1442. Count Triplets That Can Form Two Arrays of Equal XOR - Explanation

class Solution:
    def countTriplets(self, arr: List[int]) -> int:
        N = len(arr)
        res = 0

        for i in range(N - 1):
            for j in range(i + 1, N):
                for k in range(j, N):
                    a = b = 0
                    for idx in range(i, j):
                        a ^= arr[idx]
                    for idx in range(j, k + 1):
                        b ^= arr[idx]
                    if a == b:
                        res += 1

        return res

class Solution:
    def countTriplets(self, arr: List[int]) -> int:
        N = len(arr)
        res = 0

        for i in range(N - 1):
            a = 0
            for j in range(i + 1, N):
                a ^= arr[j - 1]
                b = 0
                for k in range(j, N):
                    b ^= arr[k]
                    if a == b:
                        res += 1

        return res

class Solution:
    def countTriplets(self, arr: List[int]) -> int:
        N = len(arr)
        res = 0

        for i in range(N - 1):
            cur_xor = arr[i]
            for k in range(i + 1, N):
                cur_xor ^= arr[k]
                if cur_xor == 0:
                    res += k - i

        return res

class Solution:
    def countTriplets(self, arr: List[int]) -> int:
        N = len(arr)
        res = prefix = 0
        count = defaultdict(int)  # number of prefixes
        index_sum = defaultdict(int)  # sum of indices with that prefix
        count[0] = 1

        for i in range(N):
            prefix ^= arr[i]
            if prefix in count:
                res += i * count[prefix] - index_sum[prefix]
            count[prefix] += 1
            index_sum[prefix] += i + 1

        return res