# Sort all even numbers in ascending order and then sort all odd numbers in descending order

Given an array of integers (both odd and even), sort them in such a way that the first part of the array contains odd numbers sorted in descending order, rest portion contains even numbers sorted in ascending order.

Examples:

```Input  : arr[] = {1, 2, 3, 5, 4, 7, 10}
Output : arr[] = {7, 5, 3, 1, 2, 4, 10}

Input  : arr[] = {0, 4, 5, 3, 7, 2, 1}
Output : arr[] = {7, 5, 3, 1, 0, 2, 4}
```

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Method 1 (Using Partition)

1. Partition the input array such that all odd elements are moved to left and all even elements on right. This step takes O(n).
2. Once the array is partitioned, sort left and right parts individually. This step takes O(n Log n).

Below is implementation of above idea.

 `// C++ program sort array in even and odd manner. ` `// The odd numbers are to be sorted in descending ` `// order and the even numbers in ascending order ` `#include ` `using` `namespace` `std; ` ` `  `// To do two way sort. First sort even numbers in ` `// ascending order, then odd numbers in descending ` `// order. ` `void` `twoWaySort(``int` `arr[], ``int` `n) ` `{ ` `    ``// Current indexes from left and right ` `    ``int` `l = 0, r = n - 1; ` ` `  `    ``// Count of odd numbers ` `    ``int` `k = 0; ` ` `  `    ``while` `(l < r) { ` `        ``// Find first odd number from left side. ` `        ``while` `(arr[l] % 2 != 0) { ` `            ``l++; ` `            ``k++; ` `        ``} ` ` `  `        ``// Find first even number from right side. ` `        ``while` `(arr[r] % 2 == 0 && l < r) ` `            ``r--; ` ` `  `        ``// Swap odd number present on left and even ` `        ``// number right. ` `        ``if` `(l < r) ` `            ``swap(arr[l], arr[r]); ` `    ``} ` ` `  `    ``// Sort odd number in descending order ` `    ``sort(arr, arr + k, greater<``int``>()); ` ` `  `    ``// Sort even number in ascending order ` `    ``sort(arr + k, arr + n); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 3, 2, 7, 5, 4 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``); ` `    ``twoWaySort(arr, n); ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``cout << arr[i] << ``" "``; ` `    ``return` `0; ` `} `

 `// Java program sort array in even and odd manner. ` `// The odd numbers are to be sorted in descending ` `// order and the even numbers in ascending order ` ` `  `import` `java.util.Arrays; ` `import` `java.util.Collections; ` ` `  `public` `class` `GFG { ` `    ``// To do two way sort. First sort even numbers in ` `    ``// ascending order, then odd numbers in descending ` `    ``// order. ` `    ``static` `void` `twoWaySort(Integer arr[], ``int` `n) ` `    ``{ ` `        ``// Current indexes from left and right ` `        ``int` `l = ``0``, r = n - ``1``; ` ` `  `        ``// Count of odd numbers ` `        ``int` `k = ``0``; ` ` `  `        ``while` `(l < r) { ` `            ``// Find first odd number from left side. ` `            ``while` `(arr[l] % ``2` `!= ``0``) { ` `                ``l++; ` `                ``k++; ` `            ``} ` ` `  `            ``// Find first even number from right side. ` `            ``while` `(arr[r] % ``2` `== ``0` `&& l < r) ` `                ``r--; ` ` `  `            ``// Swap odd number present on left and even ` `            ``// number right. ` `            ``if` `(l < r) { ` `                ``// swap arr[l] arr[r] ` `                ``int` `temp = arr[l]; ` `                ``arr[l] = arr[r]; ` `                ``arr[r] = temp; ` `            ``} ` `        ``} ` ` `  `        ``// Sort odd number in descending order ` `        ``Arrays.sort(arr, ``0``, k, Collections.reverseOrder()); ` ` `  `        ``// Sort even number in ascending order ` `        ``Arrays.sort(arr, k, n); ` `    ``} ` ` `  `    ``// Driver Method ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``Integer arr[] = { ``1``, ``3``, ``2``, ``7``, ``5``, ``4` `}; ` ` `  `        ``twoWaySort(arr, arr.length); ` ` `  `        ``System.out.println(Arrays.toString(arr)); ` `    ``} ` `} `

