Count distinct XOR values among pairs using numbers in range 1 to NGiven an integer N, the objective is to determine the count of distinct XOR values that can be generated from all possible pairs of numbers ranging from 1 to N, inclusive. Example 1 Input: N = 3 Output: 4 Explanation: The following are all possible pairs using elements from 1 to N inclusive. 1^1 = 0 1^2 = 3 1^3 = 2 2^2 = 0 2^3 = 1 3^3 = 0 Therefore, there are 4 distinct possible XOR values. Example 2 Input: N = 4 Output: 5 Explanation: The following are all possible pairs using elements from 1 to 4 inclusive. 1^1 = 0 1^2 = 3 1^3 = 2 1^4 = 5 2^2 = 0 2^3 = 1 2^4 = 6 3^3 = 0 3^4 = 7 4^4 = 0 Therefore, there are 7 distinct possible XOR values. Example 3 Input: N = 1 Output: 1 Explanation: There is only one value 1 ^ 1 = 0. Hence, the output is 1. Approach: Naive approachThe naive approach to count distinct XOR values among pairs of numbers in the range 1 to N in Java involves using nested loops to generate all possible pairs of numbers and calculate their XOR values. AlgorithmStep 1: Initialize a set (xorValues) to store distinct XOR values among pairs. Step 2: Loop through all pairs of numbers in the range 1 to N using two nested loops. Step 3: For each pair of numbers (i, j), calculate their XOR value and add it to the xorValues set. Step 4: Since XOR values should be counted only once, using a set ensures that duplicates are automatically eliminated. Step 5: Continue this process for all possible pairs of numbers in the range. Step 6: After the loops, the size of the xorValues set represents the count of distinct XOR values among pairs. Step 7: Return this count as the final result. ImplementationFilename: CountDistinctXORPairs.java Output: Count of distinct XOR values among pairs: 4 Time Complexity: The code employs a nested loop configuration to traverse through all possible pairs of integers within the inclusive range from 1 to N. The outer loop executes N times, and within each iteration of the outer loop, the inner loop operates i times, where i corresponds to the current value of the outer loop. The method executes around (N * (N+1))/2 iterations in total since the inner Loop gets smaller as i rises. Therefore, the overall complexity of the program is O(N^{2}), where N is the input number. Auxiliary Space: The auxiliary space complexity for the provided code to count distinct XOR values among pairs in the range 1 to N is indeed O(d), where d represents the number of distinct XOR values that can be generated for a given input N. |