Sort even-placed elements in increasing and odd-placed in decreasing order

06 Jul, 2022
We are given an array of n distinct numbers. The task is to sort all even-placed numbers in increasing and odd-placed numbers in decreasing order. The modified array should contain all sorted even-placed numbers followed by reverse sorted odd-placed numbers.
Note that the first element is considered as even placed because of its index 0. 
Examples:  
Input:  arr[] = {0, 1, 2, 3, 4, 5, 6, 7}
Output: arr[] = {0, 2, 4, 6, 7, 5, 3, 1}
Even-place elements : 0, 2, 4, 6
Odd-place elements : 1, 3, 5, 7
Even-place elements in increasing order : 
0, 2, 4, 6
Odd-Place elements in decreasing order : 
7, 5, 3, 1

Input: arr[] = {3, 1, 2, 4, 5, 9, 13, 14, 12}
Output: {2, 3, 5, 12, 13, 14, 9, 4, 1}
Even-place elements : 3, 2, 5, 13, 12
Odd-place elements : 1, 4, 9, 14
Even-place elements in increasing order : 
2, 3, 5, 12, 13
Odd-Place elements in decreasing order : 
14, 9, 4, 1 
The idea is simple. We create two auxiliary arrays evenArr[] and oddArr[] respectively. We traverse input array and put all even-placed elements in evenArr[] and odd placed elements in oddArr[]. Then we sort evenArr[] in ascending and oddArr[] in descending order. Finally, copy evenArr[] and oddArr[] to get the required result.
Implementation:
C++
Java
Python3
C#
Javascript
// Program to separately sort even-placed and odd// placed numbers and place them together in sorted// array.#include <bits/stdc++.h>using namespace std; void bitonicGenerator(int arr[], int n){    // create evenArr[] and oddArr[]    vector<int> evenArr;    vector<int> oddArr;     // Put elements in oddArr[] and evenArr[] as    // per their position    for (int i = 0; i < n; i++) {        if (!(i % 2))            evenArr.push_back(arr[i]);        else            oddArr.push_back(arr[i]);    }     // sort evenArr[] in ascending order    // sort oddArr[] in descending order    sort(evenArr.begin(), evenArr.end());    sort(oddArr.begin(), oddArr.end(), greater<int>());     int i = 0;    for (int j = 0; j < evenArr.size(); j++)        arr[i++] = evenArr[j];    for (int j = 0; j < oddArr.size(); j++)        arr[i++] = oddArr[j];} // Driver Programint main(){    int arr[] = { 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };    int n = sizeof(arr) / sizeof(arr[0]);    bitonicGenerator(arr, n);    for (int i = 0; i < n; i++)        cout << arr[i] << " ";    return 0;}
// Java Program to separately sort// even-placed and odd placed numbers// and place them together in sorted// array.import java.util.*; class GFG {     static void bitonicGenerator(int arr[], int n)    {        // create evenArr[] and oddArr[]        Vector<Integer> evenArr = new Vector<Integer>();        Vector<Integer> oddArr = new Vector<Integer>();         // Put elements in oddArr[] and evenArr[] as        // per their position        for (int i = 0; i < n; i++) {            if (i % 2 != 1) {                evenArr.add(arr[i]);            }            else {                oddArr.add(arr[i]);            }        }         // sort evenArr[] in ascending order        // sort oddArr[] in descending order        Collections.sort(evenArr);        Collections.sort(oddArr, Collections.reverseOrder());         int i = 0;        for (int j = 0; j < evenArr.size(); j++) {            arr[i++] = evenArr.get(j);        }        for (int j = 0; j < oddArr.size(); j++) {            arr[i++] = oddArr.get(j);        }    }     // Driver code    public static void main(String[] args)    {        int arr[] = { 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };        int n = arr.length;        bitonicGenerator(arr, n);        for (int i = 0; i < n; i++) {            System.out.print(arr[i] + " ");        }    }} /* This code contributed by PrinciRaj1992 */