 `# Python program to sort array  ` `# in even and odd manner  ` `# The odd numbers are to be  ` `# sorted in descending order  ` `# and the even numbers in  ` `# ascending order ` ` `  `# To do two way sort. First  ` `# sort even numbers in ascending ` `# order, then odd numbers in  ` `# descending order. ` `def` `two_way_sort(arr, arr_len): ` `     `  `    ``# Current indexes l->left ` `    ``# and r->right ` `    ``l, r ``=` `0``, arr_len ``-` `1` `     `  `    ``# Count of number of  ` `    ``# odd numbers, used in ` `    ``# slicing the array later. ` `    ``k ``=` `0` `     `  `    ``# Run till left(l) < right(r) ` `    ``while``(l < r): ` `         `  `        ``# While left(l) is odd, if yes ` `        ``# increment the left(l) plus  ` `        ``# odd count(k) if not break the ` `        ``# while for even number found  ` `        ``# here to be swaped ` `        ``while``(arr[l] ``%` `2` `!``=` `0``): ` `            ``l ``+``=` `1` `            ``k ``+``=` `1` `             `  `        ``# While right(r) is even,  ` `        ``# if yes decrement right(r) ` `        ``# if not break the while for  ` `        ``# odd number found here to ` `        ``# be swaped      ` `        ``while``(arr[r] ``%` `2` `=``=` `0` `and` `l < r): ` `            ``r ``-``=` `1` `             `  `        ``# Swap the left(l) and right(r),  ` `        ``# which is even and odd numbers  ` `        ``# encountered in above loops ` `        ``if``(l < r): ` `            ``arr[l], arr[r] ``=` `arr[r], arr[l] ` `             `  `    ``# Slice the number on the ` `    ``# basis of odd count(k) ` `    ``odd ``=` `arr[:k] ` `    ``even ``=` `arr[k:] ` `     `  `    ``# Sort the odd and  ` `    ``# even array accordingly ` `    ``odd.sort(reverse ``=` `True``) ` `    ``even.sort() ` `     `  `    ``# Extend the odd array with  ` `    ``# even values and return it. ` `    ``odd.extend(even) ` `     `  `    ``return` `odd ` `     `  `# Driver code ` `arr_len ``=` `6` `arr ``=` `[``1``, ``3``, ``2``, ``7``, ``5``, ``4``] ` `result ``=` `two_way_sort(arr, arr_len) ` `for` `i ``in` `result: ` `    ``print``(``str``(i) ``+` `" "``), ` ` `  `# This code is contributed  ` `# by JaySiyaRam `

 `// C# program sort array in even and odd manner. ` `// The odd numbers are to be sorted in descending ` `// order and the even numbers in ascending order ` `using` `System; ` `using` `System.Linq; ` ` `  `class` `GFG { ` `    ``// To do two way sort. First sort even numbers in ` `    ``// ascending order, then odd numbers in descending ` `    ``// order. ` `    ``static` `void` `twoWaySort(``int``[] arr, ``int` `n) ` `    ``{ ` `        ``// Current indexes from left and right ` `        ``int` `l = 0, r = n - 1; ` ` `  `        ``// Count of odd numbers ` `        ``int` `k = 0; ` ` `  `        ``while` `(l < r) { ` `            ``// Find first odd number from left side. ` `            ``while` `(arr[l] % 2 != 0) { ` `                ``l++; ` `                ``k++; ` `            ``} ` ` `  `            ``// Find first even number from right side. ` `            ``while` `(arr[r] % 2 == 0 && l < r) ` `                ``r--; ` ` `  `            ``// Swap odd number present on left and even ` `            ``// number right. ` `            ``if` `(l < r) { ` `                ``// swap arr[l] arr[r] ` `                ``int` `temp = arr[l]; ` `                ``arr[l] = arr[r]; ` `                ``arr[r] = temp; ` `            ``} ` `        ``} ` ` `  `        ``// Sort odd number in descending order ` `        ``Array.Sort(arr, 0, k); ` `        ``Array.Reverse(arr, 0, k); ` ` `  `        ``// Sort even number in ascending order ` `        ``Array.Sort(arr, k, n - k); ` `    ``} ` ` `  `    ``// Driver Method ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``int``[] arr = { 1, 3, 2, 7, 5, 4 }; ` ` `  `        ``twoWaySort(arr, arr.Length); ` ` `  `        ``Console.WriteLine(String.Join(``" "``, arr)); ` `    ``} ` `} ` ` `  `// This code has been contributed by 29AjayKumar `

