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

An array contains both positive and negative numbers in random order. Rearrange the array elements so that positive and negative numbers are placed alternatively. A 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 at 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]**Note:** The partition process changes the relative order of elements. I.e. the order of the appearance of elements is not maintained with this approach. See this for maintaining the order of appearance of elements in this problem.

The solution is to first separate positive and negative numbers using the partition process of QuickSort. In the partition process, consider 0 as the value of the 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 the next positive number.

`# Python program to put positive numbers at even indexes (0, // 2, 4,..) and`

`# negative numbers at odd indexes (1, 3, 5, ..)`

`# 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, ..).`

**def**`rearrange(arr, 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.`

`i `

**=****-**1

**for**`j `

**in**`range(n):`

**if**`(arr[j] < 0):`

`i `

**+=**`1`

`# swapping of arr`

`arr[i], arr[j] `

**=**`arr[j], arr[i]`

`# 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`

`pos, neg `

**=**`i`

**+**1, 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 `

**and**`neg < pos `

**and**`arr[neg] < 0):`

`# swapping of arr`

`arr[neg], arr[pos] `

**=**`arr[pos], arr[neg]`

`pos `

**+=**`1`

`neg `

**+=**`2`

`# A utility function to print an array`

**def**`printArray(arr, n):`

**for**`i `

**in**`range(n):`

**print**`(arr[i],end`

**=**" ")

`# Driver program to test above functions`

`arr `

**=**`[`

**-**1, 2, **-**3, 4, 5, 6, **-**7, 8, 9]

`n `

**=**`len(arr)`

`rearrange(arr, n)`

`printArray(arr, n)`