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This approach involves directly computing the XOR for each range specified in the queries. For each query, iterate over the specified subarray range and compute the XOR.
Time Complexity: O(n * q), where n is the number of elements in the largest range and q is the number of queries.
Space Complexity: O(q) for storing the query results.
1def xorQueries(arr, queries):
2 result = []
3 for q in queries:
4 xor_result = 0
5 for i in range(q[0], q[1] + 1):
6 xor_result ^= arr[i]
7 result.append(xor_result)
8 return result
9
10arr = [1, 3, 4, 8]
11queries = [[0, 1], [1, 2], [0, 3], [3, 3]]
12print(xorQueries(arr, queries))This Python function iterates over each query and computes the XOR over the specified subarray, appending the result to a list, which is returned at the end.
To optimize the XOR computation, we can use a prefix XOR array. Compute the XOR of all elements up to each position in the array. Then to find the XOR for a range simply subtract the prefix value before the start of the range from the prefix at the end of the range.
Time Complexity: O(n + q), where n is the number of elements and q is the number of queries.
Space Complexity: O(n) for the prefix XOR array.
1
In Python, this function calculates the prefix XOR array to allow constant time calculation of the XOR for any subarray. It then efficiently computes the result for each query.