<p>Given an integer <code>n</code>, return <em>the least number of perfect square numbers that sum to</em> <code>n</code>.</p>

<p>A <strong>perfect square</strong> is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, <code>1</code>, <code>4</code>, <code>9</code>, and <code>16</code> are perfect squares while <code>3</code> and <code>11</code> are not.</p>

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

<pre>
<strong>Input:</strong> n = 12
<strong>Output:</strong> 3
<strong>Explanation:</strong> 12 = 4 + 4 + 4.
</pre>

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

<pre>
<strong>Input:</strong> n = 13
<strong>Output:</strong> 2
<strong>Explanation:</strong> 13 = 4 + 9.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    int dp[10001][1000];
    int f(int t,int i)
    {
        if(t == 0) return 0;
        if(i*i > t) return INT_MAX;
        if(dp[t][i] != -1) return dp[t][i];
        int ans = INT_MAX;

        if(t - i*i >=0) ans = f(t- i*i,i);
        if(ans != INT_MAX) ans += 1;
        ans = min(ans,f(t,i+1));

        return dp[t][i] = ans;
    }
    int numSquares(int n) {
        memset(dp,-1,sizeof dp);
        return f(n,1);
    }
};
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