# Python3 program to separately sort# even-placed and odd placed numbers# and place them together in sorted array.def bitonicGenerator(arr, n):         # create evenArr[] and oddArr[]    evenArr = []    oddArr = []     # Put elements in oddArr[] and evenArr[]    # as per their position    for i in range(n):        if ((i % 2) == 0):            evenArr.append(arr[i])        else:            oddArr.append(arr[i])     # sort evenArr[] in ascending order    # sort oddArr[] in descending order    evenArr = sorted(evenArr)    oddArr = sorted(oddArr)    oddArr = oddArr[::-1]     i = 0    for j in range(len(evenArr)):        arr[i] = evenArr[j]        i += 1    for j in range(len(oddArr)):        arr[i] = oddArr[j]        i += 1 # Driver Codearr = [1, 5, 8, 9, 6, 7, 3, 4, 2, 0]n = len(arr)bitonicGenerator(arr, n)for i in arr:    print(i, end = " ") # This code is contributed by Mohit Kumar
// C# Program to separately sort// even-placed and odd placed numbers// and place them together in sorted// array.using System;using System.Collections.Generic; class GFG{     static void bitonicGenerator(int []arr, int n)    {        // create evenArr[] and oddArr[]        List<int> evenArr = new List<int>();        List<int> oddArr = new List<int>();        int i = 0;                 // Put elements in oddArr[] and evenArr[] as        // per their position        for (i = 0; i < n; i++)        {            if (i % 2 != 1)            {                evenArr.Add(arr[i]);            }            else            {                oddArr.Add(arr[i]);            }        }         // sort evenArr[] in ascending order        // sort oddArr[] in descending order        evenArr.Sort();        oddArr.Sort();        oddArr.Reverse();         i = 0;        for (int j = 0; j < evenArr.Count; j++)        {            arr[i++] = evenArr[j];        }        for (int j = 0; j < oddArr.Count; j++)        {            arr[i++] = oddArr[j];        }    }     // Driver code    public static void Main(String[] args)    {        int []arr = { 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };        int n = arr.Length;        bitonicGenerator(arr, n);        for (int i = 0; i < n; i++)        {            Console.Write(arr[i] + " ");        }    }} // This code contributed by Rajput-Ji
<script>// Javascript Program to separately sort// even-placed and odd placed numbers// and place them together in sorted// array.         function bitonicGenerator(arr,n)    {        // create evenArr[] and oddArr[]        let evenArr = [];        let oddArr = [];           // Put elements in oddArr[] and evenArr[] as        // per their position        for (let i = 0; i < n; i++) {            if (i % 2 != 1) {                evenArr.push(arr[i]);            }            else {                oddArr.push(arr[i]);            }        }           // sort evenArr[] in ascending order        // sort oddArr[] in descending order        evenArr.sort(function(a,b){return a-b;});        oddArr.sort(function(a,b){return b-a;});           let i = 0;        for (let j = 0; j < evenArr.length; j++) {            arr[i++] = evenArr[j];        }        for (let j = 0; j < oddArr.length; j++) {            arr[i++] = oddArr[j];        }    }          // Driver code    let arr=[1, 5, 8, 9, 6, 7, 3, 4, 2, 0 ];    let  n = arr.length;    bitonicGenerator(arr, n);    for (let i = 0; i < n; i++) {        document.write(arr[i] + " ");    }         // This code is contributed by unknown2108</script>
1 2 3 6 8 9 7 5 4 0 
Time Complexity : O(n Log n) Space Complexity : O(n)
The above problem can also be solved without the use of Auxiliary space. The idea is to swap the first half odd index positions with the second half even index positions and then sort the first half array in increasing order and the second half array in decreasing order. Thanks to SWARUPANANDA DHUA for suggesting this.
