Number of wins for each player in a series of Rock-Paper-Scissor game

Two players are playing a series of games of Rock–paper–scissors. There are a total of K games played. Player 1 has a sequence of moves denoted by string A and similarly player 2 has string B. If any player reaches the end of their string, they move back to the start of the string. The task is to count the number of games won by each of the player when exactly K games are being played.

Examples:

Input: k = 4, a = “SR”, b = “R”
Output: 0 2
Game 1: Player1 = S, Player2 = R, Winner = Player2
Game 2: Player1 = R, Player2 = R, Winner = Draw
Game 3: Player1 = S, Player2 = R, Winner = Player2
Game 4: Player1 = R, Player2 = R, Winner = Draw

Input: k = 3, a = “S”, b = “SSS”
Output: 0 0
All the games are draws.



Approach: Let length of string a be n and length of string b be m. The observation here is that the games would repeat after n * m moves. So, we can simulate the process for n * m games and then count the number of times it gets repeated. For the remaining games, we can again simulate the process since it would be now smaller than n * m. For example, in the first example above, n = 2 and m = 1. So, the games will repeat after every n * m = 2 * 1 = 2 moves i.e. (Player2, Draw), (Player2, Draw), ….., (Player2, Draw).

Below is the implementation of the above approach:

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function that returns 1 if first player wins,
// 0 in case of a draw and -1 if second player wins
int compare(char first, char second)
{
    // If both players have the same move
    // then it's a draw
    if (first == second)
        return 0;
  
    if (first == 'R') {
        if (second == 'S')
            return 1;
        else
            return -1;
    }
    if (first == 'P') {
        if (second == 'R')
            return 1;
        else
            return -1;
    }
    if (first == 'S') {
        if (second == 'P')
            return 1;
        else
            return -1;
    }
}
  
// Function that returns the count of games
// won by both the players
pair<int, int> countWins(int k, string a, string b)
{
    int n = a.length();
    int m = b.length();
    int i = 0, j = 0;
  
    // Total distinct games that can be played
    int moves = n * m;
    pair<int, int> wins = { 0, 0 };
    while (moves--) {
        int res = compare(a[i], b[j]);
  
        // Player 1 wins the current game
        if (res == 1)
            wins.first++;
  
        // Player 2 wins the current game
        if (res == -1)
            wins.second++;
        i = (i + 1) % n;
        j = (j + 1) % m;
    }
  
    // Number of times the above n * m games repeat
    int repeat = k / (n * m);
  
    // Update the games won
    wins.first *= repeat;
    wins.second *= repeat;
  
    // Remaining number of games after
    // removing repeated games
    int rem = k % (n * m);
    while (rem--) {
        int res = compare(a[i], b[j]);
  
        // Player 1 wins the current game
        if (res == 1)
            wins.first++;
  
        // Player 2 wins the current game
        if (res == -1)
            wins.second++;
        i = (i + 1) % n;
        j = (j + 1) % m;
    }
    return wins;
}
  
// Driver code
int main()
{
    int k = 4;
    string a = "SR", b = "R";
    auto wins = countWins(k, a, b);
    cout << wins.first << " " << wins.second;
}

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Output:

0 2

Time Complexity: O(N * M)



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