LeetCode 464. Can I Win--动态规划

题目链接

464. 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.

解：

如果数字可以重复，那么用动态规划开一个dp数组应该就可以解决了，但是现在数字不能重复，那么在每一次决策时，都要考虑当前哪些数可以选择，所以需要记录这个状态，最大值是20，用一个长度是21的string来记录这个状态就可以了，其中字符'0'代表不可用，'1'代表可用，用STL库的map<string,bool>存储状态string对应的是否能赢，每次得到一个状态的结果就将他放入map，每次用到一个状态是先去map中匹配，能匹配到可以直接返回布尔值，匹配不到，判断后将结果放入map。

能赢的情况：1.当前最大可选的数大于当前的desiredTotal   2.选了其中一个数之后，对方赢不了

代码：

class Solution {
public:
    bool dp(int desiredTotal, string status, map<string,bool>* container, int size) {
        if (container->find(status) != container->end())  return container->at(status);
        for (int i = size; i >= 1; i--) {
            if (status[i] == '1') {
                string a = status;
                a[i] = '0';
                if (i >= desiredTotal || dp(desiredTotal-i, a, container, size) == false) {
                    container->insert(std::pair<string, bool>(status, true));
                    return true;
                }
            }
        }
        container->insert(std::pair<string, bool>(status, false));
        return false;
    }
    bool canIWin(int maxChoosableInteger, int desiredTotal) {
        if (desiredTotal <= maxChoosableInteger)  return true;
        if (desiredTotal > maxChoosableInteger*(maxChoosableInteger+1)/2) return false;
        string status;
        for (int i = 0; i < 21; i++) status += '1';
        map<string, bool>* temp = new map<string, bool>;
        return dp(desiredTotal, status, temp, maxChoosableInteger);
    }
};