<p>In the &quot;100 game&quot; two players take turns adding, to a running total, any integer from <code>1</code> to <code>10</code>. The player who first causes the running total to <strong>reach or exceed</strong> 100 wins.</p>

<p>What if we change the game so that players <strong>cannot</strong> re-use integers?</p>

<p>For example, two players might take turns drawing from a common pool of numbers from 1 to 15 without replacement until they reach a total &gt;= 100.</p>

<p>Given two integers <code>maxChoosableInteger</code> and <code>desiredTotal</code>, return <code>true</code> if the first player to move can force a win, otherwise, return <code>false</code>. Assume both players play <strong>optimally</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 11
<strong>Output:</strong> false
<strong>Explanation:</strong>
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 &gt;= desiredTotal.
Same with other integers chosen by the first player, the second player will always win.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 0
<strong>Output:</strong> true
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> maxChoosableInteger = 10, desiredTotal = 1
<strong>Output:</strong> true
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= maxChoosableInteger &lt;= 20</code></li>
	<li><code>0 &lt;= desiredTotal &lt;= 300</code></li>
</ul>

class Solution {
public:



    bool solve(int st, int desiredTotal, int initialSum, map<int, bool>& mp, int maxChoosableInteger) {
        if (mp.find(st) != mp.end()) return mp[st];

        if (initialSum >= desiredTotal) {
            return false;
        }

        bool possible = true;
        
        // set<int>temp(st);
        int temp = st;

        for (int i = 1; i <= maxChoosableInteger; i++) {
            if (1<<i & st) {
                continue;
            }

            st = st | (1<<i);
            bool ans = solve(st, desiredTotal, initialSum + i, mp, maxChoosableInteger);
            possible = possible && ans;
            st = temp;
            if (possible == false) {
                break;
            }
        }

        // for(auto it: temp) {
        //     st.erase(st.find(it));
        //     bool ans = solve(st, desiredTotal, initialSum + it, mp, maxChoosableInteger);
        //     possible = possible && ans;
        //     st.insert(it);
        //     if (possible == false) {
        //         break;
        //     }
        // }
        mp[temp] = !possible;

        return mp[temp];
    }

    bool canIWin(int maxChoosableInteger, int desiredTotal) {
        // set<int> st;
        // map<set<int>, bool> mp;
        map<int, bool> mp;
        
        // for (int i = 1; i <= maxChoosableInteger; i++) {
        //     st.insert(i);
        // }

        if ( (maxChoosableInteger * (maxChoosableInteger + 1)) / 2   < desiredTotal) return false;

        if (maxChoosableInteger >= desiredTotal) return true;

        return solve(0, desiredTotal, 0, mp, maxChoosableInteger);
    }
};
104952