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Minimize count of swaps of adjacent elements required to make an array increasing
  • Last Updated : 16 Apr, 2021

Given an array A[] consisting of permutation of first N natural numbers, the task is to find the minimum number of operations required to modify A[] into an increasing array if an array element A[i] can be swapped with its next adjacent element A[i+1] at most twice. If it is not possible to modify the array into an increasing array, print -1.

Examples:

Input: A[] = [2,1,5,3,4]
Output: 3
Explanation: 
Operation 1: Swap (Arr[2], Arr[3]). Therefore, A[] modifies to {2, 1, 3, 5, 4}.
Operation 2: Swap(arr[3], arr[4]). Therefore, A[] modifies to {2, 1, 3, 4, 5}.
Operation 3: Swap (arr[0], arr[1]). Therefore, A[] modifies to {1, 2, 3, 4, 5}.
Therefore, the sequence of operations are: {2, 1, 5, 3, 4} → {2, 1, 3, 5, 4} → {2, 1, 3, 4, 5} → {1, 2, 3, 4, 5}

Input: A[] = [2,5,1,3,4]
Output: -1

Approach: The idea is based on the observation that if an element A[i] is present at index i, then it must have moved from either index i – 1 or i – 2. This is because, to shift to A[i] from indices left of i – 2, the number of swaps would exceed 2. Therefore, traverse the array in reverse, and check if A[i] is present at its correct position or not. If found not to be, check A[i – 1] and A[i – 2] and update the count of operations accordingly. Follow the steps to solve the problem:



  • Traverse the array, A[] over the indices [N – 1, 0] using a variable, say i.
    • Store the correct index value in a variable, say X as i + 1.
    • If the A[i] is currently not at its correct position, i.e. A[i] is not equal to X, then perform the following steps:
      • If the value of A[i – 1] is equal to X, increment count by 1 and swap A[i] and A[i-1].
      • Otherwise, if the value of A[i – 2] is equal to X, increment count by 2 and swap the pairs A[i – 2] and A[i – 1], then A[i – 2] and A[i].
      • Otherwise, update the value of count to -1 and break out of the loop, since A[i] can not be swapped more than twice.
  • After complete traversal of the array, print the value of count as the result.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to count minimum number of
// operations required to obtain an
// increasing array from given array A[]
void minimumOperations(int A[], int n)
{
    // Store the required result
    int cnt = 0;
 
    // Traverse the array A[]
    for (int i = n - 1; i >= 0; i--) {
 
        // If the current element is not
        // in its correct position
        if (A[i] != (i + 1)) {
 
            // Check if it is present at index i - 1
            if (((i - 1) >= 0)
                && A[i - 1] == (i + 1)) {
                cnt++;
                swap(A[i], A[i - 1]);
            }
 
            // Check if it is present at index i-2
            else if (((i - 2) >= 0)
                     && A[i - 2] == (i + 1)) {
                cnt += 2;
                A[i - 2] = A[i - 1];
                A[i - 1] = A[i];
                A[i] = i + 1;
            }
 
            // Otherwise, print -1 (Since A[i]
            // can not be swapped more than twice)
            else {
                cout << -1;
                return;
            }
        }
    }
 
    // Print the result
    cout << cnt;
}
 
// Driver Code
int main()
{
    // Given array
    int A[] = {7, 3, 2, 1, 4 };
 
    // Store the size of the array
    int n = sizeof(A) / sizeof(A[0]);
 
    minimumOperations(A, n);
 
    return 0;
}

Java




// Java program for the above approach
import java.util.*;
import java.lang.*;
 
class GFG{
     
// Function to count minimum number of
// operations required to obtain an
// increasing array from given array A[]
static void minimumOperations(int A[], int n)
{
     
    // Store the required result
    int cnt = 0;
 
    // Traverse the array A[]
    for(int i = n - 1; i >= 0; i--)
    {
         
        // If the current element is not
        // in its correct position
        if (A[i] != (i + 1))
        {
             
