Partition String Into Minimum Beautiful Substrings
<p>Given a binary string <code>s</code>, partition the string into one or more <strong>substrings</strong> such that each substring is <strong>beautiful</strong>.</p>

<p>A string is <strong>beautiful</strong> if:</p>

<ul>
	<li>It doesn&#39;t contain leading zeros.</li>
	<li>It&#39;s the <strong>binary</strong> representation of a number that is a power of <code>5</code>.</li>
</ul>

<p>Return <em>the <strong>minimum</strong> number of substrings in such partition. </em>If it is impossible to partition the string <code>s</code> into beautiful substrings,&nbsp;return <code>-1</code>.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters in a string.</p>

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

<pre>
<strong>Input:</strong> s = &quot;1011&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> We can paritition the given string into [&quot;101&quot;, &quot;1&quot;].
- The string &quot;101&quot; does not contain leading zeros and is the binary representation of integer 5<sup>1</sup> = 5.
- The string &quot;1&quot; does not contain leading zeros and is the binary representation of integer 5<sup>0</sup> = 1.
It can be shown that 2 is the minimum number of beautiful substrings that s can be partitioned into.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;111&quot;
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can paritition the given string into [&quot;1&quot;, &quot;1&quot;, &quot;1&quot;].
- The string &quot;1&quot; does not contain leading zeros and is the binary representation of integer 5<sup>0</sup> = 1.
It can be shown that 3 is the minimum number of beautiful substrings that s can be partitioned into.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;0&quot;
<strong>Output:</strong> -1
<strong>Explanation:</strong> We can not partition the given string into beautiful substrings.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 15</code></li>
	<li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
</ul>
Hash Table; String; Dynamic Programming; Backtracking
function minimumBeautifulSubstrings(s: string): number {
    const ss: Set<number> = new Set();
    const n = s.length;
    const f: number[] = new Array(n).fill(-1);
    for (let i = 0, x = 1; i <= n; ++i) {
        ss.add(x);
        x *= 5;
    }
    const dfs = (i: number): number => {
        if (i === n) {
            return 0;
        }
        if (s[i] === '0') {
            return n + 1;
        }
        if (f[i] !== -1) {
            return f[i];
        }
        f[i] = n + 1;
        for (let j = i, x = 0; j < n; ++j) {
            x = (x << 1) | (s[j] === '1' ? 1 : 0);
            if (ss.has(x)) {
                f[i] = Math.min(f[i], 1 + dfs(j + 1));
            }
        }
        return f[i];
    };
    const ans = dfs(0);
    return ans > n ? -1 : ans;
}
