LeetCode, ๐๐๐ฒ-18/365-DSA-Coding ๐๐จ๐ฎ๐ซ๐ง๐๐ฒโฆGoogle Prepโฆ
Today I Learned This Problem: Does Valid Array Exist?
Problem Overview:
The problem requires determining if there exists a valid array where the XOR of all the elements in the array is equal to 0. Given an array derived
, we need to check if there is a way to form a valid array such that the XOR of all its elements equals 0. This problem helps to understand the properties of the XOR operation and its role in solving bitwise manipulation problems.
Challenges Involved:
- XOR Properties: Understanding how XOR works with 0 and itself, and how this can simplify the problem.
- Efficient Calculation: Determining if the XOR of all elements in the array equals 0 without explicitly checking each possibility.
Explanation:
We use the following XOR properties to solve the problem:
- XORing a number with 0 results in the number itself.
- XORing a number with itself results in 0.
- XOR is commutative and associative.
Key Steps:
- Iterate Through Array:
- Iterate through all elements of the
derived
array and compute the cumulative XOR of all the elements.
2. Check the XOR Result:
- If the cumulative XOR of all elements equals 0, then a valid array exists.
My Solution Approach:
- Initialization:
Compute the XOR of all elements in thederived
array. Start withxor_sum = 0
. - Iterate Through Array:
Loop through each element and apply the XOR operation withxor_sum
. - Final Check:
After looping through the array, check if thexor_sum
equals 0. If true, returnTrue
(indicating that a valid array exists), otherwise returnFalse
.
Python Code:
class Solution:
def doesValidArrayExist(self, derived):
xor_sum = 0
for num in derived:
xor_sum ^= num
return xor_sum == 0
Other Possible Solutions:
- Mathematical Observation: The problem boils down to the XOR of the array elements. If the XOR of all elements is zero, the array is valid.
- Optimization: The solution works in O(n) time complexity, where
n
is the number of elements in the array. There is no need to generate pairs or explicitly check each combination, making this an efficient solution.
Learnings:
- XOR Operations: A deeper understanding of XOR and its properties in solving array-based problems.
- Optimization: Optimized the solution by leveraging the properties of XOR without generating all possible pairs.
- Bitwise Computations: Improved skills in handling bitwise operations efficiently.
Real-Life Usage:
- Cryptography: XOR is fundamental in encryption algorithms and securing data.
- Error Detection: XOR is used in parity checks and error detection algorithms.
To sum upโฆ
Thank you for reading! If this explanation clarified the problem for you, feel free to share your thoughts or suggest alternative solutions. Keep learning, coding, sharing, and growing!