Candy Race Taking Square Candies - Microsoft Top Interview Questions


Problem Statement :


You are given an integer n representing the number of candies. You are playing a game against a friend and in each round a player can take some positive, square number. A player that can't make a move loses.

Given that you go first and everyone plays optimally, return whether you will win.

Constraints

1 ≤ n ≤ 100,000

Example 1

Input

n = 11

Output

True

Explanation

First you can take 9 candies, leaving 2 candies. Then, your friend can only take 1 candy, leaving 1 
candy. Then you can take the last candy. Since your friend can't make any more moves, you win.



Solution :



                        Solution in C++ :

bool solve(int n) {
    vector<int> dp(n + 1);
    dp[0] = 0;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j * j <= i; j++) {
            if (dp[i - j * j] == 0) dp[i] = true;
        }
    }
    return dp[n];
}
                    


                        Solution in Python : 
                            
class Solution:
    def solve(self, n):
        @lru_cache(None)
        def can_win(candies):
            if candies <= 0:
                return False
            res = False
            for candy in range(int(sqrt(candies)), 0, -1):
                if candy * candy > candies:
                    break
                res = res | (not can_win(candies - candy * candy))
                if res:
                    return res
            return res

        return can_win(n)
                    

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