#3238

Easy

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Find the Number of Winning Players

Find how many players in a game win by picking more balls of a single color than their index position.

Problem Statement

You are given an integer n representing the number of players in a game and a 2D array pick where pick[i] = [xi, yi] represents that the player xi picked a ball of color yi. Each player can pick multiple balls, and some players might pick the same color multiple times.

A player wins the game if they pick strictly more than their index (xi) number of balls of the same color. Your task is to find how many players meet the condition to win. Return the count of players who win the game.

Examples

Example 1

Input: n = 4, pick = [[0,0],[1,0],[1,0],[2,1],[2,1],[2,0]]

Output: 2

Player 0 and player 1 win the game, while players 2 and 3 do not win.

Example 2

Input: n = 5, pick = [[1,1],[1,2],[1,3],[1,4]]

Output: 0

No player wins the game.

Example 3

Input: n = 5, pick = [[1,1],[2,4],[2,4],[2,4]]

Output: 1

Player 2 wins the game by picking 3 balls with color 4.

Constraints

2 <= n <= 10
1 <= pick.length <= 100
pick[i].length == 2
0 <= xi <= n - 1
0 <= yi <= 10

Solution Approach

Array Scanning and Hash Table

The most efficient way to solve this problem is by scanning the array pick and using a hash table to count the number of balls each player picks for each color. For each player, store a count of how many balls they picked of each color and compare it to their index to determine if they win.

Condition Checking

For each player, after counting the balls picked by color, compare each color's count against the player's index. If any color has a count greater than the player's index, that player wins. Keep track of the total number of winning players.

Efficient Lookup and Updates

Use a hash map (dictionary) where keys represent the colors of the balls and values represent the count of picked balls. This allows for efficient updates when iterating through the picks and checking if the player wins.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity is O(n * k), where n is the number of players and k is the average number of picks per player. The space complexity is O(n * m), where m is the number of unique colors picked by players, due to the space used by the hash table to store counts for each color for each player.

What Interviewers Usually Probe

Looking for the candidate's ability to efficiently implement a hash-based solution to count occurrences.
Evaluating if the candidate can handle the logic for counting and comparing player's index with ball counts.
Checking if the candidate can optimize the solution using an array scanning technique and hash map updates.

Common Pitfalls or Variants

Common pitfalls

Forgetting to properly compare the count of balls for each color to the player's index.
Incorrectly handling the mapping between players and their ball picks, leading to errors in counting.
Failing to account for players who pick multiple balls of the same color and how to store and compare these counts.

Follow-up variants

Adjust the problem to work with more than one ball color, where players must pick a combination of colors to win.
Extend the problem by allowing players to pick balls in multiple rounds and requiring a comparison of rounds.
Introduce a constraint where a player must win in multiple categories (e.g., both a minimum number of total balls and a particular color count).

FAQ

What is the primary pattern used in the "Find the Number of Winning Players" problem?

The problem follows the pattern of array scanning combined with hash lookup for efficient counting of picked balls by players.

How do I count the number of balls each player picks of a color?

You can use a hash table where the key is the color and the value is the count of balls picked by the player for that color.

How can I optimize this problem if there are many players or picks?

The problem can be optimized by using a hash map for fast lookups and updating counts efficiently during the scanning process.

What is the time complexity of the "Find the Number of Winning Players" problem?

The time complexity is O(n * k), where n is the number of players and k is the average number of picks per player.

What should I be careful about when implementing the solution?

Be careful about correctly counting the number of balls each player picks and ensuring that you compare it to their index properly.

terminal

Solution

Solution 1: Counting

We can use a 2D array $\textit{cnt}$ to record the number of balls of each color obtained by each player, and a hash table $\textit{s}$ to record the IDs of the winning players.

1

2

3

4

5

6

7

8

9

class Solution:
    def winningPlayerCount(self, n: int, pick: List[List[int]]) -> int:
        cnt = [[0] * 11 for _ in range(n)]
        s = set()
        for x, y in pick:
            cnt[x][y] += 1
            if cnt[x][y] > x:
                s.add(x)
        return len(s)

Continue Practicing

#3265 count almost equal pairs i #3267 count almost equal pairs ii #3186 maximum total damage with spell casting