# 548. Split Array with Equal Sum

## Description

Given an integer array nums of length n, return true if there is a triplet (i, j, k) which satisfies the following conditions:

• 0 < i, i + 1 < j, j + 1 < k < n - 1
• The sum of subarrays (0, i - 1), (i + 1, j - 1), (j + 1, k - 1) and (k + 1, n - 1) is equal.

A subarray (l, r) represents a slice of the original array starting from the element indexed l to the element indexed r.

Example 1:

Input: nums = [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


Example 2:

Input: nums = [1,2,1,2,1,2,1,2]
Output: false


Constraints:

• n == nums.length
• 1 <= n <= 2000
• -106 <= nums[i] <= 106

## Solutions

• class Solution {
public boolean splitArray(int[] nums) {
int n = nums.length;
int[] s = new int[n + 1];
for (int i = 0; i < n; ++i) {
s[i + 1] = s[i] + nums[i];
}
for (int j = 3; j < n - 3; ++j) {
Set<Integer> seen = new HashSet<>();
for (int i = 1; i < j - 1; ++i) {
if (s[i] == s[j] - s[i + 1]) {
}
}
for (int k = j + 2; k < n - 1; ++k) {
if (s[n] - s[k + 1] == s[k] - s[j + 1] && seen.contains(s[n] - s[k + 1])) {
return true;
}
}
}
return false;
}
}

• class Solution {
public:
bool splitArray(vector<int>& nums) {
int n = nums.size();
vector<int> s(n + 1);
for (int i = 0; i < n; ++i) s[i + 1] = s[i] + nums[i];
for (int j = 3; j < n - 3; ++j) {
unordered_set<int> seen;
for (int i = 1; i < j - 1; ++i)
if (s[i] == s[j] - s[i + 1])
seen.insert(s[i]);
for (int k = j + 2; k < n - 1; ++k)
if (s[n] - s[k + 1] == s[k] - s[j + 1] && seen.count(s[n] - s[k + 1]))
return true;
}
return false;
}
};

• class Solution:
def splitArray(self, nums: List[int]) -> bool:
n = len(nums)
s = [0] * (n + 1)
for i, v in enumerate(nums):
s[i + 1] = s[i] + v
for j in range(3, n - 3):
seen = set()
for i in range(1, j - 1):
if s[i] == s[j] - s[i + 1]:
for k in range(j + 2, n - 1):
if s[n] - s[k + 1] == s[k] - s[j + 1] and s[n] - s[k + 1] in seen:
return True
return False


• func splitArray(nums []int) bool {
n := len(nums)
s := make([]int, n+1)
for i, v := range nums {
s[i+1] = s[i] + v
}
for j := 3; j < n-3; j++ {
seen := map[int]bool{}
for i := 1; i < j-1; i++ {
if s[i] == s[j]-s[i+1] {
seen[s[i]] = true
}
}
for k := j + 2; k < n-1; k++ {
if s[n]-s[k+1] == s[k]-s[j+1] && seen[s[n]-s[k+1]] {
return true
}
}
}
return false
}