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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