Couples Holding Hands - Practice Coding Problems

Couples Holding Hands - Problem

The Wedding Reception Seating Challenge

Imagine you're organizing a wedding reception where n couples want to sit together and hold hands during the ceremony. Unfortunately, the guests have already taken their seats randomly in a row of 2n chairs, and now you need to help them rearrange so every couple can sit side by side!

You're given an integer array row where row[i] represents the ID of the person sitting in the i-th seat. The couples are numbered systematically: couple 1 consists of persons (0, 1), couple 2 consists of persons (2, 3), and so on, with the last couple being (2n-2, 2n-1).

Your goal is to find the minimum number of swaps needed so that every couple sits together. In each swap, you can choose any two people and have them exchange seats.

Example: If we have [0, 2, 1, 3], person 0 needs to sit next to person 1, and person 2 needs to sit next to person 3. We can swap positions 1 and 2 to get [0, 1, 2, 3] with just 1 swap!

Input & Output

example_1.py — Simple Case

$ Input: [0, 2, 1, 3]

› Output: 1

💡 Note: We need to swap person 2 and person 1. Person 0 wants to sit with person 1 (couple 0), and person 2 wants to sit with person 3 (couple 1). After swapping positions 1 and 2, we get [0,1,2,3] where both couples are together.

example_2.py — No Swaps Needed

$ Input: [3, 2, 0, 1]

› Output: 0

💡 Note: Couples are already sitting together: (3,2) form couple 1 and (0,1) form couple 0. No swaps needed since 3//2 = 2//2 = 1 and 0//2 = 1//2 = 0.

example_3.py — Complex Cycle

$ Input: [1, 4, 2, 5, 3, 0]

› Output: 2

💡 Note: Multiple couples are misplaced. Person 1 needs person 0, person 4 needs person 5, etc. This creates a cycle that requires 2 swaps to resolve: swap to get couples (0,1), (2,3), (4,5) sitting together.

Visualization

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Understanding the Visualization

Survey the Room

Walk around and note where each person is sitting, creating a mental map of positions

Check Each Table

Go to each pair of seats and see if the people sitting there are actually a couple

Find the Partner

If they're not a couple, locate where the correct partner is sitting using your position map

Make the Swap

Politely ask the misplaced person to swap seats with the correct partner

Update Your Map

Update your mental map of where everyone is now sitting after the swap

Key Takeaway

🎯 Key Insight: The optimal solution treats couple arrangement as a position-swapping problem. By maintaining a position map and using the XOR trick to find partners, we can solve this in O(n) time with minimal swaps!

Time & Space Complexity

Time Complexity

⏱️

O(n!)

We may need to try all possible arrangements in worst case, leading to factorial complexity

⚠ Quadratic Growth

Space Complexity

O(n)

Recursion stack depth can go up to n levels

⚡ Linearithmic Space

Constraints

2n == row.length
2 <= n <= 30
n is even
0 <= row[i] < 2n
All the values of row are unique
The couples are numbered consecutively starting from 0

Asked in

G Google 45 f Meta 32 a Amazon 28 ⊞ Microsoft 22

The optimal solution uses a greedy approach with position tracking. For each pair of seats, if the people aren't a couple, we find the correct partner using a position map and swap them directly into place. The key insight is that each person's partner can be found using the XOR operation: partner = person ^ 1. This works because couples are numbered consecutively (0,1), (2,3), (4,5)... Time complexity is O(n) with O(n) space for the position map.

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force (Try All Combinations)	O(n!)	O(n)	Try all possible sequences of swaps until couples are paired
Greedy Approach with Position Tracking	O(n)	O(n)	Use position map to directly find and swap partners efficiently

Brute Force (Try All Combinations) — Algorithm Steps

Check if all couples are already sitting together
For each misplaced couple, try swapping the partner with every other person
Recursively solve the remaining arrangement
Return the minimum swaps found across all possibilities

Visualization

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Step-by-Step Walkthrough

Find Misplaced Couple

Identify first couple that isn't sitting together

Try All Swaps

For the misplaced person, try swapping with everyone else

Recursive Exploration

Recursively solve the remaining arrangement after each swap

Backtrack

Undo the swap and try the next possibility

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
#include <string.h>

int isCouple(int a, int b) {
    return a / 2 == b / 2;
}

void swap(int* arr, int i, int j) {
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}

int solve(int* arr, int len, int swaps) {
    for (int i = 0; i < len; i += 2) {
        if (!isCouple(arr[i], arr[i + 1])) {
            int minSwaps = INT_MAX;
            for (int j = i + 2; j < len; j++) {
                swap(arr, i + 1, j);
                int result = solve(arr, len, swaps + 1);
                if (result < minSwaps) {
                    minSwaps = result;
                }
                swap(arr, i + 1, j);
            }
            return minSwaps;
        }
    }
    return swaps;
}

int minSwapsCouples(int* row, int len) {
    int* temp = malloc(len * sizeof(int));
    memcpy(temp, row, len * sizeof(int));
    int result = solve(temp, len, 0);
    free(temp);
    return result;
}

int main() {
    int row[20];
    int len = 0;
    char input[1000];
    fgets(input, sizeof(input), stdin);
    
    char* token = strtok(input, "[],\n");
    while (token != NULL) {
        row[len++] = atoi(token);
        token = strtok(NULL, "[],\n");
    }
    
    printf("%d\n", minSwapsCouples(row, len));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n!)

We may need to try all possible arrangements in worst case, leading to factorial complexity

⚠ Quadratic Growth

Space Complexity

O(n)

Recursion stack depth can go up to n levels

⚡ Linearithmic Space

Constraints

2n == row.length
2 <= n <= 30
n is even
0 <= row[i] < 2n
All the values of row are unique
The couples are numbered consecutively starting from 0

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Ln 1, Col 1

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Input & Output

Visualization

Time & Space Complexity

Related Problems

Constraints

Common Approaches

Brute Force (Try All Combinations) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Constraints

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