leetcode-problemset/leetcode-cn/originData/count-of-sub-multisets-with-bounded-sum.json

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            "questionId": "3091",
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            "categoryTitle": "Algorithms",
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            "title": "Count of Sub-Multisets With Bounded Sum",
            "titleSlug": "count-of-sub-multisets-with-bounded-sum",
            "content": "<p>You are given a <strong>0-indexed</strong> array <code>nums</code> of non-negative integers, and two integers <code>l</code> and <code>r</code>.</p>\n\n<p>Return <em>the <strong>count of sub-multisets</strong> within</em> <code>nums</code> <em>where the sum of elements in each subset falls within the inclusive range of</em> <code>[l, r]</code>.</p>\n\n<p>Since the answer may be large, return it modulo <code>10<sup>9 </sup>+ 7</code>.</p>\n\n<p>A <strong>sub-multiset</strong> is an <strong>unordered</strong> collection of elements of the array in which a given value <code>x</code> can occur <code>0, 1, ..., occ[x]</code> times, where <code>occ[x]</code> is the number of occurrences of <code>x</code> in the array.</p>\n\n<p><strong>Note</strong> that:</p>\n\n<ul>\n\t<li>Two <strong>sub-multisets</strong> are the same if sorting both sub-multisets results in identical multisets.</li>\n\t<li>The sum of an <strong>empty</strong> multiset is <code>0</code>.</li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,2,3], l = 6, r = 6\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> The only subset of nums that has a sum of 6 is {1, 2, 3}.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,1,4,2,7], l = 1, r = 5\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> The subsets of nums that have a sum within the range [1, 5] are {1}, {2}, {4}, {2, 2}, {1, 2}, {1, 4}, and {1, 2, 2}.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,1,3,5,2], l = 3, r = 5\n<strong>Output:</strong> 9\n<strong>Explanation:</strong> The subsets of nums that have a sum within the range [3, 5] are {3}, {5}, {1, 2}, {1, 3}, {2, 2}, {2, 3}, {1, 1, 2}, {1, 1, 3}, and {1, 2, 2}.</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 2 * 10<sup>4</sup></code></li>\n\t<li>Sum of <code>nums</code> does not exceed <code>2 * 10<sup>4</sup></code>.</li>\n\t<li><code>0 &lt;= l &lt;= r &lt;= 2 * 10<sup>4</sup></code></li>\n</ul>\n",
            "translatedTitle": "和带限制的子多重集合的数目",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的非负整数数组&nbsp;<code>nums</code>&nbsp;和两个整数&nbsp;<code>l</code> 和&nbsp;<code>r</code>&nbsp;。</p>\n\n<p>请你返回&nbsp;<code>nums</code>&nbsp;中子多重集合的和在闭区间&nbsp;<code>[l, r]</code>&nbsp;之间的 <strong>子多重集合的数目</strong> 。</p>\n\n<p>由于答案可能很大，请你将答案对&nbsp;<code>10<sup>9 </sup>+ 7</code>&nbsp;取余后返回。</p>\n\n<p><strong>子多重集合</strong> 指的是从数组中选出一些元素构成的 <strong>无序</strong>&nbsp;集合，每个元素 <code>x</code>&nbsp;出现的次数可以是&nbsp;<code>0, 1, ..., occ[x]</code>&nbsp;次，其中&nbsp;<code>occ[x]</code>&nbsp;是元素&nbsp;<code>x</code>&nbsp;在数组中的出现次数。</p>\n\n<p><b>注意：</b></p>\n\n<ul>\n\t<li>如果两个子多重集合中的元素排序后一模一样，那么它们两个是相同的&nbsp;<strong>子多重集合</strong>&nbsp;。</li>\n\t<li><strong>空</strong>&nbsp;集合的和是 <code>0</code>&nbsp;。</li>\n</ul>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [1,2,2,3], l = 6, r = 6\n<b>输出：</b>1\n<b>解释：</b>唯一和为 6 的子集合是 {1, 2, 3} 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [2,1,4,2,7], l = 1, r = 5\n<b>输出：</b>7\n<b>解释：</b>和在闭区间 [1, 5] 之间的子多重集合为 {1} ，{2} ，{4} ，{2, 2} ，{1, 2} ，{1, 4} 和 {1, 2, 2} 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [1,2,1,3,5,2], l = 3, r = 5\n<b>输出：</b>9\n<b>解释：</b>和在闭区间 [3, 5] 之间的子多重集合为 {3} ，{5} ，{1, 2} ，{1, 3} ，{2, 2} ，{2, 3} ，{1, 1, 2} ，{1, 1, 3} 和 {1, 2, 2} 。</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 &lt;= 2 * 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 2 * 10<sup>4</sup></code></li>\n\t<li><code>nums</code> 的和不超过&nbsp;<code>2 * 10<sup>4</sup></code> 。</li>\n\t<li><code>0 &lt;= l &lt;= r &lt;= 2 * 10<sup>4</sup></code></li>\n</ul>\n",
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                "Since the sum of <code>nums</code>is at most <code>20000</code>, the number of distinct elements of nums is <code>200</code>.",
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