LeetCode-in-Java
464. Can I Win
Medium
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 game 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 and desiredTotal, return true if the first player to move can force a win, otherwise, return false. Assume both players play optimally.
Example 1:
Input: maxChoosableInteger = 10, desiredTotal = 11
Output: false
Explanation:
No matter which integer the first player choose, the first player will lose.
The first player can choose an integer from 1 up to 10.
If the first player choose 1, the second player can only choose integers from 2 up to 10.
The second player will win by choosing 10 and get a total = 11, which is >= desiredTotal.
Same with other integers chosen by the first player, the second player will always win.
Example 2:
Input: maxChoosableInteger = 10, desiredTotal = 0
Output: true
Example 3:
Input: maxChoosableInteger = 10, desiredTotal = 1
Output: true
Constraints:
1 <= maxChoosableInteger <= 200 <= desiredTotal <= 300
Solution
public class Solution {
public boolean canIWin(int maxChoosableInteger, int desiredTotal) {
if (desiredTotal <= maxChoosableInteger) {
return true;
}
if (1.0 * maxChoosableInteger * (1 + maxChoosableInteger) / 2 < desiredTotal) {
return false;
}
return canWin(0, new Boolean[1 << maxChoosableInteger], desiredTotal, maxChoosableInteger);
}
private boolean canWin(int state, Boolean[] dp, int desiredTotal, int maxChoosableInteger) {
// state is the bitmap representation of the current state of choosable integers left
// dp[state] represents whether the current player can win the game at state
if (dp[state] != null) {
return dp[state];
}
for (int i = 1; i <= maxChoosableInteger; i++) {
// current number to pick
int cur = 1 << (i - 1);
if ((cur & state) == 0
&& (i >= desiredTotal
|| !canWin(state | cur, dp, desiredTotal - i, maxChoosableInteger))) {
// i is greater than the desired total
// or the other player cannot win after the current player picks i
dp[state] = true;
return dp[state];
}
}
dp[state] = false;
return dp[state];
}
}