九章算法 | 拼多多面试题：和相同的二元子数组

描述

在由若干 0 和 1 组成的数组 A 中，有多少个和为 S 的非空子数组。

• A.length <= 30000
• 0 <= S <= A.length
• A[i] 为 0 或 1

在线评测地址

LintCode 领扣

样例1

Input: A = [1,0,1,0,1], S = 2 
Output: 4 
Explanation:  
The 4 subarrays are bolded below: 
[1,0,1] 
[1,0,1] 
[1,0,1,0] 
[0,1,0,1] 

样例2

Input: A = [0,0,0,0,0,0,1,0,0,0], S = 0 
Output: 27 
Explanation:  
And 27 subarrays for S. 

题解

前缀和：定义一个数组sumN+1，si表示数组A中前i个元素之和，然后遍历sum数组，计算si+S(含义：前i个元素之和是si,找和为S的子数组个数)。求si+S的个数

public class Solution { 
    /** 
     * @param A: an array 
     * @param S: the sum 
     * @return: the number of non-empty subarrays 
     */ 
    public int numSubarraysWithSum(int[] A, int S) { 
        // Write your code here. 
        if (A == null || A.length == 0) { 
            return 0; 
        } 
        int prefixSum = 0; 
        int res = 0; 
        // counts[i] means the number of prefixSum = i 
        int[] counts = new int[A.length + 1]; 
        counts[0] = 1; 
        for (int i = 0; i < A.length; i++) { 
            prefixSum += A[i]; 
            if (prefixSum >= S) { 
                res += counts[prefixSum - S]; 
            } 
            counts[prefixSum]++; 
        } 
        return res; 
    } 
} 
 

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