MATGAME - Matrix Game
Two players A and B play the following game.
1) First, a matrix M of size N*M is chosen, and filled with non-zero numbers.
2) Player A starts the game and the players play alternately.
3) In his turn, a player chooses any row which has at least one non zero number in it. In this row, the leftmost non zero number is chosen. Let this number be K. The player subtracts any number between 1 and K inclusive from it.
4) The game ends when all the numbers in the matrix M are 0.
5) The player who plays last wins the game.
Given N,M and the initial matrix, determine who wins the game. Assume that both players play optimally.
The first line contains the number of test cases T.
Each test case consists of 2 numbers N and M. There follow N lines each having M integers. The jth number on the ith line is the number M[i][j]. There is a blank line between consecutive test cases.
Output T lines, one for each case. Output "FIRST" if player A wins, else output "SECOND".
Sample Input :
2 1 1
T <= 1000
1 <= N,M <= 50
The initial matrix values are between 1 and 50 inclusive.
Has anyone done this without using Sprague Grundy number? I would like to know an alternative approach.
@luv_misra Second should win
Md. Najim Ahmed:
i dont know much game theory but man... i had fun solving it :v and that even in one attempt ...
: : still coding -_- :: first player will take 2 in his first move. THEN they both take one. First player wins!
: : still coding -_- ::
in second test case if each player substracts 1 in his/her turn each time...the answer will be second..?
uff!!.. my first game theory question.. nice :D
great problem :)
someone please post some more test cases
just that number..not the whole row