Program to count number of unhappy friends in Python

In this problem, we need to count unhappy friends based on their preferences and pairings. A friend is unhappy if they are paired with someone but prefer another person who also prefers them back over their current partners.

Problem Definition

Given preferences and pairs, a friend x is unhappy if:

• x is paired with y
• There exists a friend u (paired with v) such that:
• x prefers u over y, and
• u prefers x over v

Algorithm Steps

We solve this by building a preference graph:

• Create a graph where graph[person][preferred] = 1 means person prefers 'preferred' over their current partner
• For each pair, record all friends preferred over the current partner
• Check if any preferred friend also prefers the person back

Example

Let's understand with the given example where preferences = [[1, 2, 3], [3, 2, 0], [3, 1, 0], [1, 2, 0]] and pairs = [[0, 1], [2, 3]]:

from collections import defaultdict

def solve(preferences, pairs):
    graph = defaultdict(dict)
    
    # Build preference graph
    for start, end in pairs:
        # For start person, record all friends preferred over end
        for pref in preferences[start]:
            if pref == end:
                break
            graph[start][pref] = 1
        
        # For end person, record all friends preferred over start
        for pref in preferences[end]:
            if pref == start:
                break
            graph[end][pref] = 1

    unhappy = 0
    
    # Count unhappy friends
    for start, end in pairs:
        # Check if start is unhappy
        for pref in graph[start]:
            if graph[pref].get(start, None):
                unhappy += 1
                break
        
        # Check if end is unhappy
        for pref in graph[end]:
            if graph[pref].get(end, None):
                unhappy += 1
                break
    
    return unhappy

preferences = [[1, 2, 3], [3, 2, 0], [3, 1, 0], [1, 2, 0]]
pairs = [[0, 1], [2, 3]]
print(solve(preferences, pairs))

2

How It Works

In the example:

• Person 0 is paired with 1 but prefers 3 over 1, and person 3 prefers 0 over their partner 2 ? unhappy
• Person 1 is paired with 0 and prefers 3 over 0, but person 3 doesn't prefer 1 over 2 ? happy
• Person 2 is paired with 3 and has no one preferred over 3 ? happy
• Person 3 is paired with 2 but prefers 1 over 2, and person 1 prefers 3 over their partner 0 ? unhappy

Conclusion

This solution uses a preference graph to efficiently identify mutual preferences between friends. The algorithm has O(n²) time complexity where n is the number of friends.