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            "questionId": "3479",
            "questionFrontendId": "3234",
            "categoryTitle": "Algorithms",
            "boundTopicId": 2859186,
            "title": "Count the Number of Substrings With Dominant Ones",
            "titleSlug": "count-the-number-of-substrings-with-dominant-ones",
            "content": "<p>You are given a binary string <code>s</code>.</p>\n\n<p>Return the number of <span data-keyword=\"substring-nonempty\">substrings</span> with <strong>dominant</strong> ones.</p>\n\n<p>A string has <strong>dominant</strong> ones if the number of ones in the string is <strong>greater than or equal to</strong> the <strong>square</strong> of the number of zeros in the string.</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;00011&quot;</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The substrings with dominant ones are shown in the table below.</p>\n</div>\n\n<table>\n\t<thead>\n\t\t<tr>\n\t\t\t<th>i</th>\n\t\t\t<th>j</th>\n\t\t\t<th>s[i..j]</th>\n\t\t\t<th>Number of Zeros</th>\n\t\t\t<th>Number of Ones</th>\n\t\t</tr>\n\t</thead>\n\t<tbody>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>3</td>\n\t\t\t<td>1</td>\n\t\t\t<td>0</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>4</td>\n\t\t\t<td>4</td>\n\t\t\t<td>1</td>\n\t\t\t<td>0</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>3</td>\n\t\t\t<td>01</td>\n\t\t\t<td>1</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>4</td>\n\t\t\t<td>11</td>\n\t\t\t<td>0</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>4</td>\n\t\t\t<td>011</td>\n\t\t\t<td>1</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t</tbody>\n</table>\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;101101&quot;</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">16</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The substrings with <strong>non-dominant</strong> ones are shown in the table below.</p>\n\n<p>Since there are 21 substrings total and 5 of them have non-dominant ones, it follows that there are 16 substrings with dominant ones.</p>\n</div>\n\n<table>\n\t<thead>\n\t\t<tr>\n\t\t\t<th>i</th>\n\t\t\t<th>j</th>\n\t\t\t<th>s[i..j]</th>\n\t\t\t<th>Number of Zeros</th>\n\t\t\t<th>Number of Ones</th>\n\t\t</tr>\n\t</thead>\n\t<tbody>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>1</td>\n\t\t\t<td>0</td>\n\t\t\t<td>1</td>\n\t\t\t<td>0</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>4</td>\n\t\t\t<td>4</td>\n\t\t\t<td>0</td>\n\t\t\t<td>1</td>\n\t\t\t<td>0</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>4</td>\n\t\t\t<td>0110</td>\n\t\t\t<td>2</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>0</td>\n\t\t\t<td>4</td>\n\t\t\t<td>10110</td>\n\t\t\t<td>2</td>\n\t\t\t<td>3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>5</td>\n\t\t\t<td>01101</td>\n\t\t\t<td>2</td>\n\t\t\t<td>3</td>\n\t\t</tr>\n\t</tbody>\n</table>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= s.length &lt;= 4 * 10<sup>4</sup></code></li>\n\t<li><code>s</code> consists only of characters <code>&#39;0&#39;</code> and <code>&#39;1&#39;</code>.</li>\n</ul>\n",
            "translatedTitle": "统计 1 显著的字符串的数量",
