couples_holding_hands

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765. Couples Holding Hands (Hard)

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:

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

Related Topics

[Greedy] [Union Find] [Graph]

Similar Questions

1. First Missing Positive (Hard)
2. Missing Number (Easy)
3. K-Similar Strings (Hard)

Hints

Hint 1

Say there are N two-seat couches. For each couple, draw an edge from the couch of one partner to the couch of the other partner.