Rearrange positive and negative numbers in O(n) time and O(1) extra space

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An array contains both positive and negative numbers in random order. Rearrange the array elements so that positive and negative numbers are placed alternatively. Number of positive and negative numbers need not be equal. If there are more positive numbers they appear at the end of the array. If there are more negative numbers, they too appear in the end of the array.

For example, if the input array is [-1, 2, -3, 4, 5, 6, -7, 8, 9], then the output should be [9, -7, 8, -3, 5, -1, 2, 4, 6]

The solution is to first separate positive and negative numbers using partition process of QuickSort. In the partition process, consider 0 as value of pivot element so that all negative numbers are placed before positive numbers. Once negative and positive numbers are separated, we start from the first negative number and first positive number, and swap every alternate negative number with next positive number.

// A C++ program to put positive numbers at even indexes (0,
// 2, 4,..) and negative numbers at odd indexes (1, 3, 5, ..)
#include <stdio.h>
// prototype for swap
void swap(int *a, int *b);
// The main function that rearranges elements of given array.
// It puts  positive elements at even indexes (0, 2, ..) and
// negative numbers at odd indexes (1, 3, ..).
void rearrange(int arr[], int n)
{
    // The following few lines are similar to partition process
    // of QuickSort.  The idea is to consider 0 as pivot and
    // divide the array around it.
    int i = -1;
    for (int j = 0; j < n; j++)
    {
        if (arr[j] < 0)
        {
            i++;
            swap(&arr[i], &arr[j]);
        }
    }
    // Now all positive numbers are at end and negative numbers
    // at the beginning of array. Initialize indexes for starting
    // point of positive and negative numbers to be swapped
    int pos = i+1, neg = 0;
    // Increment the negative index by 2 and positive index by 1,
    // i.e., swap every alternate negative number with next
    // positive number
    while (pos < n && neg < pos && arr[neg] < 0)
    {
        swap(&arr[neg], &arr[pos]);
        pos++;
        neg += 2;
    }
}
// A utility function to swap two elements
void swap(int *a, int *b)
{
    int temp = *a;
    *a = *b;
    *b = temp;
}
// A utility function to print an array
void printArray(int arr[], int n)
{
    for (int i = 0; i < n; i++)
        printf("%4d ", arr[i]);
}
// Driver program to test above functions
int main()
{
    int arr[] = {-1, 2, -3, 4, 5, 6, -7, 8, 9};
    int n = sizeof(arr)/sizeof(arr[0]);
    rearrange(arr, n);
    printArray(arr, n);
    return 0;
}

Output:

    4   -3    5   -1    6   -7    2    8    9

Time Complexity: O(n) where n is number of elements in given array.
Auxiliary Space: O(1)

Note that the partition process changes relative order of elements.

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rakesh

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