            "translatedContent": "<p>给你一个二进制字符串 <code>s</code>。</p>\n\n<p>请你统计并返回其中 <strong>1 显著 </strong> 的 <span data-keyword=\"substring-nonempty\">子字符串</span> 的数量。</p>\n\n<p>如果字符串中 1 的数量 <strong>大于或等于</strong> 0 的数量的 <strong>平方</strong>，则认为该字符串是一个 <strong>1 显著</strong> 的字符串 。</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 = \"00011\"</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">5</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>1 显著的子字符串如下表所示。</p>\n</div>\n\n<table>\n\t<thead>\n\t\t<tr>\n\t\t\t<th>i</th>\n\t\t\t<th>j</th>\n\t\t\t<th>s[i..j]</th>\n\t\t\t<th>0 的数量</th>\n\t\t\t<th>1 的数量</th>\n\t\t</tr>\n\t</thead>\n\t<tbody>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>3</td>\n\t\t\t<td>1</td>\n\t\t\t<td>0</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>4</td>\n\t\t\t<td>4</td>\n\t\t\t<td>1</td>\n\t\t\t<td>0</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>3</td>\n\t\t\t<td>01</td>\n\t\t\t<td>1</td>\n\t\t\t<td>1</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>3</td>\n\t\t\t<td>4</td>\n\t\t\t<td>11</td>\n\t\t\t<td>0</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>2</td>\n\t\t\t<td>4</td>\n\t\t\t<td>011</td>\n\t\t\t<td>1</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t</tbody>\n</table>\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 = \"101101\"</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">16</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>1 不显著的子字符串如下表所示。</p>\n\n<p>总共有 21 个子字符串，其中 5 个是 1 不显著字符串，因此有 16 个 1 显著子字符串。</p>\n</div>\n\n<table>\n\t<thead>\n\t\t<tr>\n\t\t\t<th>i</th>\n\t\t\t<th>j</th>\n\t\t\t<th>s[i..j]</th>\n\t\t\t<th>0 的数量</th>\n\t\t\t<th>1 的数量</th>\n\t\t</tr>\n\t</thead>\n\t<tbody>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>1</td>\n\t\t\t<td>0</td>\n\t\t\t<td>1</td>\n\t\t\t<td>0</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>4</td>\n\t\t\t<td>4</td>\n\t\t\t<td>0</td>\n\t\t\t<td>1</td>\n\t\t\t<td>0</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>4</td>\n\t\t\t<td>0110</td>\n\t\t\t<td>2</td>\n\t\t\t<td>2</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>0</td>\n\t\t\t<td>4</td>\n\t\t\t<td>10110</td>\n\t\t\t<td>2</td>\n\t\t\t<td>3</td>\n\t\t</tr>\n\t\t<tr>\n\t\t\t<td>1</td>\n\t\t\t<td>5</td>\n\t\t\t<td>01101</td>\n\t\t\t<td>2</td>\n\t\t\t<td>3</td>\n\t\t</tr>\n\t</tbody>\n</table>\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;= 4 * 10<sup>4</sup></code></li>\n\t<li><code>s</code> 仅包含字符 <code>'0'</code> 和 <code>'1'</code>。</li>\n</ul>\n",
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                "Let us fix the starting index <code>l</code> of the substring and count the number of indices <code>r</code> such that <code>l <= r</code> and the substring <code>s[l..r]</code> has dominant ones.",
                "A substring with dominant ones has at most <code>sqrt(n)</code> zeros.",
                "We cannot iterate over every <code>r</code> and check if the  <code>s[l..r]</code> has dominant ones. Instead, we iterate over the next <code>sqrt(n)</code> zeros to the left of <code>l</code> and count the number of substrings with dominant ones where the current zero is the rightmost zero of the substring."
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<code>out-of-bounds<\\/code> \\u548c <code>use-after-free<\\/code> \\u9519\\u8bef\\u3002<\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u60f3\\u4f7f\\u7528\\u54c8\\u5e0c\\u8868\\u8fd0\\u7b97, \\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 <a href=\\\"https:\\/\\/troydhanson.github.io\\/uthash\\/\\\" target=\\\"_blank\\\">uthash<\\/a>\\u3002 \\\"uthash.h\\\"\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5bfc\\u5165\\u3002\\u8bf7\\u770b\\u5982\\u4e0b\\u793a\\u4f8b:<\\/p>\\r\\n\\r\\n<p><b>1. \\u5f80\\u54c8\\u5e0c\\u8868\\u4e2d\\u6dfb\\u52a0\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n<pre>\\r\\nstruct hash_entry {\\r\\n    int id;            \\/* we'll use this field as the key *\\/\\r\\n    char name[10];\\r\\n    UT_hash_handle hh; \\/* makes this structure hashable *\\/\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = 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