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"question": {
"questionId": "2854",
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"categoryTitle": "Algorithms",
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"title": "Decremental String Concatenation",
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"content": "<p>You are given a <strong>0-indexed</strong> array <code>words</code> containing <code>n</code> strings.</p>\n\n<p>Let&#39;s define a <strong>join</strong> operation <code>join(x, y)</code> between two strings <code>x</code> and <code>y</code> as concatenating them into <code>xy</code>. However, if the last character of <code>x</code> is equal to the first character of <code>y</code>, one of them is <strong>deleted</strong>.</p>\n\n<p>For example <code>join(&quot;ab&quot;, &quot;ba&quot;) = &quot;aba&quot;</code> and <code>join(&quot;ab&quot;, &quot;cde&quot;) = &quot;abcde&quot;</code>.</p>\n\n<p>You are to perform <code>n - 1</code> <strong>join</strong> operations. Let <code>str<sub>0</sub> = words[0]</code>. Starting from <code>i = 1</code> up to <code>i = n - 1</code>, for the <code>i<sup>th</sup></code> operation, you can do one of the following:</p>\n\n<ul>\n\t<li>Make <code>str<sub>i</sub> = join(str<sub>i - 1</sub>, words[i])</code></li>\n\t<li>Make <code>str<sub>i</sub> = join(words[i], str<sub>i - 1</sub>)</code></li>\n</ul>\n\n<p>Your task is to <strong>minimize</strong> the length of <code>str<sub>n - 1</sub></code>.</p>\n\n<p>Return <em>an integer denoting the minimum possible length of</em> <code>str<sub>n - 1</sub></code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> words = [&quot;aa&quot;,&quot;ab&quot;,&quot;bc&quot;]\n<strong>Output:</strong> 4\n<strong>Explanation: </strong>In this example, we can perform join operations in the following order to minimize the length of str<sub>2</sub>: \nstr<sub>0</sub> = &quot;aa&quot;\nstr<sub>1</sub> = join(str<sub>0</sub>, &quot;ab&quot;) = &quot;aab&quot;\nstr<sub>2</sub> = join(str<sub>1</sub>, &quot;bc&quot;) = &quot;aabc&quot; \nIt can be shown that the minimum possible length of str<sub>2</sub> is 4.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> words = [&quot;ab&quot;,&quot;b&quot;]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> In this example, str<sub>0</sub> = &quot;ab&quot;, there are two ways to get str<sub>1</sub>: \njoin(str<sub>0</sub>, &quot;b&quot;) = &quot;ab&quot; or join(&quot;b&quot;, str<sub>0</sub>) = &quot;bab&quot;. \nThe first string, &quot;ab&quot;, has the minimum length. Hence, the answer is 2.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> words = [&quot;aaa&quot;,&quot;c&quot;,&quot;aba&quot;]\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> In this example, we can perform join operations in the following order to minimize the length of str<sub>2</sub>: \nstr<sub>0</sub> = &quot;aaa&quot;\nstr<sub>1</sub> = join(str<sub>0</sub>, &quot;c&quot;) = &quot;aaac&quot;\nstr<sub>2</sub> = join(&quot;aba&quot;, str<sub>1</sub>) = &quot;abaaac&quot;\nIt can be shown that the minimum possible length of str<sub>2</sub> is 6.\n</pre>\n\n<div class=\"notranslate\" style=\"all: initial;\">&nbsp;</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= words.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= words[i].length &lt;= 50</code></li>\n\t<li>Each character in <code>words[i]</code> is an English lowercase letter</li>\n</ul>\n",
