Program to check whether Amal can win stone game or not in Python

Python Server Side Programming Programming

Suppose there are two players Amal and Bimal, they are playing a game, and with Amal starts first. Initially, there are n different stones in a pile. On each player's turn, he makes a move consisting of removing any square number (non-zero) of stones from the pile. Also, if one player is unable to make a move, he loses the game. So if we have n, we have to check whether Amal can win the game or not.

So, if the input is like n = 21, then the output will be True because at first Amal can take 16, then Bimal takes 4, then Amal takes 1 and wins the game.

To solve this, we will follow these steps −

squares := a new list
square := 1
increase := 3
while square <= n, do
- insert square at the end of squares
- square := square + increase
- increase := increase + 2
insert square at the end of squares
dp := a blank list of size (n + 1)
dp[0] := False
for k in range 1 to n, do
- s := 0
- dp[k] := False
- while squares[s] <= k and dp[k] is empty, do
  - if dp[k - squares[s]] is empty, then
    - dp[k] := True
  - s := s + 1
return last element of dp

Example

Let us see the following implementation to get better understanding

def solve(n):
   squares = []
   square = 1
   increase = 3
   while square <= n:
      squares.append(square)
      square += increase
      increase += 2
   squares.append(square)

   dp = [None] * (n + 1)
   dp[0] = False
   for k in range(1, n + 1):
      s = 0
      dp[k] = False
      while squares[s] <= k and not dp[k]:
         if not dp[k - squares[s]]:
            dp[k] = True
         s += 1
   return dp[-1]

n = 21
print(solve(n))

Input

Output

True

Arnab Chakraborty

Updated on: 2021-10-06T08:42:04+05:30

196 Views

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