leetcode-problemset/leetcode-cn/originData/length-of-the-longest-subsequence-that-sums-to-target.json

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            "categoryTitle": "Algorithms",
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            "title": "Length of the Longest Subsequence That Sums to Target",
            "titleSlug": "length-of-the-longest-subsequence-that-sums-to-target",
            "content": "<p>You are given a <strong>0-indexed</strong> array of integers <code>nums</code>, and an integer <code>target</code>.</p>\n\n<p>Return <em>the <strong>length of the longest subsequence</strong> of</em> <code>nums</code> <em>that sums up to</em> <code>target</code>. <em>If no such subsequence exists, return</em> <code>-1</code>.</p>\n\n<p>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,4,5], target = 9\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> There are 3 subsequences with a sum equal to 9: [4,5], [1,3,5], and [2,3,4]. The longest subsequences are [1,3,5], and [2,3,4]. Hence, the answer is 3.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [4,1,3,2,1,5], target = 7\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> There are 5 subsequences with a sum equal to 7: [4,3], [4,1,2], [4,2,1], [1,1,5], and [1,3,2,1]. The longest subsequence is [1,3,2,1]. Hence, the answer is 4.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,1,5,4,5], target = 3\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> It can be shown that nums has no subsequence that sums up to 3.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>\n\t<li><code>1 &lt;= target &lt;= 1000</code></li>\n</ul>\n",
            "translatedTitle": "和为目标值的最长子序列的长度",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>nums</code>&nbsp;和一个整数&nbsp;<code>target</code>&nbsp;。</p>\n\n<p>返回和为 <code>target</code>&nbsp;的 <code>nums</code>&nbsp;子序列中，子序列&nbsp;<strong>长度的最大值&nbsp;</strong>。如果不存在和为 <code>target</code>&nbsp;的子序列，返回 <code>-1</code>&nbsp;。</p>\n\n<p><strong>子序列</strong> 指的是从原数组中删除一些或者不删除任何元素后，剩余元素保持原来的顺序构成的数组。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [1,2,3,4,5], target = 9\n<b>输出：</b>3\n<b>解释：</b>总共有 3 个子序列的和为 9 ：[4,5] ，[1,3,5] 和 [2,3,4] 。最长的子序列是 [1,3,5] 和 [2,3,4] 。所以答案为 3 。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [4,1,3,2,1,5], target = 7\n<b>输出：</b>4\n<strong>解释：</strong>总共有 5 个子序列的和为 7 ：[4,3] ，[4,1,2] ，[4,2,1] ，[1,1,5] 和 [1,3,2,1] 。最长子序列为 [1,3,2,1] 。所以答案为 4 。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [1,1,5,4,5], target = 3\n<b>输出：</b>-1\n<b>解释：</b>无法得到和为 3 的子序列。\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 &lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>\n\t<li><code>1 &lt;= target &lt;= 1000</code></li>\n</ul>\n",
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            "hints": [
                "Use dynamic programming.",
                "Let <code>dp[i][j]</code> be the maximum length of any subsequence of <code>nums[0..i - 1]</code> that sums to <code>j</code>.",
                "<code>dp[0][0] = 1</code>, and <code>dp[0][j] = 1</code> for all <code>target ≥ j > 0</code>.",
                "<code>dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - nums[i -1])</code> for all <code>n ≥ i > 0</code> and <code>target ≥ j > nums[i - 1]</code>."
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