leetcode-1013-Partition-Array-Into-Three-Parts-With-Equal-Sum

描述


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:

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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:

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

Example 3:

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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

分析


水题。

解决方案1(Java)


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class Solution {
public boolean canThreePartsEqualSum(int[] A) {
int sum = 0;
for (int i = 0; i < A.length; i++) {
sum += A[i];
}
if (sum % 3 != 0) {
return false;
}

sum = sum / 3;
int sumA = A[0], sumC = A[A.length-1];
int i = 1, j = A.length-2;
while (i < j) {
if (sumA != sum) {
sumA += A[i++];
}
if (sumC != sum) {
sumC += A[j--];
}

if (sumA == sum && sumC == sum && i <= j) {
return true;
}
}
return false;
}
}

解决方案(Golang)


使用前缀和解决。

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func canThreePartsEqualSum(arr []int) bool {
arrLen := len(arr)
preSum := make([]int, arrLen)
sufSum := make([]int, arrLen)
preSum[0] = arr[0]
for i := 1; i < arrLen; i++ {
preSum[i] = preSum[i-1] + arr[i]
}
if preSum[arrLen-1] % 3 != 0 {
return false
}

sufSum[arrLen-1] = arr[arrLen-1]
for i := arrLen-2; i >= 0; i-- {
sufSum[i] = sufSum[i+1] + arr[i]
}

for i := 0; i < arrLen; i++ {
if preSum[i] * 3 != preSum[arrLen-1] {
continue
}
for j := i+2; j < arrLen; j++ {
if sufSum[j] == preSum[i] {
return true
}
}
}
return false
}

题目来源