Minimum Cost to Convert String II
<p>You are given two <strong>0-indexed</strong> strings <code>source</code> and <code>target</code>, both of length <code>n</code> and consisting of <strong>lowercase</strong> English characters. You are also given two <strong>0-indexed</strong> string arrays <code>original</code> and <code>changed</code>, and an integer array <code>cost</code>, where <code>cost[i]</code> represents the cost of converting the string <code>original[i]</code> to the string <code>changed[i]</code>.</p>

<p>You start with the string <code>source</code>. In one operation, you can pick a <strong>substring</strong> <code>x</code> from the string, and change it to <code>y</code> at a cost of <code>z</code> <strong>if</strong> there exists <strong>any</strong> index <code>j</code> such that <code>cost[j] == z</code>, <code>original[j] == x</code>, and <code>changed[j] == y</code>. You are allowed to do <strong>any</strong> number of operations, but any pair of operations must satisfy <strong>either</strong> of these two conditions:</p>

<ul>
	<li>The substrings picked in the operations are <code>source[a..b]</code> and <code>source[c..d]</code> with either <code>b &lt; c</code> <strong>or</strong> <code>d &lt; a</code>. In other words, the indices picked in both operations are <strong>disjoint</strong>.</li>
	<li>The substrings picked in the operations are <code>source[a..b]</code> and <code>source[c..d]</code> with <code>a == c</code> <strong>and</strong> <code>b == d</code>. In other words, the indices picked in both operations are <strong>identical</strong>.</li>
</ul>

<p>Return <em>the <strong>minimum</strong> cost to convert the string </em><code>source</code><em> to the string </em><code>target</code><em> using <strong>any</strong> number of operations</em>. <em>If it is impossible to convert</em> <code>source</code> <em>to</em> <code>target</code>,<em> return</em> <code>-1</code>.</p>

<p><strong>Note</strong> that there may exist indices <code>i</code>, <code>j</code> such that <code>original[j] == original[i]</code> and <code>changed[j] == changed[i]</code>.</p>

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

<pre>
<strong>Input:</strong> source = &quot;abcd&quot;, target = &quot;acbe&quot;, original = [&quot;a&quot;,&quot;b&quot;,&quot;c&quot;,&quot;c&quot;,&quot;e&quot;,&quot;d&quot;], changed = [&quot;b&quot;,&quot;c&quot;,&quot;b&quot;,&quot;e&quot;,&quot;b&quot;,&quot;e&quot;], cost = [2,5,5,1,2,20]
<strong>Output:</strong> 28
<strong>Explanation:</strong> To convert &quot;abcd&quot; to &quot;acbe&quot;, do the following operations:
- Change substring source[1..1] from &quot;b&quot; to &quot;c&quot; at a cost of 5.
- Change substring source[2..2] from &quot;c&quot; to &quot;e&quot; at a cost of 1.
- Change substring source[2..2] from &quot;e&quot; to &quot;b&quot; at a cost of 2.
- Change substring source[3..3] from &quot;d&quot; to &quot;e&quot; at a cost of 20.
The total cost incurred is 5 + 1 + 2 + 20 = 28. 
It can be shown that this is the minimum possible cost.
</pre>

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

<pre>
<strong>Input:</strong> source = &quot;abcdefgh&quot;, target = &quot;acdeeghh&quot;, original = [&quot;bcd&quot;,&quot;fgh&quot;,&quot;thh&quot;], changed = [&quot;cde&quot;,&quot;thh&quot;,&quot;ghh&quot;], cost = [1,3,5]
<strong>Output:</strong> 9
<strong>Explanation:</strong> To convert &quot;abcdefgh&quot; to &quot;acdeeghh&quot;, do the following operations:
- Change substring source[1..3] from &quot;bcd&quot; to &quot;cde&quot; at a cost of 1.
- Change substring source[5..7] from &quot;fgh&quot; to &quot;thh&quot; at a cost of 3. We can do this operation because indices [5,7] are disjoint with indices picked in the first operation.
- Change substring source[5..7] from &quot;thh&quot; to &quot;ghh&quot; at a cost of 5. We can do this operation because indices [5,7] are disjoint with indices picked in the first operation, and identical with indices picked in the second operation.
The total cost incurred is 1 + 3 + 5 = 9.
It can be shown that this is the minimum possible cost.
</pre>

