Sort an array containing two types of elements

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This problem appears in multiple forms as mentioned below. If we take a closer look at the below problems, we can notice that the problem is mainly a variation of partition algorithm in QuickSort.

Sort a Binary Array

Given an array of 0s and 1s in random order. Segregate 0s on left side and 1s on right side of the array.

Examples: 

Input : arr[] = [0, 1, 0, 1, 0, 0, 1, 1, 1, 0]
Output : arr[] = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1]

Input : arr[] = [1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1]
Output : arr[] = [0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]

Please refer Segregate 0s and 1s in an array for detailed solution.

Move all zeros to end of array

Given an array of integers arr[], the task is to move all the zeros to the end of the array while maintaining the relative order of all non-zero elements.

Examples: 

Input: arr[] = [1, 2, 0, 4, 3, 0, 5, 0]
Output: arr[] = [1, 2, 4, 3, 5, 0, 0, 0]
Explanation: There are three 0s that are moved to the end.

Input: arr[] = [10, 20, 30]
Output: arr[] = [10, 20, 30]
Explanation: No change in array as there are no 0s.

Input: arr[] = [0, 0]
Output: arr[] = [0, 0]
Explanation: No change in array as there are all 0s.

Refer here Move all zeros to end of array for detailed solution.

Separate Even and Odd Numbers

Given an array of integers. Segregate even numbers on left side and odd numbers on right side of the array.

Examples:

Input: arr = [0, 1, 2, 3, 4]
Output: arr = [0, 2, 4, 1, 3]
Explanation: [0, 2, 4] are even and [1, 3] are odd numbers. Please note that [2, 0, 4, 3, 1] or [4, 2, 0, 1, 3] are also valid outputs. We only need to make sure that all even elements are before all odd.

Input : arr ={1, 5, 11}
Output : arr= {1, 5, 11}
Explanation All numbers are odd.

Please refer Segregate Even and Odd Numbers and Stable Binary Sort for reference,

Separate Negative and Positive Numbers

Given an array of integers, the task is to arrange the elements such that all negative integers appear before all the positive integers in the array.

Examples:

Input: arr[] = [12, 11, -13, -5, 6, -7, 5, -3, -6]
Output: [-13, -5, -7, -3, -6, 12, 11, 6, 5]
Explanation: All negative elements [-13, -5, -7, -3, -6] were arranged before positive numbers [12, 11, 6, 5]. Note that there can be more than one possible output.

Input: arr[] = [11, -13, 6, -7, 5]
Output: [-13, -7, 11, 6, 5]
Explanation: All negative elements [-13, -7] were arranged before positive numbers [11, 6, 5].

We have two type of approaches to solve this problem:

• Separate positive and negative with order preserved
• Separate positive and negative with order preserved and O(1) space