464. Can I Win

发表于 | 分类于 | | 阅读次数:

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

1
2
3
4
5
6
7
8
9
10
11
12
13
14
>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.
>

分析

最开始的方法就是深搜加回溯，用一个set来存储所有数组，然后每次选一个从set中删除，向下搜索，然后再回溯加上原来删除的元素。tag给的提示是DP，虽然知道应该把走过的路径记下来，但是set不知道怎么做。

看来网上的答案才知道，因为备选的数字是连续的，所以可以建一个数组，下标就是对应的数字，如何用数组的值记录这个数字是不是已经被使用过了，这样的话数组的不同状态对应不同的答案，就可以用一个map记录下来，避免重复搜索。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40

private static int format(boolean[] state){
	int re=0;
	for(int i=0; i<state.length; i++){
		re<<=1;
		if(state[i]){
			re|=1;
		}
	}
	return re;
}

private static boolean isOK(boolean[] state, Map<Integer, Boolean> map, int tar){
	int key=format(state);
	if(map.containsKey(key)){
		return map.get(key);
	}
	for(int i=0; i<state.length; i++){
		if(!state[i]){
			state[i]=true;
			if(i+1>=tar||!isOK(state, map, tar-i-1)){
				map.put(key, true);
				state[i]=false;
				return true;
			}
			state[i]=false;
		}
	}
	map.put(key, false);
	return false;
}

public static boolean canIWin(int maxChoosableInteger, int desiredTotal) {
	if((1+maxChoosableInteger)*maxChoosableInteger<desiredTotal*2){
		return false;
	}
    boolean[] state=new boolean[maxChoosableInteger];
	Map<Integer, Boolean> map=new HashMap<Integer, Boolean>();       
	return isOK(state, map, desiredTotal);
}