You’re given a list of integers nums. Write a function that returns a boolean representing whether there exists a zero-sum subarray of nums.

A zero-sum subarray is any subarray where all the values add up to zero. A subarray is any contiguous section of the array. For the purposes of this problem, a subarray can be as small as one element and as long as the original array.

Sample Input

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1nums = [-5, -5, 2, 3, -2]

Sample Output

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1True // The subarray [-5, 2, 3] has a sum of 0

Hints

Hint 1

A good way to approach this problem is to first think of a simpler version. How would you check if the entire array sum is zero?

Hint 2

If the entire array does not sum to zero, then you need to check if there are any smaller sub-arrays that sum to zero. For this, it can be helpful to keep track of all the sums from [0, i], where i is every index in the array.

Hint 3

After recording all sums from [0, i], what would it mean if a sum is repeated?

Optimal Space & Time Complexity

O(n) time | O(n) space - where n is the length of nums

Solution-1
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1function zeroSumSubarray(nums) {
2
3    for (let i = 0; i < nums.length; i++) {
4      let sum = nums[i]
5      if (sum === 0) {
6        return true
7      }
8      
9      for (let j = i + 1; j < nums.length; j++) {
10        sum = sum + nums[j]
11        if (sum === 0) {
12          console.log(nums[i], nums[j])
13          return true
14        }
15      }
16    }
17  
18  return false;
19}

Solution-2
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1function zeroSumSubarray(nums) {
2  // Write your code here.
3  const sums = new Set([0])
4  let currentSum = 0
5  for (const num of nums) {
6    currentSum += num
7    if(sums.has(currentSum)) return true
8    sums.add(currentSum)
9  }
10  return false
11}

🧝‍♂️