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"categoryTitle": "Algorithms",
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"title": "Number of Great Partitions",
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"content": "<p>You are given an array <code>nums</code> consisting of <strong>positive</strong> integers and an integer <code>k</code>.</p>\n\n<p><strong>Partition</strong> the array into two ordered <strong>groups</strong> such that each element is in exactly <strong>one</strong> group. A partition is called great if the <strong>sum</strong> of elements of each group is greater than or equal to <code>k</code>.</p>\n\n<p>Return <em>the number of <strong>distinct</strong> great partitions</em>. Since the answer may be too large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>Two partitions are considered distinct if some element <code>nums[i]</code> is in different groups in the two partitions.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,4], k = 4\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> The great partitions are: ([1,2,3], [4]), ([1,3], [2,4]), ([1,4], [2,3]), ([2,3], [1,4]), ([2,4], [1,3]) and ([4], [1,2,3]).\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,3,3], k = 4\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There are no great partitions for this array.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [6,6], k = 2\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> We can either put nums[0] in the first partition or in the second partition.\nThe great partitions will be ([6], [6]) and ([6], [6]).\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length, k &lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
"translatedTitle": "好分区的数目",
"translatedContent": "<p>给你一个正整数数组 <code>nums</code> 和一个整数 <code>k</code> 。</p>\n\n<p><strong>分区</strong> 的定义是:将数组划分成两个有序的 <strong>组</strong> ,并满足每个元素 <strong>恰好</strong> 存在于 <strong>某一个</strong> 组中。如果分区中每个组的元素和都大于等于 <code>k</code> ,则认为分区是一个好分区。</p>\n\n<p>返回 <strong>不同</strong> 的好分区的数目。由于答案可能很大,请返回对 <code>10<sup>9</sup> + 7</code> <strong>取余</strong> 后的结果。</p>\n\n<p>如果在两个分区中,存在某个元素 <code>nums[i]</code> 被分在不同的组中,则认为这两个分区不同。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<strong>输入:</strong>nums = [1,2,3,4], k = 4\n<strong>输出:</strong>6\n<strong>解释:</strong>好分区的情况是 ([1,2,3], [4]), ([1,3], [2,4]), ([1,4], [2,3]), ([2,3], [1,4]), ([2,4], [1,3]) 和 ([4], [1,2,3]) 。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>nums = [3,3,3], k = 4\n<strong>输出:</strong>0\n<strong>解释:</strong>数组中不存在好分区。\n</pre>\n\n<p><strong class=\"example\">示例 3</strong></p>\n\n<pre>\n<strong>输入:</strong>nums = [6,6], k = 2\n<strong>输出:</strong>2\n<strong>解释:</strong>可以将 nums[0] 放入第一个分区或第二个分区中。\n好分区的情况是 ([6], [6]) 和 ([6], [6]) 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length, k &lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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"If the sum of the array is smaller than 2*k, then it is impossible to find a great partition.",
"Solve the reverse problem, that is, find the number of partitions where the sum of elements of at least one of the two groups is smaller than k."
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