mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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188 lines
18 KiB
JSON
188 lines
18 KiB
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"title": "Count of Sub-Multisets With Bounded Sum",
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"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> </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> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 2 * 10<sup>4</sup></code></li>\n\t<li><code>0 <= nums[i] <= 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 <= l <= r <= 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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"Let <code>dp[x]</code> be the number of submultisets of <code>nums</code> with sum <code>x</code>.",
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"The answer to the problem is <code>dp[l] + dp[l+1] + … + dp[r]</code>.",
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"Use coin change dp to transition between states."
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