Output:
```7 5 3 1 2 4
```

Time complexity: O(n log n)
space complexity: O(1)

Method 2 (Using negative multiplication) :

1. Make all odd numbers negative.
2. Sort all numbers.
3. Revert the changes made in step 1 to get original elements back.
 `// C++ program sort array in even and odd manner. ` `// The odd numbers are to be sorted in descending ` `// order and the even numbers in ascending order ` `#include ` `using` `namespace` `std; ` ` `  `// To do two way sort. First sort even numbers in ` `// ascending order, then odd numbers in descending ` `// order. ` `void` `twoWaySort(``int` `arr[], ``int` `n) ` `{ ` `    ``// Make all odd numbers negative ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``if` `(arr[i] & 1) ``// Check for odd ` `            ``arr[i] *= -1; ` ` `  `    ``// Sort all numbers ` `    ``sort(arr, arr + n); ` ` `  `    ``// Retaining original array ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``if` `(arr[i] & 1) ` `            ``arr[i] *= -1; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 3, 2, 7, 5, 4 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``); ` `    ``twoWaySort(arr, n); ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``cout << arr[i] << ``" "``; ` `    ``return` `0; ` `} `

 `// Java program sort array in even and odd manner. ` `// The odd numbers are to be sorted in descending ` `// order and the even numbers in ascending order ` ` `  `import` `java.util.Arrays; ` ` `  `public` `class` `GFG { ` `    ``// To do two way sort. First sort even numbers in ` `    ``// ascending order, then odd numbers in descending ` `    ``// order. ` `    ``static` `void` `twoWaySort(``int` `arr[], ``int` `n) ` `    ``{ ` `        ``// Make all odd numbers negative ` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `            ``if` `((arr[i] & ``1``) != ``0``) ``// Check for odd ` `                ``arr[i] *= -``1``; ` ` `  `        ``// Sort all numbers ` `        ``Arrays.sort(arr); ` ` `  `        ``// Retaining original array ` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `            ``if` `((arr[i] & ``1``) != ``0``) ` `                ``arr[i] *= -``1``; ` `    ``} ` ` `  `    ``// Driver Method ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[] = { ``1``, ``3``, ``2``, ``7``, ``5``, ``4` `}; ` ` `  `        ``twoWaySort(arr, arr.length); ` ` `  `        ``System.out.println(Arrays.toString(arr)); ` `    ``} ` `} `

 `# Python 3 program to sort array in  ` `# even and odd manner. The odd ` `# numkbers are to be sorted in  ` `# descending order and the even  ` `# numbers in ascending order ` ` `  `# To do two way sort. First sort  ` `# even numbers in ascending order, ` `# then odd numbers in descending order. ` `def` `twoWaySort(arr, n): ` ` `  `    ``# Make all odd numbers negative ` `    ``for` `i ``in` `range``(``0``, n): ` `         `  `        ``# Check for odd ` `        ``if` `(arr[i] & ``1``):  ` `            ``arr[i] ``*``=` `-``1` ` `  `    ``# Sort all numbers ` `    ``arr.sort() ` ` `  `    ``# Retaining original array ` `    ``for` `i ``in` `range``(``0``, n): ` `        ``if` `(arr[i] & ``1``): ` `            ``arr[i] ``*``=` `-``1` ` `  `# Driver code ` `arr ``=` `[``1``, ``3``, ``2``, ``7``, ``5``, ``4``] ` `n ``=` `len``(arr) ` `twoWaySort(arr, n); ` `for` `i ``in` `range``(``0``, n): ` `    ``print``(arr[i], end ``=` `" "``) ` `     `  `# This code is contributed by Smitha Dinesh Semwal `

