Sunday, November 20, 2016

LeetCode 464 - Can I Win


https://leetcode.com/problems/can-i-win/
In the "100 game," two players take turns adding, to a running total, any integer from 1..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 of 1..15 without replacement until they reach a total >= 100.
Given an integer maxChoosableInteger and another integer desiredTotal, determine if the first player to move can force a win, assuming both players play optimally.
You can always assume that maxChoosableInteger will not be larger than 20 and desiredTotal will not be larger than 300.
Example


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.
http://bookshadow.com/weblog/2016/11/20/leetcode-can-i-win/
记忆化搜索 + 位运算
由于maxChoosableInteger不大于20,因此可以通过整数state表示当前已经选择了哪些数字
state的第i位为1时,表示选择了数字i + 1
利用字典dp记录已经搜索过的状态
def canIWin(self, maxChoosableInteger, desiredTotal): """ :type maxChoosableInteger: int :type desiredTotal: int :rtype: bool """ dp = dict() def search(state, total): for x in range(maxChoosableInteger, 0, -1): if not state & (1 << (x - 1)): if total + x >= desiredTotal: dp[state] = True return True break for x in range(1, maxChoosableInteger + 1): if not state & (1 << (x - 1)): nstate = state | (1 << (x - 1)) if nstate not in dp: dp[nstate] = search(nstate, total + x) if not dp[nstate]: dp[state] = True return True dp[state] = False return False if maxChoosableInteger >= desiredTotal: return True if (1 + maxChoosableInteger) * maxChoosableInteger < 2 * desiredTotal: return False return search(0, 0)


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