leetcode-problemset/leetcode-cn/originData/minimum-cost-to-convert-string-i.json

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        "question": {
            "questionId": "3235",
            "questionFrontendId": "2976",
            "categoryTitle": "Algorithms",
            "boundTopicId": 2575704,
            "title": "Minimum Cost to Convert String I",
            "titleSlug": "minimum-cost-to-convert-string-i",
            "content": "<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 letters. You are also given two <strong>0-indexed</strong> character arrays <code>original</code> and <code>changed</code>, and an integer array <code>cost</code>, where <code>cost[i]</code> represents the cost of changing the character <code>original[i]</code> to the character <code>changed[i]</code>.</p>\n\n<p>You start with the string <code>source</code>. In one operation, you can pick a character <code>x</code> from the string and change it to the character <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>.</p>\n\n<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. If it is impossible to convert</em> <code>source</code> <em>to</em> <code>target</code>, <em>return</em> <code>-1</code>.</p>\n\n<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>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<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]\n<strong>Output:</strong> 28\n<strong>Explanation:</strong> To convert the string &quot;abcd&quot; to string &quot;acbe&quot;:\n- Change value at index 1 from &#39;b&#39; to &#39;c&#39; at a cost of 5.\n- Change value at index 2 from &#39;c&#39; to &#39;e&#39; at a cost of 1.\n- Change value at index 2 from &#39;e&#39; to &#39;b&#39; at a cost of 2.\n- Change value at index 3 from &#39;d&#39; to &#39;e&#39; at a cost of 20.\nThe total cost incurred is 5 + 1 + 2 + 20 = 28.\nIt can be shown that this is the minimum possible cost.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> source = &quot;aaaa&quot;, target = &quot;bbbb&quot;, original = [&quot;a&quot;,&quot;c&quot;], changed = [&quot;c&quot;,&quot;b&quot;], cost = [1,2]\n<strong>Output:</strong> 12\n<strong>Explanation:</strong> To change the character &#39;a&#39; to &#39;b&#39; change the character &#39;a&#39; to &#39;c&#39; at a cost of 1, followed by changing the character &#39;c&#39; to &#39;b&#39; at a cost of 2, for a total cost of 1 + 2 = 3. To change all occurrences of &#39;a&#39; to &#39;b&#39;, a total cost of 3 * 4 = 12 is incurred.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> source = &quot;abcd&quot;, target = &quot;abce&quot;, original = [&quot;a&quot;], changed = [&quot;e&quot;], cost = [10000]\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> It is impossible to convert source to target because the value at index 3 cannot be changed from &#39;d&#39; to &#39;e&#39;.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= source.length == target.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>source</code>, <code>target</code> consist of lowercase English letters.</li>\n\t<li><code>1 &lt;= cost.length == original.length == changed.length &lt;= 2000</code></li>\n\t<li><code>original[i]</code>, <code>changed[i]</code> are lowercase English letters.</li>\n\t<li><code>1 &lt;= cost[i] &lt;= 10<sup>6</sup></code></li>\n\t<li><code>original[i] != changed[i]</code></li>\n</ul>\n",
            "translatedTitle": "转换字符串的最小成本 I",
            "translatedContent": "<p>给你两个下标从 <strong>0</strong> 开始的字符串 <code>source</code> 和 <code>target</code> ，它们的长度均为 <code>n</code> 并且由 <strong>小写 </strong>英文字母组成。</p>\n\n<p>另给你两个下标从 <strong>0</strong> 开始的字符数组 <code>original</code> 和 <code>changed</code> ，以及一个整数数组 <code>cost</code> ，其中 <code>cost[i]</code> 代表将字符 <code>original[i]</code> 更改为字符 <code>changed[i]</code> 的成本。</p>\n\n<p>你从字符串 <code>source</code> 开始。在一次操作中，<strong>如果 </strong>存在 <strong>任意</strong> 下标 <code>j</code> 满足 <code>cost[j] == z</code>&nbsp; 、<code>original[j] == x</code> 以及 <code>changed[j] == y</code> 。你就可以选择字符串中的一个字符 <code>x</code> 并以 <code>z</code> 的成本将其更改为字符 <code>y</code> 。</p>\n\n<p>返回将字符串 <code>source</code> 转换为字符串 <code>target</code> 所需的<strong> 最小 </strong>成本。如果不可能完成转换，则返回 <code>-1</code> 。</p>\n\n<p><strong>注意</strong>，可能存在下标 <code>i</code> 、<code>j</code> 使得 <code>original[j] == original[i]</code> 且 <code>changed[j] == changed[i]</code> 。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>source = \"abcd\", target = \"acbe\", original = [\"a\",\"b\",\"c\",\"c\",\"e\",\"d\"], changed = [\"b\",\"c\",\"b\",\"e\",\"b\",\"e\"], cost = [2,5,5,1,2,20]\n<strong>输出：</strong>28\n<strong>解释：</strong>将字符串 \"abcd\" 转换为字符串 \"acbe\" ：\n- 更改下标 1 处的值 'b' 为 'c' ，成本为 5 。\n- 更改下标 2 处的值 'c' 为 'e' ，成本为 1 。\n- 更改下标 2 处的值 'e' 为 'b' ，成本为 2 。\n- 更改下标 3 处的值 'd' 为 'e' ，成本为 20 。\n产生的总成本是 5 + 1 + 2 + 20 = 28 。\n可以证明这是可能的最小成本。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>source = \"aaaa\", target = \"bbbb\", original = [\"a\",\"c\"], changed = [\"c\",\"b\"], cost = [1,2]\n<strong>输出：</strong>12\n<strong>解释：</strong>要将字符 'a' 更改为 'b'：\n- 将字符 'a' 更改为 'c'，成本为 1 \n- 将字符 'c' 更改为 'b'，成本为 2 \n产生的总成本是 1 + 2 = 3。\n将所有 'a' 更改为 'b'，产生的总成本是 3 * 4 = 12 。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>source = \"abcd\", target = \"abce\", original = [\"a\"], changed = [\"e\"], cost = [10000]\n<strong>输出：</strong>-1\n<strong>解释：</strong>无法将 source 字符串转换为 target 字符串，因为下标 3 处的值无法从 'd' 更改为 'e' 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= source.length == target.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>source</code>、<code>target</code> 均由小写英文字母组成</li>\n\t<li><code>1 &lt;= cost.length== original.length == changed.length &lt;= 2000</code></li>\n\t<li><code>original[i]</code>、<code>changed[i]</code> 是小写英文字母</li>\n\t<li><code>1 &lt;= cost[i] &lt;= 10<sup>6</sup></code></li>\n\t<li><code>original[i] != changed[i]</code></li>\n</ul>\n",
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                "Construct a graph with each letter as a node, and construct an edge <code>(a, b)</code> with weight <code>c</code> if we can change from character <code>a</code> to letter <code>b</code> with cost <code>c</code>. (Keep the one with the smallest cost in case there are multiple edges between <code>a</code> and <code>b</code>).",
                "Calculate the shortest path for each pair of characters <code>(source[i], target[i])</code>. The sum of cost over all <code>i</code> in the range <code>[0, source.length - 1]</code>. If there is no path between <code>source[i]</code> and <code>target[i]</code>, the answer is <code>-1</code>.",
                "Any shortest path algorithms will work since we only have <code>26</code> nodes. Since we only have at most <code>26 * 26</code> pairs, we can save the result to avoid re-calculation.",
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