<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 func(string& s, bool turn, int total, int maxi, unordered_map<string, bool>& dp)
    {
        if(total<=0) return false;
        if(dp.find(s)!=dp.end()) return dp[s];
        for(int i=1; i<=maxi; i++)
        {
            if(s[i]=='1') continue;
            s[i] = '1';
            if(func(s,!turn, total-i, maxi, dp)==false)
            {
                s[i] = '0';
                return dp[s] = true;
            } 
            s[i] = '0';
        }
        return dp[s] = false;
        
    }
    bool canIWin(int maxi, int total) {
        if(total<2) return 1;
        unordered_map<string, bool> mp;
        if (((1 + maxi) / 2 * maxi) < total) {
            return false;
        }
        string s = string(21,'0'); // 1 indexed
        unordered_map<string, bool> dp;
        return func(s,false,total, maxi,dp);
    }
};
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