leetcode-problemset/leetcode-cn/originData/find-all-possible-stable-binary-arrays-i.json

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        "question": {
            "questionId": "3406",
            "questionFrontendId": "3129",
            "categoryTitle": "Algorithms",
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            "title": "Find All Possible Stable Binary Arrays I",
            "titleSlug": "find-all-possible-stable-binary-arrays-i",
            "content": "<p>You are given 3 positive integers <code>zero</code>, <code>one</code>, and <code>limit</code>.</p>\n\n<p>A <span data-keyword=\"binary-array\">binary array</span> <code>arr</code> is called <strong>stable</strong> if:</p>\n\n<ul>\n\t<li>The number of occurrences of 0 in <code>arr</code> is <strong>exactly </strong><code>zero</code>.</li>\n\t<li>The number of occurrences of 1 in <code>arr</code> is <strong>exactly</strong> <code>one</code>.</li>\n\t<li>Each <span data-keyword=\"subarray-nonempty\">subarray</span> of <code>arr</code> with a size greater than <code>limit</code> must contain <strong>both </strong>0 and 1.</li>\n</ul>\n\n<p>Return the <em>total</em> number of <strong>stable</strong> binary arrays.</p>\n\n<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</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\">zero = 1, one = 1, limit = 2</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>The two possible stable binary arrays are <code>[1,0]</code> and <code>[0,1]</code>, as both arrays have a single 0 and a single 1, and no subarray has a length greater than 2.</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\">zero = 1, one = 2, limit = 1</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">1</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The only possible stable binary array is <code>[1,0,1]</code>.</p>\n\n<p>Note that the binary arrays <code>[1,1,0]</code> and <code>[0,1,1]</code> have subarrays of length 2 with identical elements, hence, they are not stable.</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\">zero = 3, one = 3, limit = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">14</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>All the possible stable binary arrays are <code>[0,0,1,0,1,1]</code>, <code>[0,0,1,1,0,1]</code>, <code>[0,1,0,0,1,1]</code>, <code>[0,1,0,1,0,1]</code>, <code>[0,1,0,1,1,0]</code>, <code>[0,1,1,0,0,1]</code>, <code>[0,1,1,0,1,0]</code>, <code>[1,0,0,1,0,1]</code>, <code>[1,0,0,1,1,0]</code>, <code>[1,0,1,0,0,1]</code>, <code>[1,0,1,0,1,0]</code>, <code>[1,0,1,1,0,0]</code>, <code>[1,1,0,0,1,0]</code>, and <code>[1,1,0,1,0,0]</code>.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= zero, one, limit &lt;= 200</code></li>\n</ul>\n",
            "translatedTitle": "找出所有稳定的二进制数组 I",
            "translatedContent": "<p>给你 3 个正整数&nbsp;<code>zero</code>&nbsp;，<code>one</code>&nbsp;和&nbsp;<code>limit</code>&nbsp;。</p>\n\n<p>一个 <span data-keyword=\"binary-array\">二进制数组</span> <code>arr</code> 如果满足以下条件，那么我们称它是 <strong>稳定的</strong> ：</p>\n\n<ul>\n\t<li>0 在&nbsp;<code>arr</code>&nbsp;中出现次数 <strong>恰好</strong>&nbsp;为<strong>&nbsp;</strong><code>zero</code>&nbsp;。</li>\n\t<li>1 在&nbsp;<code>arr</code>&nbsp;中出现次数 <strong>恰好</strong>&nbsp;为&nbsp;<code>one</code>&nbsp;。</li>\n\t<li><code>arr</code> 中每个长度超过 <code>limit</code>&nbsp;的 <span data-keyword=\"subarray-nonempty\">子数组</span> 都 <strong>同时</strong> 包含 0 和 1 。</li>\n</ul>\n\n<p>请你返回 <strong>稳定</strong>&nbsp;二进制数组的 <em>总</em> 数目。</p>\n\n<p>由于答案可能很大，将它对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<b>取余</b>&nbsp;后返回。</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><span class=\"example-io\"><b>输入：</b>zero = 1, one = 1, limit = 2</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>2</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>两个稳定的二进制数组为&nbsp;<code>[1,0]</code> 和&nbsp;<code>[0,1]</code>&nbsp;，两个数组都有一个 0 和一个 1 ，且没有子数组长度大于 2 。</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\">zero = 1, one = 2, limit = 1</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>1</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>唯一稳定的二进制数组是&nbsp;<code>[1,0,1]</code>&nbsp;。</p>\n\n<p>二进制数组&nbsp;<code>[1,1,0]</code> 和&nbsp;<code>[0,1,1]</code>&nbsp;都有长度为 2 且元素全都相同的子数组，所以它们不稳定。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>zero = 3, one = 3, limit = 2</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>14</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>所有稳定的二进制数组包括&nbsp;<code>[0,0,1,0,1,1]</code>&nbsp;，<code>[0,0,1,1,0,1]</code>&nbsp;，<code>[0,1,0,0,1,1]</code>&nbsp;，<code>[0,1,0,1,0,1]</code>&nbsp;，<code>[0,1,0,1,1,0]</code>&nbsp;，<code>[0,1,1,0,0,1]</code>&nbsp;，<code>[0,1,1,0,1,0]</code>&nbsp;，<code>[1,0,0,1,0,1]</code>&nbsp;，<code>[1,0,0,1,1,0]</code>&nbsp;，<code>[1,0,1,0,0,1]</code>&nbsp;，<code>[1,0,1,0,1,0]</code>&nbsp;，<code>[1,0,1,1,0,0]</code>&nbsp;，<code>[1,1,0,0,1,0]</code>&nbsp;和&nbsp;<code>[1,1,0,1,0,0]</code>&nbsp;。</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;= zero, one, limit &lt;= 200</code></li>\n</ul>\n",
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                "Let <code>dp[a][b][c = 0/1][d]</code> be the number of stable arrays with exactly <code>a</code> 0s, <code>b</code> 1s and consecutive <code>d</code> value of <code>c</code>’s at the end.",
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