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

<pre>
<strong>Input:</strong> source = &quot;abcdefgh&quot;, target = &quot;addddddd&quot;, original = [&quot;bcd&quot;,&quot;defgh&quot;], changed = [&quot;ddd&quot;,&quot;ddddd&quot;], cost = [100,1578]
<strong>Output:</strong> -1
<strong>Explanation:</strong> It is impossible to convert &quot;abcdefgh&quot; to &quot;addddddd&quot;.
If you select substring source[1..3] as the first operation to change &quot;abcdefgh&quot; to &quot;adddefgh&quot;, you cannot select substring source[3..7] as the second operation because it has a common index, 3, with the first operation.
If you select substring source[3..7] as the first operation to change &quot;abcdefgh&quot; to &quot;abcddddd&quot;, you cannot select substring source[1..3] as the second operation because it has a common index, 3, with the first operation.
</pre>

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

<ul>
	<li><code>1 &lt;= source.length == target.length &lt;= 1000</code></li>
	<li><code>source</code>, <code>target</code> consist only of lowercase English characters.</li>
	<li><code>1 &lt;= cost.length == original.length == changed.length &lt;= 100</code></li>
	<li><code>1 &lt;= original[i].length == changed[i].length &lt;= source.length</code></li>
	<li><code>original[i]</code>, <code>changed[i]</code> consist only of lowercase English characters.</li>
	<li><code>original[i] != changed[i]</code></li>
	<li><code>1 &lt;= cost[i] &lt;= 10<sup>6</sup></code></li>
</ul>
Graph; Trie; Array; String; Dynamic Programming; Shortest Path
type Node struct {
	children [26]*Node
	v        int
}

func newNode() *Node {
	return &Node{v: -1}
}

func minimumCost(source string, target string, original []string, changed []string, cost []int) int64 {
	inf := 1 << 60
	root := newNode()
	idx := 0
	m := len(cost)
	g := make([][]int, m<<1)
	for i := range g {
		g[i] = make([]int, m<<1)
		for j := range g[i] {
			g[i][j] = inf
		}
		g[i][i] = 0
	}
	insert := func(w string) int {
		node := root
		for _, c := range w {
			i := c - 'a'
			if node.children[i] == nil {
				node.children[i] = newNode()
			}
			node = node.children[i]
		}
		if node.v < 0 {
			node.v = idx
			idx++
		}
		return node.v
	}
	for i := range original {
		x := insert(original[i])
		y := insert(changed[i])
		g[x][y] = min(g[x][y], cost[i])
	}
	for k := 0; k < idx; k++ {
		for i := 0; i < idx; i++ {
			if g[i][k] >= inf {
				continue
			}
			for j := 0; j < idx; j++ {
				g[i][j] = min(g[i][j], g[i][k]+g[k][j])
			}
		}
	}
	n := len(source)
	f := make([]int, n)
	for i := range f {
		f[i] = -1
	}
	var dfs func(int) int
	dfs = func(i int) int {
		if i >= n {
			return 0
		}
		if f[i] >= 0 {
			return f[i]
		}
		f[i] = inf
		if source[i] == target[i] {
			f[i] = dfs(i + 1)
		}
		p, q := root, root
		for j := i; j < n; j++ {
			p = p.children[source[j]-'a']
			q = q.children[target[j]-'a']
			if p == nil || q == nil {
				break
			}
			if p.v < 0 || q.v < 0 {
				continue
			}
			f[i] = min(f[i], dfs(j+1)+g[p.v][q.v])
		}
		return f[i]
	}
	ans := dfs(0)
	if ans >= inf {
		ans = -1
	}
	return int64(ans)
}