464. Can I Win

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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

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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.

解法1：

当dp不太好想的时候考虑用一下memorization来减少复杂度。
这题粗暴思路就是一个dfs，来判断对于一组数是否能win。
那么我们可以把当前数字使用情况转变成一个key来存储起来。
转成key的思路是把每一位数字如果没被用过变为0，用过了变为1.
C++

1

Java

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public class Solution {
    private HashMap<Integer, Boolean> map = new HashMap<Integer, Boolean>();
    public boolean canIWin(int maxChoosableInteger, int desiredTotal) {
        int sum = (1 + maxChoosableInteger) * maxChoosableInteger / 2;
        if (sum < desiredTotal) {
            return false;
        }
        if (maxChoosableInteger >= desiredTotal) {
            return true;
        }
        boolean[] used = new boolean[maxChoosableInteger + 1];
        return helper(used, desiredTotal, maxChoosableInteger);
    }
    private boolean helper(boolean[] used, int desiredTotal, int max) {
        if (desiredTotal <= 0) {
            return false;
        }
        int key = transform(used);
        if (map.containsKey(key)) {
            return map.get(key);
        }
        for (int i = 1; i <= max; i++) {
            if (!used[i]) {
                used[i] = true;
                boolean sub = helper(used, desiredTotal - i, max);
                used[i] = false;
                if (!sub) {
                    map.put(key, true);
                    return true;
                }
            }
        }
        map.put(key, false);
        return false;
    }
    private int transform(boolean[] used) {
        int num = 0;
        for (boolean i : used) {
            num <<= 1;
            if (i) {
                num |= 1;
            }
        }
        return num;
    }
}