [2,5,0]
[1,2] [2,2] [5,0]

Example 3:

Input: nums = [3,2,1]
Output: 0
Explanation: There is no good way to split nums.

 

Constraints:

  • 3 <= nums.length <= 105
  • 0 <= nums[i] <= 104

Rust Solution

struct Solution;

const MOD: i64 = 1_000_000_007;

impl Solution {
    fn ways_to_split(nums: Vec<i32>) -> i32 {
        let n = nums.len();
        let mut prefix: Vec<i32> = vec![];
        let mut prev = 0;
        let mut res = 0;
        for i in 0..n {
            prev += nums[i];
            prefix.push(prev);
        }
        let total = prev;
        let mut mid_start = 0;
        let mut mid_end = 0;
        for i in 0..n {
            let left = prefix[i];
            mid_start = mid_start.max(i + 1);
            while mid_start < n && prefix[mid_start] - left < left {
                mid_start += 1;
            }
            while mid_end + 1 < n && total - prefix[mid_end] >= prefix[mid_end] - left {
                mid_end += 1;
            }
            if mid_end >= mid_start {
                res += (mid_end - mid_start) as i64;
                res %= MOD;
            }
        }
        res as i32
    }
}

#[test]
fn test() {
    let nums = vec![1, 1, 1];
    let res = 1;
    assert_eq!(Solution::ways_to_split(nums), res);
    let nums = vec![1, 2, 2, 2, 5, 0];
    let res = 3;
    assert_eq!(Solution::ways_to_split(nums), res);
    let nums = vec![3, 2, 1];
    let res = 0;
    assert_eq!(Solution::ways_to_split(nums), res);
    let nums = vec![0, 3, 3];
    let res = 1;
    assert_eq!(Solution::ways_to_split(nums), res);
}

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