            // Check if it is present at index i - 1
            if (((i - 1) >= 0) &&
                A[i - 1] == (i + 1))
            {
                cnt++;
                int t = A[i];
                A[i] = A[i-1];
                A[i-1] = t;
            }
 
            // Check if it is present at index i-2
            else if (((i - 2) >= 0) &&
                     A[i - 2] == (i + 1))
            {
                cnt += 2;
                A[i - 2] = A[i - 1];
                A[i - 1] = A[i];
                A[i] = i + 1;
            }
 
            // Otherwise, print -1 (Since A[i]
            // can not be swapped more than twice)
            else
            {
                System.out.println(-1);
                return;
            }
        }
    }
 
    // Print the result
    System.out.println(cnt);
}
 
// Driver code
public static void main(String[] args)
{
     
    // Given array
    int A[] = { 7, 3, 2, 1, 4 };
 
    // Store the size of the array
    int n = A.length;
 
    minimumOperations(A, n);
}
}
 
// This code is contributed by souravghosh0416

Python3




# Python 3 program for the above approach
 
# Function to count minimum number of
# operations required to obtain an
# increasing array from given array A[]
def minimumOperations(A, n):
 
    # Store the required result
    cnt = 0
 
    # Traverse the array A[]
    for i in range(n - 1, -1, -1):
 
        # If the current element is not
        # in its correct position
        if (A[i] != (i + 1)):
 
            # Check if it is present at index i - 1
            if (((i - 1) >= 0)
                    and A[i - 1] == (i + 1)):
                cnt += 1
                A[i], A[i - 1] = A[i - 1], A[i]
 
            # Check if it is present at index i-2
            elif (((i - 2) >= 0)
                  and A[i - 2] == (i + 1)):
                cnt += 2
                A[i - 2] = A[i - 1]
                A[i - 1] = A[i]
                A[i] = i + 1
 
            # Otherwise, print -1 (Since A[i]
            # can not be swapped more than twice)
            else:
                print(-1)
                return
 
    # Print the result
    print(cnt)
 
# Driver Code
if __name__ == "__main__":
 
    # Given array
    A = [7, 3, 2, 1, 4]
 
    # Store the size of the array
    n = len(A)
 
    minimumOperations(A, n)
 
    # Thi code is contributed by ukasp.

Javascript




<script>
 
// Javascript program for the above approach   
 
// Function to count minimum number of
    // operations required to obtain an
    // increasing array from given array A
    function minimumOperations(A , n) {
 
        // Store the required result
        var cnt = 0;
 
        // Traverse the array A
        for (i = n - 1; i >= 0; i--) {
 
            // If the current element is not
            // in its correct position
            if (A[i] != (i + 1)) {
 
                // Check if it is present at index i - 1
                if (((i - 1) >= 0) && A[i - 1] == (i + 1)) {
                    cnt++;
                    var t = A[i];
                    A[i] = A[i - 1];
                    A[i - 1] = t;
                }
 
                // Check if it is present at index i-2
                else if (((i - 2) >= 0) && A[i - 2] == (i + 1)) {
                    cnt += 2;
                    A[i - 2] = A[i - 1];
                    A[i - 1] = A[i];
                    A[i] = i + 1;
                }
 
                // Otherwise, prvar -1 (Since A[i]
                // can not be swapped more than twice)
                else {
                    document.write(-1);
                    return;
                }
            }
        }
 
        // Prvar the result
        document.write(cnt);
    }
 
    // Driver code
     
 
        // Given array
        var A = [ 7, 3, 2, 1, 4 ];
 
        // Store the size of the array
        var n = A.length;
 
        minimumOperations(A, n);
 
// This code contributed by Rajput-Ji
 
</script>
Output: 
-1

 

Time Complexity: O(N)
Auxiliary Space: O(1)

 

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