1013. Partition Array Into Three Parts With Equal Sum

Description

Given an array of integers arr, return true 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 (arr[0] + arr[1] + ... + arr[i] == arr[i + 1] + arr[i + 2] + ... + arr[j - 1] == arr[j] + arr[j + 1] + ... + arr[arr.length - 1])

 

Example 1:

Input: arr = [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: arr = [0,2,1,-6,6,7,9,-1,2,0,1]
Output: false

Example 3:

Input: arr = [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 <= arr.length <= 5 * 104
  • -104 <= arr[i] <= 104

Solutions

Solution 1

Python Code
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class Solution:
    def canThreePartsEqualSum(self, arr: List[int]) -> bool:
        s = sum(arr)
        if s % 3 != 0:
            return False
        i, j = 0, len(arr) - 1
        a = b = 0
        while i < len(arr):
            a += arr[i]
            if a == s // 3:
                break
            i += 1
        while ~j:
            b += arr[j]
            if b == s // 3:
                break
            j -= 1
        return i < j - 1

Java Code
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class Solution {
    public boolean canThreePartsEqualSum(int[] arr) {
        int s = 0;
        for (int v : arr) {
            s += v;
        }
        if (s % 3 != 0) {
            return false;
        }
        int i = 0, j = arr.length - 1;
        int a = 0, b = 0;
        while (i < arr.length) {
            a += arr[i];
            if (a == s / 3) {
                break;
            }
            ++i;
        }
        while (j >= 0) {
            b += arr[j];
            if (b == s / 3) {
                break;
            }
            --j;
        }
        return i < j - 1;
    }
}

C++ Code
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class Solution {
public:
    bool canThreePartsEqualSum(vector<int>& arr) {
        int s = 0;
        for (int v : arr) s += v;
        if (s % 3) return false;
        int i = 0, j = arr.size() - 1;
        int a = 0, b = 0;
        while (i < arr.size()) {
            a += arr[i];
            if (a == s / 3) {
                break;
            }
            ++i;
        }
        while (~j) {
            b += arr[j];
            if (b == s / 3) {
                break;
            }
            --j;
        }
        return i < j - 1;
    }
};

Go Code
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func canThreePartsEqualSum(arr []int) bool {
	s := 0
	for _, v := range arr {
		s += v
	}
	if s%3 != 0 {
		return false
	}
	i, j := 0, len(arr)-1
	a, b := 0, 0
	for i < len(arr) {
		a += arr[i]
		if a == s/3 {
			break
		}
		i++
	}
	for j >= 0 {
		b += arr[j]
		if b == s/3 {
			break
		}
		j--
	}
	return i < j-1
}