[LeetCode] 464. Can I Win 我能赢吗

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.

给了一组数字，两个人玩游戏，每人每次可选一个数字，看数字总和谁先到给定值，判断第一玩的人能否保证能赢。

Java:

public class Solution {
    Map<Integer, Boolean> map;
    boolean[] used;
    public boolean canIWin(int maxChoosableInteger, int desiredTotal) {
        int sum = (1+maxChoosableInteger)*maxChoosableInteger/2;
        if(sum < desiredTotal) return false;
        if(desiredTotal <= 0) return true;
        
        map = new HashMap();
        used = new boolean[maxChoosableInteger+1];
        return helper(desiredTotal);
    }
    
    public boolean helper(int desiredTotal){
        if(desiredTotal <= 0) return false;
        int key = format(used);
        if(!map.containsKey(key)){
    // try every unchosen number as next step
            for(int i=1; i<used.length; i++){
                if(!used[i]){
                    used[i] = true;
     // check whether this lead to a win (i.e. the other player lose)
                    if(!helper(desiredTotal-i)){
                        map.put(key, true);
                        used[i] = false;
                        return true;
                    }
                    used[i] = false;
                }
            }
            map.put(key, false);
        }
        return map.get(key);
    }
   
// transfer boolean[] to an Integer 
    public int format(boolean[] used){
        int num = 0;
        for(boolean b: used){
            num <<= 1;
            if(b) num |= 1;
        }
        return num;
    }
}

Python:　　

def canIWin(self, maxChoosableInteger, desiredTotal):
        """
        :type maxChoosableInteger: int
        :type desiredTotal: int
        :rtype: bool
        """
        if (1 + maxChoosableInteger) * maxChoosableInteger/2 < desiredTotal:
            return False
        self.memo = {}
        return self.helper(range(1, maxChoosableInteger + 1), desiredTotal)

        
    def helper(self, nums, desiredTotal):
        
        hash = str(nums)
        if hash in self.memo:
            return self.memo[hash]
        
        if nums[-1] >= desiredTotal:
            return True
            
        for i in range(len(nums)):
            if not self.helper(nums[:i] + nums[i+1:], desiredTotal - nums[i]):
                self.memo[hash]= True
                return True
        self.memo[hash] = False
        return False

Python:　　

# Memoization solution.
class Solution(object):
    def canIWin(self, maxChoosableInteger, desiredTotal):
        """
        :type maxChoosableInteger: int
        :type desiredTotal: int
        :rtype: bool
        """
        def canIWinHelper(maxChoosableInteger, desiredTotal, visited, lookup):
            if visited in lookup:
                return lookup[visited]

            mask = 1
            for i in xrange(maxChoosableInteger):
                if visited & mask == 0:
                    if i + 1 >= desiredTotal or 
                       not canIWinHelper(maxChoosableInteger, desiredTotal - (i + 1), visited | mask, lookup):
                        lookup[visited] = True
                        return True
                mask <<= 1
            lookup[visited] = False
            return False

        if (1 + maxChoosableInteger) * (maxChoosableInteger / 2) < desiredTotal:
            return False

        return canIWinHelper(maxChoosableInteger, desiredTotal, 0, {})　　

C++:

class Solution {
public:
    bool canIWin(int maxChoosableInteger, int desiredTotal) {
        if (maxChoosableInteger >= desiredTotal) return true;
        if (maxChoosableInteger * (maxChoosableInteger + 1) / 2 < desiredTotal) return false;
        unordered_map<int, bool> m;
        return canWin(maxChoosableInteger, desiredTotal, 0, m);
    }
    bool canWin(int length, int total, int used, unordered_map<int, bool>& m) {
        if (m.count(used)) return m[used];
        for (int i = 0; i < length; ++i) {
            int cur = (1 << i);
            if ((cur & used) == 0) {
                if (total <= i + 1 || !canWin(length, total - (i + 1), cur | used, m)) {
                    m[used] = true;
                    return true;
                }
            }
        }
        m[used] = false;
        return false;
    }
};

　　

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