Implementation:
C++
Java
Python3
C#
Javascript
// Program to sort even-placed elements in increasing and// odd-placed in decreasing order with constant space complexity #include <bits/stdc++.h>using namespace std; void bitonicGenerator(int arr[], int n){    // first odd index    int i = 1;     // last index    int j = n - 1;     // if last index is odd    if (j % 2 != 0)        // decrement j to even index        j--;     // swapping till half of array    while (i < j) {        swap(arr[i], arr[j]);        i += 2;        j -= 2;    }     // Sort first half in increasing    sort(arr, arr + (n + 1) / 2);     // Sort second half in decreasing    sort(arr + (n + 1) / 2, arr + n, greater<int>());} // Driver Programint main(){    int arr[] = { 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };    int n = sizeof(arr) / sizeof(arr[0]);    bitonicGenerator(arr, n);    for (int i = 0; i < n; i++)        cout << arr[i] << " ";    return 0;}// This code is contributed by SWARUPANANDA DHUA
// Program to sort even-placed elements in increasing and// odd-placed in decreasing order with constant space complexityimport java.util.Arrays;class GFG {     static void bitonicGenerator(int arr[], int n)    {        // first odd index        int i = 1;         // last index        int j = n - 1;         // if last index is odd        if (j % 2 != 0)            // decrement j to even index            j--;         // swapping till half of array        while (i < j) {            arr = swap(arr, i, j);            i += 2;            j -= 2;        }         // Sort first half in increasing        Arrays.sort(arr, 0, (n + 1) / 2);         // Sort second half in decreasing        Arrays.sort(arr, (n + 1) / 2, n);        int low = (n + 1) / 2, high = n - 1;        // Reverse the second half        while (low < high) {            Integer temp = arr[low];            arr[low] = arr[high];            arr[high] = temp;            low++;            high--;        }    }    static int[] swap(int[] arr, int i, int j)    {        int temp = arr[i];        arr[i] = arr[j];        arr[j] = temp;        return arr;    }    // Driver Program    public static void main(String[] args)    {        int arr[] = { 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };        int n = arr.length;        bitonicGenerator(arr, n);        for (int i = 0; i < n; i++)            System.out.print(arr[i] + " ");    }}// This code has been contributed by 29AjayKumar
# Python3 Program to sort even-placed elements in increasing and# odd-placed in decreasing order with constant space complexitydef bitonicGenerator(arr, n):     # first odd index    i = 1     # last index    j = n - 1         # if last index is odd    if (j % 2 != 0):                 # decrement j to even index        j = j - 1             # swapping till half of array    while (i < j) :        arr[j], arr[i] = arr[i], arr[j]        i = i + 2        j = j - 2             arr_f = []    arr_s = []         for i in range(int((n + 1) / 2)) :        arr_f.append(arr[i])         i = int((n + 1) / 2)    while( i < n ) :        arr_s.append(arr[i])        i = i + 1         # Sort first half in increasing    arr_f.sort()     # Sort second half in decreasing    arr_s.sort(reverse = True)         for i in arr_s:        arr_f.append(i)         return arr_f # Driver Programarr = [ 1, 5, 8, 9, 6, 7, 3, 4, 2, 0]n = len(arr)arr = bitonicGenerator(arr, n)print(arr) # This code is contributed by Arnab Kundu
// Program to sort even-placed elements in// increasing and odd-placed in decreasing order// with constant space complexityusing System;     class GFG{    static void bitonicGenerator(int []arr, int n)    {        // first odd index        int i = 1;         // last index        int j = n - 1;         // if last index is odd        if (j % 2 != 0)                     // decrement j to even index            j--;         // swapping till half of array        while (i < j)        {            arr = swap(arr, i, j);            i += 2;            j -= 2;        }         // Sort first half in increasing        Array.Sort(arr, 0, (n + 1) / 2);         // Sort second half in decreasing        Array.Sort(arr, (n + 1) / 2,                   n - ((n + 1) / 2));        int low = (n + 1) / 2, high = n - 1;                 // Reverse the second half        while (low < high)        {            int temp = arr[low];            arr[low] = arr[high];            arr[high] = temp;            low++;            high--;        }    }         static int[] swap(int[] arr, int i, int j)    {        int temp = arr[i];        arr[i] = arr[j];        arr[j] = temp;        return arr;    }         // Driver Code    public static void Main(String[] args)    {        int []arr = { 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };        int n = arr.Length;        bitonicGenerator(arr, n);        for (int i = 0; i < n; i++)            Console.Write(arr[i] + " ");    }} // This code is contributed by PrinciRaj1992
