CouplesHoldingHands.java

package math;

/**
 * Created by gouthamvidyapradhan on 23/06/2018.
 * N couples sit in 2N seats arranged in a row and want to hold hands. We want to know the minimum number of swaps so
 * that every couple is sitting side by side. A swap consists of choosing any two people, then they stand up and
 * switch  seats.

 The people and seats are represented by an integer from 0 to 2N-1, the couples are numbered in order, the first
 couple  being (0, 1), the second couple being (2, 3), and so on with the last couple being (2N-2, 2N-1).

 The couples' initial seating is given by row[i] being the value of the person who is initially sitting in the i-th
 seat.

 Example 1:

 Input: row = [0, 2, 1, 3]
 Output: 1
 Explanation: We only need to swap the second (row[1]) and third (row[2]) person.
 Example 2:

 Input: row = [3, 2, 0, 1]
 Output: 0
 Explanation: All couples are already seated side by side.
 Note:

 len(row) is even and in the range of [4, 60].
 row is guaranteed to be a permutation of 0...len(row)-1.

 Solution: O(N ^ 2). Find the index i of every even-number n and (n + 1)th number. If the index i of number n is even
 then swap the number (n + 1) with index i + 1, else swap the number (n + 1) with index i - 1. Count the total swaps
 and return the answer.
 */
public class CouplesHoldingHands {
    /**
     * Main method
     * @param args
     * @throws Exception
     */
    public static void main(String[] args) throws Exception{
        int[] A = {1, 3, 4, 0, 2, 5};
        System.out.println(new CouplesHoldingHands().minSwapsCouples(A));
    }

    public int minSwapsCouples(int[] row) {
        int N = row.length;
        int count = 0;
        for(int i = 0; i < N; i +=2){
            int pos = find(row, i);
            if((pos % 2) == 0){
                if(row[pos + 1] != i + 1){
                    int nexNumPos = find(row, i + 1);
                    swap(row, pos + 1, nexNumPos);
                    count ++;
                }
            } else{
                if(row[pos - 1] != i + 1){
                    int nexNumPos = find(row, i + 1);
                    swap(row, pos - 1, nexNumPos);
                    count ++;
                }
            }
        }
        return count;
    }

    private int find(int[] A, int n){
        for(int i = 0; i < A.length; i ++){
            if(A[i] == n){
                return i;
            }
        }
        return -1;
    }

    private void swap(int[] A, int i, int j){
        int temp = A[i];
        A[i] = A[j];
        A[j] = temp;
    }
}