Question

1013. Partition Array Into Three Parts With Equal Sum

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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

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

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;
  }
}

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;
  }
};

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
}