 `// Java program sort array in even and ` `// odd manner. The odd numbers are to ` `// be sorted in descending order and ` `// the even numbers in ascending order ` `using` `System; ` ` `  `public` `class` `GFG { ` ` `  `    ``// To do two way sort. First sort ` `    ``// even numbers in ascending order, ` `    ``// then odd numbers in descending ` `    ``// order. ` `    ``static` `void` `twoWaySort(``int``[] arr, ``int` `n) ` `    ``{ ` ` `  `        ``// Make all odd numbers negative ` `        ``for` `(``int` `i = 0; i < n; i++) ` ` `  `            ``// Check for odd ` `            ``if` `((arr[i] & 1) != 0) ` `                ``arr[i] *= -1; ` ` `  `        ``// Sort all numbers ` `        ``Array.Sort(arr); ` ` `  `        ``// Retaining original array ` `        ``for` `(``int` `i = 0; i < n; i++) ` `            ``if` `((arr[i] & 1) != 0) ` `                ``arr[i] *= -1; ` `    ``} ` ` `  `    ``// Driver Method ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int``[] arr = { 1, 3, 2, 7, 5, 4 }; ` ` `  `        ``twoWaySort(arr, arr.Length); ` ` `  `        ``for` `(``int` `i = 0; i < arr.Length; i++) ` `            ``Console.Write(arr[i] + ``" "``); ` `    ``} ` `} ` ` `  `// This code is contributed by Smitha `

 ` `

Output:
`7 5 3 1 2 4 `

Time complexity: O(n log n)
Space complexity: O(n)

This method may not work when input array contains negative numbers. However, there is a way to handle this. We count the positive odd integers in the input array then sort again. Readers may refer this for implementation.

Method 3 (Using comparator):
This problem can be easily solved by using the inbuilt sort function with a custom compare method. On comparing any two elements there will be three cases:

1. When both the elements are even: In this case, the smaller element must appear in the left of the larger element in the sorted array.
2. When both the elements are odd: The larger element must appear on left of the smaller element.
3. One is odd and the other is even: The element which is odd must appear on the left of the even element.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Utility function to print ` `// the contents of the array ` `void` `printArr(``int` `arr[], ``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``cout << arr[i] << ``" "``; ` `} ` ` `  `// To do two way sort. Make comparator function ` `// for the inbuilt sort function of c++ such that ` `// odd numbers are placed before even in descending ` `// and ascending order respectively ` `bool` `compare(``int` `a, ``int` `b) ` `{ ` `    ``// If both numbers are even, smaller number should ` `    ``// be placed at lower index ` `    ``if` `(a % 2 == 0 && b % 2 == 0) ` `        ``return` `a < b; ` ` `  `    ``// If both numbers are odd larger number ` `    ``// should be placed at lower index ` `    ``if` `(a % 2 != 0 && b % 2 != 0) ` `        ``return` `b < a; ` ` `  `    ``// If a is odd and b is even, a should be placed before b ` `    ``if` `(a % 2 != 0) ` `        ``return` `true``; ` ` `  `    ``// If b is odd and a is even, b should be placed before a ` `    ``return` `false``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 3, 2, 7, 5, 4 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``); ` ` `  `    ``// Sort the array ` `    ``sort(arr, arr + n, compare); ` ` `  `    ``// Print the sorted array ` `    ``printArr(arr, n); ` ` `  `    ``return` `0; ` `} ` ` `  `// This code is contributed by Nikhil Yadav `

Thanks to Amandeep Singh for suggesting this solution.

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