leetcode-problemset/leetcode-cn/originData/palindrome-rearrangement-queries.json

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        "question": {
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            "title": "Palindrome Rearrangement Queries",
            "titleSlug": "palindrome-rearrangement-queries",
            "content": "<p>You are given a <strong>0-indexed</strong> string <code>s</code> having an <strong>even</strong> length <code>n</code>.</p>\n\n<p>You are also given a <strong>0-indexed</strong> 2D integer array, <code>queries</code>, where <code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>, c<sub>i</sub>, d<sub>i</sub>]</code>.</p>\n\n<p>For each query <code>i</code>, you are allowed to perform the following operations:</p>\n\n<ul>\n\t<li>Rearrange the characters within the <strong>substring</strong> <code>s[a<sub>i</sub>:b<sub>i</sub>]</code>, where <code>0 &lt;= a<sub>i</sub> &lt;= b<sub>i</sub> &lt; n / 2</code>.</li>\n\t<li>Rearrange the characters within the <strong>substring</strong> <code>s[c<sub>i</sub>:d<sub>i</sub>]</code>, where <code>n / 2 &lt;= c<sub>i</sub> &lt;= d<sub>i</sub> &lt; n</code>.</li>\n</ul>\n\n<p>For each query, your task is to determine whether it is possible to make <code>s</code> a <strong>palindrome</strong> by performing the operations.</p>\n\n<p>Each query is answered <strong>independently</strong> of the others.</p>\n\n<p>Return <em>a <strong>0-indexed</strong> array </em><code>answer</code><em>, where </em><code>answer[i] == true</code><em> if it is possible to make </em><code>s</code><em> a palindrome by performing operations specified by the </em><code>i<sup>th</sup></code><em> query, and </em><code>false</code><em> otherwise.</em></p>\n\n<ul>\n\t<li>A <strong>substring</strong> is a contiguous sequence of characters within a string.</li>\n\t<li><code>s[x:y]</code> represents the substring consisting of characters from the index <code>x</code> to index <code>y</code> in <code>s</code>, <strong>both inclusive</strong>.</li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;abcabc&quot;, queries = [[1,1,3,5],[0,2,5,5]]\n<strong>Output:</strong> [true,true]\n<strong>Explanation:</strong> In this example, there are two queries:\nIn the first query:\n- a<sub>0</sub> = 1, b<sub>0</sub> = 1, c<sub>0</sub> = 3, d<sub>0</sub> = 5.\n- So, you are allowed to rearrange s[1:1] =&gt; a<u>b</u>cabc and s[3:5] =&gt; abc<u>abc</u>.\n- To make s a palindrome, s[3:5] can be rearranged to become =&gt; abc<u>cba</u>.\n- Now, s is a palindrome. So, answer[0] = true.\nIn the second query:\n- a<sub>1</sub> = 0, b<sub>1</sub> = 2, c<sub>1</sub> = 5, d<sub>1</sub> = 5.\n- So, you are allowed to rearrange s[0:2] =&gt; <u>abc</u>abc and s[5:5] =&gt; abcab<u>c</u>.\n- To make s a palindrome, s[0:2] can be rearranged to become =&gt; <u>cba</u>abc.\n- Now, s is a palindrome. So, answer[1] = true.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;abbcdecbba&quot;, queries = [[0,2,7,9]]\n<strong>Output:</strong> [false]\n<strong>Explanation:</strong> In this example, there is only one query.\na<sub>0</sub> = 0, b<sub>0</sub> = 2, c<sub>0</sub> = 7, d<sub>0</sub> = 9.\nSo, you are allowed to rearrange s[0:2] =&gt; <u>abb</u>cdecbba and s[7:9] =&gt; abbcdec<u>bba</u>.