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// 464. Can I Win
#include "leetcode.h"
/*
* in the 100 game two players take turns adding, to a running total, any
* integer from 1 to 10. the player who first causes the running total to reach
* or exceed 100 wins. what if we change the same so that players cannot re-use
* integers? for example, two players might take turns drawing from a common
* pool of numbers from 1 to 15 without replacement until they reach a total >=
* 100. given two integers 'maxChoosableInteger' nad 'desiredTotal', return true
* if the first player to move can force a win, otherwise, return false. assume
* both players play optimally.
*/
static int mem[1 << 20] = {};
bool dfs(int maxChoosableInteger, int desiredTotal, int k) {
if (mem[k])
return mem[k] > 0;
if (desiredTotal <= 0)
return false;
for (int i = 0; i < maxChoosableInteger; ++i)
if (!(k & (1 << i)) &
!dfs(maxChoosableInteger, desiredTotal - i - 1, k | (1 << i))) {
mem[k] = 1;
return true;
}
mem[k] = -1;
return false;
}
bool canIWin(int maxChoosableInteger, int desiredTotal) {
int sum = maxChoosableInteger * (maxChoosableInteger + 1) / 2;
if (desiredTotal < 2)
return true;
else if (sum < desiredTotal)
return false;
else if (sum == desiredTotal)
return maxChoosableInteger % 2;
else
return dfs(maxChoosableInteger, desiredTotal, 0);
}
int main() {
printf("%d\n", canIWin(10, 11)); // expect: 0
printf("%d\n", canIWin(10, 0)); // expect: 1
printf("%d\n", canIWin(10, 1)); // expect: 1
}
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