[leetcode 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.

dfs深度优先搜索，搜索的过程中增加一个map来保存中途搜索结果避免重复搜索

看了discuss，将boolean数组转换为int值，来保存，黑科技

AC代码：
public class Solution {
private static Map<Integer, Boolean> map;
private static boolean[] used;

public static 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 static boolean helper(int desiredTotal){
if(desiredTotal <= 0) return false;
int key = format(used);
if(!map.containsKey(key)){

for(int i=1; i<used.length; i++){
if(!used[i]){
used[i] = true;
if(!helper(desiredTotal-i)){
map.put(key, true);
used[i] = false;
return true;
}
used[i] = false;
}
}
map.put(key, false);
}
return map.get(key);
}

public static int format(boolean[] used){
int num = 0;
for(boolean b: used){
num <<= 1;
if(b) num |= 1;
}
return num;
}
}
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