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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.
1function xorQueries(arr, queries) {
2 let result = [];
3 for (let q of queries) {
4 let xor_result = 0;
5 for (let i = q[0]; i <= q[1]; i++) {
6 xor_result ^= arr[i];
7 }
8 result.push(xor_result);
9 }
10 return result;
11}
12
13const arr = [1, 3, 4, 8];
14const queries = [[0, 1], [1, 2], [0, 3], [3, 3]];
15console.log(xorQueries(arr, queries));This JavaScript function processes each query to compute the XOR for the specified range. The result is stored in an array which is returned and printed to the console.
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
class XorQueries {
public static int[] XorQueries(int[] arr, int[][] queries) {
int n = arr.Length;
int[] prefixXor = new int[n + 1];
for (int i = 1; i <= n; i++) {
prefixXor[i] = prefixXor[i - 1] ^ arr[i - 1];
}
int[] result = new int[queries.Length];
for (int i = 0; i < queries.Length; i++) {
result[i] = prefixXor[queries[i][1] + 1] ^ prefixXor[queries[i][0]];
}
return result;
}
static void Main() {
int[] arr = {1, 3, 4, 8};
int[][] queries = new int[][] {
new int[] {0, 1},
new int[] {1, 2},
new int[] {0, 3},
new int[] {3, 3}
};
int[] result = XorQueries(arr, queries);
Console.WriteLine(string.Join(" ", result));
}
}This C# solution constructs a prefix XOR array to efficiently compute the XOR for each query range. It uses a prefix accumulation approach to store XORs up to each point in the array, making subsequence calculations straightforward.