930. Binary Subarrays With Sum

Problem Statement

Given a binary array nums and an integer goal, return the number of non-empty subarrays with a sum goal.

A subarray is a contiguous part of the array.

Example 1:

Input: nums = [1,0,1,0,1], goal = 2
Output: 4
Explanation: The 4 subarrays are bolded and underlined below:
[1,0,1,0,1]
[1,0,1,0,1]
[1,0,1,0,1]
[1,0,1,0,1]

Example 2:

Input: nums = [0,0,0,0,0], goal = 0
Output: 15

Constraints:

1 <= nums.length <= 3 * 104
nums[i] is either 0 or 1.
0 <= goal <= nums.length

Intuition

Approach 1:

HashMAp and Prefix sum
Intuition

1 0 0 0  1 1
1 1 1 1 )2 3

goal = 2
At prefix sum = 3 we subtract prefix sum = 1
We get sum = 2 arrays

Appraoch 2:
Sliding Window 

Atmost k - Atmost k-1

Video Links

Approach 1:

Hash Map

C++

class Solution {
public:
    int numSubarraysWithSum(vector<int>& nums, int goal) {
        unordered_map<int,int> mp;
        int sum=0, ans=0;
        mp[0]=1;

        for(int i=0; i<nums.size(); i++){
            sum += nums[i];

            if(mp[sum-goal])
                ans += mp[sum-goal];
            mp[sum]++;
        }

        return ans;
    }
};

Approach 2:

Sliding Window

C++

class Solution {
public:
    int Atmost(vector<int>& nums, int goal){
        if(goal < 0)   return 0;
        int low=0, ans=0;
        int sum=goal; 
        for(int high=0; high<nums.size(); high++){
            sum -= nums[high];

            while(sum<0)
                sum += nums[low++];

            ans += high-low+1;
        }

        return ans;
    }

    int numSubarraysWithSum(vector<int>& nums, int goal) {
        return Atmost(nums, goal) - Atmost(nums, goal-1);
    }
};

Approach 3:

C++

Approach 4:

C++