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.
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:
Time Complexity: O(N * M)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Largest odd divisor Game to check which player wins
- Game Theory (Normal - form game) | Set 1 (Introduction)
- Design a Chess Game
- Predict the winner in Coin Game
- Minimum possible final health of the last monster in a game
- Expectimax Algorithm in Game Theory
- Implementation of Tic-Tac-Toe for 2 person game (User vs. User)
- Count the number of walks of length N where cost of each walk is equal to a given number
- Count the number of pop operations on stack to get each element of the array
- Number of comparisons in each direction for m queries in linear search
- Find number of segments covering each point in an given array
- Number of steps to sort the array by changing order of three elements in each step
- Maximum number of nodes which can be reached from each node in a graph.
- Check if frequency of characters are in Recaman Series
- Find the kth element in the series generated by the given N ranges
- Find geometric sum of the series using recursion
- Generate a string of size N whose each substring of size M has exactly K distinct characters
- Pair with minimum absolute difference after solving each query
- Minimize the sum of the squares of the sum of elements of each group the array is divided into
- Pairs of strings which on concatenating contains each character of "string"
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.