Integer Break
<p>Given an integer <code>n</code>, break it into the sum of <code>k</code> <strong>positive integers</strong>, where <code>k &gt;= 2</code>, and maximize the product of those integers.</p>

<p>Return <em>the maximum product you can get</em>.</p>

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

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 1
<strong>Explanation:</strong> 2 = 1 + 1, 1 &times; 1 = 1.
</pre>

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

<pre>
<strong>Input:</strong> n = 10
<strong>Output:</strong> 36
<strong>Explanation:</strong> 10 = 3 + 3 + 4, 3 &times; 3 &times; 4 = 36.
</pre>

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

<ul>
	<li><code>2 &lt;= n &lt;= 58</code></li>
</ul>
Math; Dynamic Programming
impl Solution {
    pub fn integer_break(n: i32) -> i32 {
        let n = n as usize;
        let mut f = vec![0; n + 1];
        f[1] = 1;
        for i in 2..=n {
            for j in 1..i {
                f[i] = f[i].max(f[i - j] * j).max((i - j) * j);
            }
        }
        f[n] as i32
    }
}
