leetcode-problemset/leetcode-cn/originData/number-of-ways-to-select-buildings.json

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            "categoryTitle": "Algorithms",
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            "title": "Number of Ways to Select Buildings",
            "titleSlug": "number-of-ways-to-select-buildings",
            "content": "<p>You are given a <strong>0-indexed</strong> binary string <code>s</code> which represents the types of buildings along a street where:</p>\n\n<ul>\n\t<li><code>s[i] = &#39;0&#39;</code> denotes that the <code>i<sup>th</sup></code> building is an office and</li>\n\t<li><code>s[i] = &#39;1&#39;</code> denotes that the <code>i<sup>th</sup></code> building is a restaurant.</li>\n</ul>\n\n<p>As a city official, you would like to <strong>select</strong> 3 buildings for random inspection. However, to ensure variety, <strong>no two consecutive</strong> buildings out of the <strong>selected</strong> buildings can be of the same type.</p>\n\n<ul>\n\t<li>For example, given <code>s = &quot;0<u><strong>0</strong></u>1<u><strong>1</strong></u>0<u><strong>1</strong></u>&quot;</code>, we cannot select the <code>1<sup>st</sup></code>, <code>3<sup>rd</sup></code>, and <code>5<sup>th</sup></code> buildings as that would form <code>&quot;0<strong><u>11</u></strong>&quot;</code> which is <strong>not</strong> allowed due to having two consecutive buildings of the same type.</li>\n</ul>\n\n<p>Return <em>the <b>number of valid ways</b> to select 3 buildings.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;001101&quot;\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> \nThe following sets of indices selected are valid:\n- [0,2,4] from &quot;<u><strong>0</strong></u>0<strong><u>1</u></strong>1<strong><u>0</u></strong>1&quot; forms &quot;010&quot;\n- [0,3,4] from &quot;<u><strong>0</strong></u>01<u><strong>10</strong></u>1&quot; forms &quot;010&quot;\n- [1,2,4] from &quot;0<u><strong>01</strong></u>1<u><strong>0</strong></u>1&quot; forms &quot;010&quot;\n- [1,3,4] from &quot;0<u><strong>0</strong></u>1<u><strong>10</strong></u>1&quot; forms &quot;010&quot;\n- [2,4,5] from &quot;00<u><strong>1</strong></u>1<u><strong>01</strong></u>&quot; forms &quot;101&quot;\n- [3,4,5] from &quot;001<u><strong>101</strong></u>&quot; forms &quot;101&quot;\nNo other selection is valid. Thus, there are 6 total ways.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;11100&quot;\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> It can be shown that there are no valid selections.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= s.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>\n</ul>\n",
            "translatedTitle": "选择建筑的方案数",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的二进制字符串&nbsp;<code>s</code>&nbsp;，它表示一条街沿途的建筑类型，其中：</p>\n\n<ul>\n\t<li><code>s[i] = '0'</code>&nbsp;表示第&nbsp;<code>i</code>&nbsp;栋建筑是一栋办公楼，</li>\n\t<li><code>s[i] = '1'</code>&nbsp;表示第&nbsp;<code>i</code>&nbsp;栋建筑是一间餐厅。</li>\n</ul>\n\n<p>作为市政厅的官员，你需要随机<strong>&nbsp;选择</strong>&nbsp;3 栋建筑。然而，为了确保多样性，选出来的 3 栋建筑 <strong>相邻</strong>&nbsp;的两栋不能是同一类型。</p>\n\n<ul>\n\t<li>比方说，给你&nbsp;<code>s = \"0<em><strong>0</strong></em>1<em><strong>1</strong></em>0<em><strong>1</strong></em>\"</code>&nbsp;，我们不能选择第&nbsp;<code>1</code>&nbsp;，<code>3</code>&nbsp;和&nbsp;<code>5</code>&nbsp;栋建筑，因为得到的子序列是&nbsp;<code>\"0<em><strong>11</strong></em>\"</code>&nbsp;，有相邻两栋建筑是同一类型，所以 <strong>不合</strong>&nbsp;题意。</li>\n</ul>\n\n<p>请你返回可以选择 3 栋建筑的 <strong>有效方案数</strong>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>s = \"001101\"\n<b>输出：</b>6\n<b>解释：</b>\n以下下标集合是合法的：\n- [0,2,4] ，从 \"<em><strong>0</strong></em>0<em><strong>1</strong></em>1<em><strong>0</strong></em>1\" 得到 \"010\"\n- [0,3,4] ，从 \"<em><strong>0</strong></em>01<em><strong>10</strong></em>1\" 得到 \"010\"\n- [1,2,4] ，从 \"0<em><strong>01</strong></em>1<em><strong>0</strong></em>1\" 得到 \"010\"\n- [1,3,4] ，从 \"0<em><strong>0</strong></em>1<em><strong>10</strong></em>1\" 得到 \"010\"\n- [2,4,5] ，从 \"00<em><strong>1</strong></em>1<em><strong>01</strong></em>\" 得到 \"101\"\n- [3,4,5] ，从 \"001<em><strong>101</strong></em>\" 得到 \"101\"\n没有别的合法选择，所以总共有 6 种方法。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>s = \"11100\"\n<b>输出：</b>0\n<b>解释：</b>没有任何符合题意的选择。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= s.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>s[i]</code>&nbsp;要么是&nbsp;<code>'0'</code>&nbsp;，要么是&nbsp;<code>'1'</code>&nbsp;。</li>\n</ul>\n",
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            "hints": [
                "There are only 2 valid patterns: ‘101’ and ‘010’. Think about how we can construct these 2 patterns from smaller patterns.",
                "Count the number of subsequences of the form ‘01’ or ‘10’ first. Let n01[i] be the number of ‘01’ subsequences that exist in the prefix of s up to the ith building. How can you compute n01[i]?",
                "Let n0[i] and n1[i] be the number of ‘0’s and ‘1’s that exists in the prefix of s up to i respectively. Then n01[i] = n01[i – 1] if s[i] == ‘0’, otherwise n01[i] = n01[i – 1] + n0[i – 1].",
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