"translatedTitle": "字符串连接删减字母",
"translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的数组&nbsp;<code>words</code>&nbsp;,它包含 <code>n</code>&nbsp;个字符串。</p>\n\n<p>定义 <strong>连接</strong>&nbsp;操作&nbsp;<code>join(x, y)</code>&nbsp;表示将字符串&nbsp;<code>x</code> 和&nbsp;<code>y</code>&nbsp;连在一起,得到&nbsp;<code>xy</code>&nbsp;。如果&nbsp;<code>x</code>&nbsp;的最后一个字符与&nbsp;<code>y</code>&nbsp;的第一个字符相等,连接后两个字符中的一个会被&nbsp;<strong>删除</strong>&nbsp;。</p>\n\n<p>比方说&nbsp;<code>join(\"ab\", \"ba\") = \"aba\"</code>&nbsp;&nbsp;<code>join(\"ab\", \"cde\") = \"abcde\"</code>&nbsp;。</p>\n\n<p>你需要执行&nbsp;<code>n - 1</code>&nbsp;次&nbsp;<strong>连接</strong>&nbsp;操作。令&nbsp;<code>str<sub>0</sub> = words[0]</code>&nbsp;,从&nbsp;<code>i = 1</code> 直到&nbsp;<code>i = n - 1</code>&nbsp;,对于第&nbsp;<code>i</code>&nbsp;个操作,你可以执行以下操作之一:</p>\n\n<ul>\n\t<li>令&nbsp;<code>str<sub>i</sub> = join(str<sub>i - 1</sub>, words[i])</code></li>\n\t<li>令&nbsp;<code>str<sub>i</sub> = join(words[i], str<sub>i - 1</sub>)</code></li>\n</ul>\n\n<p>你的任务是使&nbsp;<code>str<sub>n - 1</sub></code>&nbsp;的长度<strong>&nbsp;最小&nbsp;</strong>。</p>\n\n<p>请你返回一个整数,表示&nbsp;<code>str<sub>n - 1</sub></code>&nbsp;的最小长度。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<b>输入:</b>words = [\"aa\",\"ab\",\"bc\"]\n<b>输出:</b>4\n<strong>解释:</strong>这个例子中,我们按以下顺序执行连接操作,得到 <code>str<sub>2</sub></code> 的最小长度:\n<code>str<sub>0</sub> = \"aa\"</code>\n<code>str<sub>1</sub> = join(str<sub>0</sub>, \"ab\") = \"aab\"\n</code><code>str<sub>2</sub> = join(str<sub>1</sub>, \"bc\") = \"aabc\"</code> \n<code>str<sub>2</sub></code> 的最小长度为 4 。</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<b>输入:</b>words = [\"ab\",\"b\"]\n<b>输出:</b>2\n<b>解释:</b>这个例子中str<sub>0</sub> = \"ab\",可以得到两个不同的 str<sub>1</sub>\njoin(str<sub>0</sub>, \"b\") = \"ab\" 或者 join(\"b\", str<sub>0</sub>) = \"bab\" 。\n第一个字符串 \"ab\" 的长度最短,所以答案为 2 。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre>\n<b>输入:</b>words = [\"aaa\",\"c\",\"aba\"]\n<b>输出:</b>6\n<b>解释:</b>这个例子中,我们按以下顺序执行连接操作,得到 <code>str<sub>2</sub>&nbsp;的最小长度:</code>\n<code>str<sub>0</sub> = \"</code>aaa\"\n<code>str<sub>1</sub> = join(str<sub>0</sub>, \"c\") = \"aaac\"</code>\n<code>str<sub>2</sub> = join(\"aba\", str<sub>1</sub>) = \"abaaac\"</code>\n<code>str<sub>2</sub></code> 的最小长度为 6 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= words.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= words[i].length &lt;= 50</code></li>\n\t<li><code>words[i]</code>&nbsp;中只包含小写英文字母。</li>\n</ul>\n",
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"Notice that the first and last characters of a string are sufficient to determine the length of its concatenation with any other string.",
"Define dp[i][first][last] as the shortest concatenation length of the first i words starting with a character first and ending with a character last. Convert characters to their ASCII codes if your programming language cannot implicitly convert them to array indices."
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