<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:
    
    unordered_map<int, bool> mp;
    
    bool helper(int maxChoosableInteger, bitset<20> &chosen, int desiredTotal) {
        if(desiredTotal <= 0) return true;
        
        if(mp.find((int)chosen.to_ulong()) != mp.end()) {
            return mp[(int)chosen.to_ulong()];
        }

        bool allChosen = true;
        for(int i=1; i<=maxChoosableInteger; i++) {
            if(!chosen[i-1]) {
                allChosen = false;
            }
        }
        if(allChosen) {
            return false; // nothing left to choose
        }

        for(int i=1; i<=maxChoosableInteger; i++) {
            if(!chosen[i-1]) {
                if(i >= desiredTotal) {
                    return true;
                }
                chosen[i-1] = true; // choose i
                if(!helper(maxChoosableInteger, chosen, desiredTotal - i)){
                    chosen[i-1] = false;
                    mp[(int)chosen.to_ulong()] = true;
                    return true;
                }
                chosen[i-1] = false;
            }
        }

        mp[(int)chosen.to_ulong()] = false;
        return false;   
    }

    bool canIWin(int maxChoosableInteger, int desiredTotal) {
        // vector<bool> chosen(maxChoosableInteger, false);
        bitset<20> chosen{0};
        
        if(maxChoosableInteger*(maxChoosableInteger + 1)/2 < desiredTotal){
            return false; // not enough numbers
        }

        return helper(maxChoosableInteger, chosen, desiredTotal);
    }
};
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