\nIt is not possible to make s a palindrome by rearranging these substrings because s[3:6] is not a palindrome.\nSo, answer[0] = false.</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;acbcab&quot;, queries = [[1,2,4,5]]\n<strong>Output:</strong> [true]\n<strong>Explanation: </strong>In this example, there is only one query.\na<sub>0</sub> = 1, b<sub>0</sub> = 2, c<sub>0</sub> = 4, d<sub>0</sub> = 5.\nSo, you are allowed to rearrange s[1:2] =&gt; a<u>cb</u>cab and s[4:5] =&gt; acbc<u>ab</u>.\nTo make s a palindrome s[1:2] can be rearranged to become a<u>bc</u>cab.\nThen, s[4:5] can be rearranged to become abcc<u>ba</u>.\nNow, s is a palindrome. So, answer[0] = true.</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n == s.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= queries.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>queries[i].length == 4</code></li>\n\t<li><code>a<sub>i</sub> == queries[i][0], b<sub>i</sub> == queries[i][1]</code></li>\n\t<li><code>c<sub>i</sub> == queries[i][2], d<sub>i</sub> == queries[i][3]</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub> &lt;= b<sub>i</sub> &lt; n / 2</code></li>\n\t<li><code>n / 2 &lt;= c<sub>i</sub> &lt;= d<sub>i</sub> &lt; n </code></li>\n\t<li><code>n</code> is even.</li>\n\t<li><code>s</code> consists of only lowercase English letters.</li>\n</ul>\n",
            "translatedTitle": "回文串重新排列查询",
            "translatedContent": "<p>给你一个长度为 <strong>偶数</strong>&nbsp;<code>n</code>&nbsp;，下标从 <strong>0</strong>&nbsp;开始的字符串&nbsp;<code>s</code>&nbsp;。</p>\n\n<p>同时给你一个下标从 <strong>0</strong>&nbsp;开始的二维整数数组&nbsp;<code>queries</code>&nbsp;，其中&nbsp;<code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>, c<sub>i</sub>, d<sub>i</sub>]</code>&nbsp;。</p>\n\n<p>对于每个查询&nbsp;<code>i</code>&nbsp;，你需要执行以下操作：</p>\n\n<ul>\n\t<li>将下标在范围&nbsp;<code>0 &lt;= a<sub>i</sub> &lt;= b<sub>i</sub> &lt; n / 2</code>&nbsp;内的&nbsp;<strong>子字符串</strong>&nbsp;<code>s[a<sub>i</sub>:b<sub>i</sub>]</code>&nbsp;中的字符重新排列。</li>\n\t<li>将下标在范围 <code>n / 2 &lt;= c<sub>i</sub> &lt;= d<sub>i</sub> &lt; n</code>&nbsp;内的 <strong>子字符串</strong>&nbsp;<code>s[c<sub>i</sub>:d<sub>i</sub>]</code>&nbsp;中的字符重新排列。</li>\n</ul>\n\n<p>对于每个查询，你的任务是判断执行操作后能否让 <code>s</code>&nbsp;变成一个 <strong>回文串</strong> 。</p>\n\n<p>每个查询与其他查询都是 <strong>独立的</strong>&nbsp;。</p>\n\n<p>请你返回一个下标从 <strong>0</strong>&nbsp;开始的数组<em>&nbsp;</em><code>answer</code>&nbsp;，如果第&nbsp;<code>i</code>&nbsp;个查询执行操作后，可以将&nbsp;<code>s</code>&nbsp;变为一个回文串，那么<em>&nbsp;</em><code>answer[i] =&nbsp;true</code>，否则为<em>&nbsp;</em><code>false</code>&nbsp;。</p>\n\n<ul>\n\t<li><strong>子字符串</strong>&nbsp;指的是一个字符串中一段连续的字符序列。</li>\n\t<li><code>s[x:y]</code>&nbsp;表示 <code>s</code>&nbsp;中从下标 <code>x</code>&nbsp;到 <code>y</code>&nbsp;且两个端点 <strong>都包含</strong>&nbsp;的子字符串。</li>\n</ul>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>s = \"abcabc\", queries = [[1,1,3,5],[0,2,5,5]]\n<b>输出：</b>[true,true]\n<b>解释：</b>这个例子中，有 2 个查询：\n第一个查询：\n- a<sub>0</sub> = 1, b<sub>0</sub> = 1, c<sub>0</sub> = 3, d<sub>0</sub> = 5\n- 你可以重新排列 s[1:1] =&gt; a<em><strong>b</strong></em>cabc 和 s[3:5] =&gt; abc<em><strong>abc</strong></em>&nbsp;。\n- 为了让 s 变为回文串，s[3:5] 可以重新排列得到 =&gt; abc<strong><em>cba </em></strong>。\n- 现在 s 是一个回文串。所以 answer[0] = true 。