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Solution Explanation: doesValidArrayExist

This repository provides solutions to the problem of determining if a valid original array exists for a given derived array. The solutions are implemented in C++, Java, JavaScript, Python, and Go. Below, you'll find step-by-step explanations for each language.

C++ Code Explanation

Step 1: Understanding the Problem

  • The derived array is formed by XORing adjacent elements of the original array.
  • We need to check if at least one valid original array exists that satisfies the conditions for the given derived array.

Step 2: Initial Assumption

  • Assume the first element of the original array (original[0]) is 0. Compute the rest of the array using the XOR formula.

Step 3: Simulate the Array

  • Iterate through the derived array and calculate each subsequent element of the original array.

Step 4: Wrap-Around Validation

  • After iterating through all elements, check if the wrap-around condition ( \text{original}[n-1] \oplus \text{original}[0] = \text{derived}[n-1] ) holds.

Step 5: Repeat for Another Assumption

  • Repeat steps 2–4, assuming original[0] = 1.

Step 6: Combine Results

  • If either assumption produces a valid original array, return true. Otherwise, return false.

Java Code Explanation

Step 1: Problem Understanding

  • Similar to the C++ solution, the derived array is generated through XOR operations. The goal is to reverse this process and validate if a possible original array exists.

Step 2: Initial Setup

  • Assume the value of original[0] is 0. Begin calculating the rest of the elements in the original array.

Step 3: Deriving Subsequent Elements

  • For each element in the derived array, compute the next value of the original array using XOR operations.

Step 4: Final Check

  • Once the iteration completes, check the wrap-around condition to ensure the array satisfies all constraints.

Step 5: Alternate Assumption

  • Repeat the process, assuming original[0] is 1.

Step 6: Final Decision

  • Return true if any of the two assumptions lead to a valid original array.

JavaScript Code Explanation

Step 1: Identify the Goal

  • Reconstruct the original array from the derived array by testing both possible initial values (0 and 1) for original[0].

Step 2: First Case Simulation

  • Assume original[0] is 0.
  • Use a loop to calculate the remaining elements of the original array by applying XOR operations with the derived array.

Step 3: Verify Wrap-Around

  • After constructing the original array, check the wrap-around condition ( \text{original}[n-1] \oplus \text{original}[0] = \text{derived}[n-1] ).

Step 4: Test Second Case

  • Repeat the process with the assumption that original[0] is 1.

Step 5: Return Result

  • If any of the two cases pass all validations, return true.

Python Code Explanation

Step 1: Define the Problem

  • The problem involves reconstructing an array (original) using XOR operations in reverse based on a derived array.

Step 2: Simulate for original[0] = 0

  • Assume the first value of the original array is 0.
  • Compute the next elements using ( \text{original}[i+1] = \text{derived}[i] \oplus \text{original}[i] ).

Step 3: Validate the Wrap-Around

  • After simulating the array, check if the last element wraps back correctly to the first element as per the derived array.

Step 4: Simulate for original[0] = 1

  • Repeat the steps above with original[0] set to 1.

Step 5: Decision

  • If either simulation produces a valid array, return true.

Go Code Explanation

Step 1: Problem Analysis

  • Reconstruct the original array using XOR operations with the derived array, testing both possible starting values for original[0].

Step 2: First Assumption

  • Begin with original[0] = 0. Iterate through the derived array and compute the rest of the original array.

Step 3: Wrap-Around Validation

  • After constructing the original array, ensure the wrap-around condition holds true.

Step 4: Second Assumption

  • Repeat the entire process, assuming original[0] = 1.

Step 5: Combine Results

  • If any of the two assumptions lead to a valid solution, return true.

Complexity Analysis

  • Time Complexity: ( O(n) ) for all implementations, as we iterate through the derived array twice (once for each assumption).
  • Space Complexity: ( O(1) ), since no extra space is required.

Additional Notes

  • This approach is efficient and leverages the properties of XOR for simplicity.
  • Solutions are designed to handle edge cases, such as a single-element array or all zeros in the derived array.

Feel free to explore the full implementations in the respective language files! 😊