leetcode-problemset/leetcode-cn/originData/maximum-number-of-subsequences-after-one-inserting.json

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        "question": {
            "questionId": "3948",
            "questionFrontendId": "3628",
            "categoryTitle": "Algorithms",
            "boundTopicId": 3732707,
            "title": "Maximum Number of Subsequences After One Inserting",
            "titleSlug": "maximum-number-of-subsequences-after-one-inserting",
            "content": "<p>You are given a string <code>s</code> consisting of uppercase English letters.</p>\n\n<p>You are allowed to insert <strong>at most one</strong> uppercase English letter at <strong>any</strong> position (including the beginning or end) of the string.</p>\n\n<p>Return the <strong>maximum</strong> number of <code>&quot;LCT&quot;</code> <span data-keyword=\"subsequence-string-nonempty\">subsequences</span> that can be formed in the resulting string after <strong>at most one insertion</strong>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">s = &quot;LMCT&quot;</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>We can insert a <code>&quot;L&quot;</code> at the beginning of the string s to make <code>&quot;LLMCT&quot;</code>, which has 2 subsequences, at indices [0, 3, 4] and [1, 3, 4].</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">s = &quot;LCCT&quot;</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>We can insert a <code>&quot;L&quot;</code> at the beginning of the string s to make <code>&quot;LLCCT&quot;</code>, which has 4 subsequences, at indices [0, 2, 4], [0, 3, 4], [1, 2, 4] and [1, 3, 4].</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">s = &quot;L&quot;</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">0</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>Since it is not possible to obtain the subsequence <code>&quot;LCT&quot;</code> by inserting a single letter, the result is 0.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>s</code> consists of uppercase English letters.</li>\n</ul>\n",
            "translatedTitle": "插入一个字母的最大子序列数",
            "translatedContent": "<p>给你一个由大写英文字母组成的字符串 <code>s</code>。</p>\n\n<p>你可以在字符串的&nbsp;<strong>任意&nbsp;</strong>位置（包括字符串的开头或结尾）<strong>最多插入一个&nbsp;</strong>大写英文字母。</p>\n\n<p>返回在&nbsp;<strong>最多插入一个字母&nbsp;</strong>后，字符串中可以形成的 <code>\"LCT\"</code> 子序列的&nbsp;<strong>最大&nbsp;</strong>数量。</p>\n\n<p><strong>子序列&nbsp;</strong>是从另一个字符串中删除某些字符（可以不删除）且不改变剩余字符顺序后得到的一个&nbsp;<strong>非空&nbsp;</strong>字符串。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">s = \"LMCT\"</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>可以在字符串 <code>s</code> 的开头插入一个 <code>\"L\"</code>，变为 <code>\"LLMCT\"</code>，其中包含 2 个子序列，分别位于下标&nbsp;[0, 3, 4] 和 [1, 3, 4]。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">s = \"LCCT\"</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>可以在字符串 <code>s</code> 的开头插入一个 <code>\"L\"</code>，变为 <code>\"LLCCT\"</code>，其中包含 4 个子序列，分别位于下标&nbsp;[0, 2, 4]、[0, 3, 4]、[1, 2, 4] 和 [1, 3, 4]。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">s = \"L\"</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">0</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>插入一个字母无法获得子序列 <code>\"LCT\"</code>，结果为 0。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>s</code> 仅由大写英文字母组成。</li>\n</ul>\n",
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            "hints": [
                "Precompute <code>preL</code>, <code>preLC</code>, <code>sufT</code>, and <code>sufCT</code> arrays to count L’s, LC’s, T’s, and CT’s at each position.",
                "Compute <code>base</code> as the sum over all i of <code>preLC[i] * sufT[i]</code>.",
                "For each insert position i, compute gains <code>sufCT[i]</code> for ‘L’, <code>preL[i] * sufT[i]</code> for ‘C’, and <code>preLC[i]</code> for ‘T’, and take the maximum of <code>base</code> and <code>base + gain</code>."
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