Write a program in JAVA Programming langaugue. Given an array of integers, in which each elements repeats twice except one. Your task is to find that element in O(n) Time complexity and O(1) Space Complexity.

Write a program in JAVA Programming langaugue. Given an array of integers, in which each elements repeats twice except one. Your task is to find that element in O(n) Time complexity and O(1) Space Complexity.

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter8: Arrays And Strings

Section: Chapter Questions

Problem 24PE

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Concept explainers

Randomized Select Algorithm

A randomized algorithm is defined as one that uses a certain amount of randomization in its logic or operation. It is said to be an algorithm that depends on the random number to perform its operation. It is used for reducing the overall time complexity, space complexity in the standard algorithm. The randomized algorithm uses the concept of random numbers to find the solutions to the different kinds of problems and also to improve the problem solutions.

Question

Write a program in JAVA Programming langaugue.
Given an array of integers, in which each elements repeats twice except one.
Your task is to find that element in O(n) Time complexity and O(1) Space Complexity.

Expert Solution

Step 1

Required :

Java program that finds in an array, the only number which doesn't repeats itself.

Constraints : Time complexity : O(n), Space Complexity : O(1)

The idea is to use XOR operator. It has the following properties :

XOR of a number with itself is 0

XOR of a number with 0 is the number itself.

For example,

5 ^ 5 = 0

5 ^ 0 = 5

Where ^ is the XOR operator.

So consider the following array is given :

{4, 8, 3, 6, 3, 8, 9, 6, 4}

Here, 9 is the only non repeating element.

So we do XOR for all the elements :

4 ^ 8 ^ 3 ^ 6 ^ 3 ^ 8 ^ 9 ^ 6 ^ 4

Rearranging, we get :

4 ^ 4 ^ 8 ^ 8 ^ 3 ^ 3 ^ 6 ^ 6 ^ 9

Using above properties, we have

0 ^ 0 ^ 0 ^ 0 ^ 9

= 9

This the required element.

Below is the Java program as required.

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