\n第二个查询：\n- a<sub>1</sub> = 0, b<sub>1</sub> = 2, c<sub>1</sub> = 5, d<sub>1</sub> = 5.\n- 你可以重新排列 s[0:2] =&gt; <em><strong>abc</strong></em>abc 和 s[5:5] =&gt; abcab<strong><em>c</em></strong>&nbsp;。\n- 为了让 s 变为回文串，s[0:2] 可以重新排列得到 =&gt; <em><strong>cba</strong></em>abc 。\n- 现在 s 是一个回文串，所以 answer[1] = true 。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>s = \"abbcdecbba\", queries = [[0,2,7,9]]\n<b>输出：</b>[false]\n<b>解释：</b>这个示例中，只有一个查询。\na<sub>0</sub> = 0, b<sub>0</sub> = 2, c<sub>0</sub> = 7, d<sub>0</sub> = 9.\n你可以重新排列 s[0:2] =&gt; <em><strong>abb</strong></em>cdecbba 和 s[7:9] =&gt; abbcdec<em><strong>bba</strong></em>&nbsp;。\n无法通过重新排列这些子字符串使 s 变为一个回文串，因为 s[3:6] 不是一个回文串。\n所以 answer[0] = false 。</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>s = \"acbcab\", queries = [[1,2,4,5]]\n<b>输出：</b>[true]\n<strong>解释：</strong>这个示例中，只有一个查询。\na<sub>0</sub> = 1, b<sub>0</sub> = 2, c<sub>0</sub> = 4, d<sub>0</sub> = 5.\n你可以重新排列 s[1:2] =&gt; a<em><strong>cb</strong></em>cab 和 s[4:5] =&gt; acbc<strong><em>ab</em></strong>&nbsp;。\n为了让 s 变为回文串，s[1:2] 可以重新排列得到 =&gt; a<em><strong>bc</strong></em>cab<code>&nbsp;</code>。\n然后 s[4:5] 重新排列得到 abcc<em><strong>ba</strong></em>&nbsp;。\n现在 s 是一个回文串，所以 answer[0] = true 。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n == s.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= queries.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>queries[i].length == 4</code></li>\n\t<li><code>a<sub>i</sub> == queries[i][0], b<sub>i</sub> == queries[i][1]</code></li>\n\t<li><code>c<sub>i</sub> == queries[i][2], d<sub>i</sub> == queries[i][3]</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub> &lt;= b<sub>i</sub> &lt; n / 2</code></li>\n\t<li><code>n / 2 &lt;= c<sub>i</sub> &lt;= d<sub>i</sub> &lt; n </code></li>\n\t<li><code>n</code>&nbsp;是一个偶数。</li>\n\t<li><code>s</code> 只包含小写英文字母。</li>\n</ul>\n",
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                "Consider two indices, <code>x</code> on the left side and its symmetrical index <code>y</code> on the right side.",
                "Store the frequencies of all of the letters in both intervals <code>[a<sub>i</sub>, b<sub>i</sub>]</code> and <code>[c<sub>i</sub>, d<sub>i</sub>]</code> in a query.",
                "If <code>x</code> is not in <code>[a<sub>i</sub>, b<sub>i</sub>]</code> and <code>y</code> is not in <code>[c<sub>i</sub>, d<sub>i</sub>]</code>, they must be the same.",
                "If <code>x</code> is in <code>[a<sub>i</sub>, b<sub>i</sub>]</code> and <code>y</code> is not in <code>[c<sub>i</sub>, d<sub>i</sub>]</code>, remove one occurrence of the character at index <code>y</code> from the frequency array on the left side.",
                "Similarly, if <code>x</code> is not in <code>[a<sub>i</sub>, b<sub>i</sub>]</code> and <code>y</code> is in <code>[c<sub>i</sub>, d<sub>i</sub>]</code>, remove one occurrence of the character at index <code>x</code> from the frequency array on the right side.",
                "Finally, check whether the two frequency arrays are the same, and the indices that don't fall into any of the intervals are the same as well.",
                "Use prefix-sum + hashing to improve the time complexity."
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