-
Notifications
You must be signed in to change notification settings - Fork 1
/
CanIWin.java
50 lines (47 loc) · 1.75 KB
/
CanIWin.java
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
41
42
43
44
45
46
47
48
49
50
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
/**
* 464. Can I Win
* @author LBW
* 记忆化回溯(动态规划)
* 博弈DP问题
*/
public class CanIWin {
public boolean canIWin(int maxChoosableInteger, int desiredTotal) {
if (maxChoosableInteger >= desiredTotal)
return true;
if ((1 + maxChoosableInteger) * maxChoosableInteger / 2 < desiredTotal)
return false;
int[] state = new int[maxChoosableInteger+1];
Map<String, Boolean> memo = new HashMap<>();
boolean res = dfs(state, memo, maxChoosableInteger, desiredTotal);
return res;
}
private boolean dfs(int[] state, Map<String, Boolean> memo, int maxChoosableInteger, int desiredTotal) {
String key = Arrays.toString(state); // 这里一定不能是 state.toString(),否则是Java默认的类名+地址 字符串
if (memo.containsKey(key))
return memo.get(key);
for (int i = 1; i <= maxChoosableInteger; i++) {
if (state[i] == 1)
continue;
// choose and backtrack
state[i] = 1;
// i比目标大,或者选择后对手会输,那么就进入赢的情况。
if (i >= desiredTotal || !dfs(state, memo, maxChoosableInteger, desiredTotal - i)) {
memo.put(key, true);
state[i] = 0;
return true;
}
// 注意即使没有赢,也要回溯
state[i] = 0;
}
// 所有选择都尝试后都不能确保赢,那么就输。
memo.put(key, false);
return false;
}
public static void main(String[] args) {
CanIWin canIWin = new CanIWin();
canIWin.canIWin(10, 40);
}
}