explanation.md

Solution Explanation: Maximum XOR Queries

This repository contains a solution for solving the Maximum XOR Queries problem in multiple programming languages: C++, Java, JavaScript, Python, and Go. Each solution is broken down step-by-step for ease of understanding.

Problem Summary

Given an array of numbers (nums) and a parameter maximumBit, we are to find the maximum XOR result for each query by choosing an integer k that maximizes the XOR between k and the cumulative XOR of all elements in nums. The k must be within a range defined by maximumBit.

Steps to Solution

The approach is the same across all languages but adapted to the syntax of each language. Here’s a language-by-language breakdown of how each solution works.

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C++ Code Explanation

1. Initialize Variables:

   • We start by defining XORed, an integer to store the cumulative XOR of all elements in nums.
   • We also define max_k, which is the maximum value achievable with maximumBit bits. This is calculated as 2^maximumBit - 1.

2. Compute Initial XOR:

   • Using a loop, XOR all elements in nums together to get an initial cumulative XOR (XORed) of the entire array.

3. Process Each Query in Reverse:

   • We loop from the last element of nums to the first.
   • For each query, calculate k as XORed ^ max_k. This gives the integer k that maximizes the XOR.
   • Append k to our answer array.
   • Update XORed by removing the effect of the last element in nums.

4. Return the Result:

   • The final answer array contains the results for all queries, and we return it.

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Java Code Explanation

1. Initialize Variables:

   • Define XORed to store the cumulative XOR of all elements in nums.
   • Calculate max_k as (1 << maximumBit) - 1 to get the maximum value achievable within maximumBit bits.

2. Compute Initial XOR:

   • Use a loop to XOR all elements in nums, updating XORed with each element.

3. Reverse Loop for Queries:

   • Loop backward from the last element of nums.
   • For each query, calculate k as XORed ^ max_k.
   • Store k in the answer array.
   • Update XORed by XORing it with the current element to "remove" its effect.

4. Return the Final Answer:

   • The answer array now contains all query results, which we return as our solution.

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JavaScript Code Explanation

1. Initialize Variables:

   • Define XORed to store the cumulative XOR of all numbers in nums.
   • Calculate max_k as (1 << maximumBit) - 1 to get the highest possible value within maximumBit bits.

2. Compute Initial XOR:

   • Loop over nums and calculate the cumulative XOR (XORed).

3. Process Each Query in Reverse:

   • Start from the last element of nums and work backwards.
   • For each query, calculate k as XORed ^ max_k.
   • Store k in the answer array.
   • Update XORed by removing the effect of the last element.

4. Return the Final Array:

   • Return answer as the array containing all query results.

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Python Code Explanation

1. Initialize Variables:

   • Define XORed to hold the cumulative XOR of all elements in nums.
   • Calculate max_k as (1 << maximumBit) - 1 to get the largest value allowed by maximumBit.

2. Compute Cumulative XOR:

   • Loop through each number in nums to calculate the cumulative XOR.

3. Process Each Query in Reverse:

   • Start from the last element of nums and process each in reverse.
   • For each query, calculate k as XORed ^ max_k to get the maximum XOR.
   • Append k to the answer list.
   • Update XORed by XORing it with the last element in nums.

4. Return Results:

   • answer now holds the maximum XOR result for each query, which we return as the solution.

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Go Code Explanation

1. Initialize Variables:

   • Define XORed to keep the cumulative XOR of all elements in nums.
   • Calculate max_k as (1 << maximumBit) - 1 to get the maximum possible integer with maximumBit bits.

2. Compute Initial XOR:

   • XOR all elements in nums to get the cumulative XOR.

3. Process Each Query in Reverse:

   • Start from the end of nums and move backwards.
   • For each query, calculate k as XORed ^ max_k.
   • Add k to the answer slice.
   • Update XORed by removing the effect of the last element.

4. Return the Result Slice:

   • Return answer as the final result, containing the XOR values for each query.