<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 canIWin(int maxChoosableInteger, int desiredTotal) 
	{
		if (desiredTotal == 0)
			return true; 

		unsigned int available = 0; 
		int sum = 0; 
		for (int i = 1; i <= maxChoosableInteger; i++) {
			bitset(available, i);
			sum += i; 
		}
		if (sum < desiredTotal)
			return false; 

		cache.clear(); 

		return solve(available, maxChoosableInteger, 0, desiredTotal, true);
	}
private:
	bool solve(unsigned int& available, int maxnum, int cursum, int target, bool player)
	{
		if (cursum >= target)
			return !player; 
		if (available == 0)
			return player; 

		if (cache.find(available) != cache.end())
			return cache[available]; 

		bool winner = !player; 

		for (int i = maxnum; i > 0; i--)
		{
			if (isset(available, i)) {
				auto copy = available; 
				bitclear(copy, i); 
				winner = solve(copy, maxnum, cursum + i, target, !player); 
				if (winner == player)
					break; 
			}
		}

		cache.insert(make_pair(available, winner)); 
		return winner; 
	}
	void bitset(unsigned int& bits, int pos)
	{
		unsigned int mask = (1 << pos); 
		bits |= mask; 
	}
	void bitclear(unsigned int& bits, int pos)
	{
		unsigned int mask = (1 << pos);
		mask = mask ^ 0xffffffff; 
		bits &= mask;
	}
	bool isset(unsigned int& bits, int pos)
	{
		unsigned int mask = (1 << pos); 
		return (bits & mask) != 0; 
	}
	unordered_map<unsigned int, bool>cache; 
};
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