<script>// Program to sort even-placed elements in increasing and// odd-placed in decreasing order with constant space complexityfunction bitonicGenerator(arr, n){     // first odd index        let i = 1;          // last index        let j = n - 1;          // if last index is odd        if (j % 2 != 0)            // decrement j to even index            j--;          // swapping till half of array        while (i < j) {            arr = swap(arr, i, j);            i += 2;            j -= 2;        }                 // Sort first half in increasing        // Sort second half in decreasing        let temp1 = arr.slice(0,Math.floor((n+1)/2)).sort(function(a,b){return a-b;});        let temp2 = arr.slice(Math.floor((n+1)/2),n).sort(function(a,b){return b-a;});        arr = temp1.concat(temp2);                    return arr;} function swap(arr, i, j){    let temp = arr[i];        arr[i] = arr[j];        arr[j] = temp;        return arr;} // Driver Programlet arr = [1, 5, 8, 9, 6, 7, 3, 4, 2, 0 ];let n = arr.length;arr = bitonicGenerator(arr, n);document.write(arr.join(" ")); // This code is contributed by rag2127</script>
1 2 3 6 8 9 7 5 4 0 
Time Complexity : O(n Log n) Space Complexity : O(1)
Another approach:Another efficient approach to solve the problem in O(1) Auxiliary space is by Using negative multiplication.
The steps involved are as follows:
 Multiply all the elements at even placed index by -1.Sort the whole array. In this way, we can get all even placed index in the starting as they are negative numbers now.Now revert the sign of these elements.After this reverse the first half of the array which contains an even placed number to make it in increasing order.And then reverse the rest half of the array to make odd placed numbers in decreasing order.
 Multiply all the elements at even placed index by -1.
Sort the whole array. In this way, we can get all even placed index in the starting as they are negative numbers now.
Now revert the sign of these elements.
After this reverse the first half of the array which contains an even placed number to make it in increasing order.
And then reverse the rest half of the array to make odd placed numbers in decreasing order.
Note: This method is only applicable if all the elements in the array are non-negative.
An illustrative example of the above approach:
Let given array: arr[] = {0, 1, 2, 3, 4, 5, 6, 7}Array after multiplying by -1 to even placed elements: arr[] = {0, 1, -2, 3, -4, 5, -6, 7}Array after sorting: arr[] = {-6, -4, -2, 0, 1, 3, 5, 7}Array after reverting negative values: arr[] = {6, 4, 2, 0, 1, 3, 5, 7}After reversing the first half of array: arr[] = {0, 2, 4, 6, 1, 3, 5, 7}After reversing the second half of array: arr[] = {0, 2, 4, 6, 7, 5, 3, 1}
Below is the code for the above approach:
C++
// C++ Program to sort even-placed elements in increasing and// odd-placed in decreasing order with constant space complexity#include <bits/stdc++.h>using namespace std; void bitonicGenerator(int arr[], int n){    // Making all even placed index    // element negative    for (int i = 0; i < n; i++) {        if (i % 2==0)            arr[i]=-1*arr[i];    }         // Sorting the whole array    sort(arr,arr+n);         // Finding the middle value of    // the array    int mid=(n-1)/2;         // Reverting the changed sign    for (int i = 0; i <= mid; i++) {            arr[i]=-1*arr[i];    }         // Reverse first half of array    reverse(arr,arr+mid+1);    // Reverse second half of array    reverse(arr+mid+1,arr+n);} // Driver Programint main(){    int arr[] = { 1, 5, 8, 9, 6, 7, 3, 4, 2, 0 };    int n = sizeof(arr) / sizeof(arr[0]);    bitonicGenerator(arr, n);    for (int i = 0; i < n; i++)        cout << arr[i] << " ";    return 0;} // This code is contributed by Pushpesh Raj.
1 2 3 6 8 9 7 5 4 0 
Time Complexity: O(n*log(n)) Space Complexity: O(1)
This article is contributed by Shivam Pradhan (anuj_charm). If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks. 
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