# leetcode\_1013

Given an array A of integers, return true if and only if we can partition the array into three non-empty parts with equal sums.

Formally, we can partition the array if we can find indexes i+1 < j with (A\[0] + A\[1] + ... + A\[i] == A\[i+1] + A\[i+2] + ... + A\[j-1] == A\[j] + A\[j-1] + ... + A\[A.length - 1])

Example 1:

Input: A = \[0,2,1,-6,6,-7,9,1,2,0,1] Output: true Explanation: 0 + 2 + 1 = -6 + 6 - 7 + 9 + 1 = 2 + 0 + 1 Example 2:

Input: A = \[0,2,1,-6,6,7,9,-1,2,0,1] Output: false Example 3:

Input: A = \[3,3,6,5,-2,2,5,1,-9,4] Output: true Explanation: 3 + 3 = 6 = 5 - 2 + 2 + 5 + 1 - 9 + 4

Constraints:

3 <= A.length <= 50000 -10^4 <= A\[i] <= 10^4

## Solutions

1. **straight forward**
2. Find the first two part with sum equals to `total/3`, then break and check if the remaining sum is equal to `total/3`.

```cpp
class Solution {
public:
    bool canThreePartsEqualSum(vector<int>& A) {
        int sum = accumulate(A.begin(), A.end(), 0);
        if (sum % 3 != 0) return false;

        int target = sum / 3, cnt = 0, cur = 0;
        int i = 0;
        while (i < A.size()) {
            cur += A[i]; sum -= A[i++];
            if (cur == target) {
                if (++cnt == 2) break;
                cur = 0;
            }
        }

        return i < A.size() && sum == target;
    }
};
```

1. **two pointers**

```cpp
class Solution {
public:
    bool canThreePartsEqualSum(vector<int>& A) {
        if (A.size() < 3) return false;
        int sum = accumulate(A.begin(), A.end(), 0);
        if (sum % 3 != 0) return false;

        // make sure each part has at least 1 element.
        int target = sum / 3, suma = A[0], sumb = A.back();
        int i = 1, j = A.size() - 2;
        while (i < j) {
            if (suma != target)
                suma += A[i++];
            if (sumb != target)
                sumb += A[j--];
            if (i > j) return false;
            if (suma == target && sumb == target)
                break;
        }

        return suma == sumb  && suma == target;
    }
};
```