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| 1 | +# [2389. 和有限的最长子序列](https://leetcode.cn/problems/longest-subsequence-with-limited-sum) |
| 2 | + |
| 3 | +[English Version](/solution/2300-2399/2389.Longest%20Subsequence%20With%20Limited%20Sum/README_EN.md) |
| 4 | + |
| 5 | +## 题目描述 |
| 6 | + |
| 7 | +<!-- 这里写题目描述 --> |
| 8 | + |
| 9 | +<p>给你一个长度为 <code>n</code> 的整数数组 <code>nums</code> ,和一个长度为 <code>m</code> 的整数数组 <code>queries</code> 。</p> |
| 10 | + |
| 11 | +<p>返回一个长度为 <code>m</code> 的数组<em> </em><code>answer</code><em> </em>,其中<em> </em><code>answer[i]</code><em> </em>是 <code>nums</code> 中<span style=""> </span>元素之和小于等于 <code>queries[i]</code> 的 <strong>子序列</strong> 的 <strong>最大</strong> 长度<span style=""> </span><span style=""> </span>。</p> |
| 12 | + |
| 13 | +<p><strong>子序列</strong> 是由一个数组删除某些元素(也可以不删除)但不改变剩余元素顺序得到的一个数组。</p> |
| 14 | + |
| 15 | +<p> </p> |
| 16 | + |
| 17 | +<p><strong>示例 1:</strong></p> |
| 18 | + |
| 19 | +<pre> |
| 20 | +<strong>输入:</strong>nums = [4,5,2,1], queries = [3,10,21] |
| 21 | +<strong>输出:</strong>[2,3,4] |
| 22 | +<strong>解释:</strong>queries 对应的 answer 如下: |
| 23 | +- 子序列 [2,1] 的和小于或等于 3 。可以证明满足题目要求的子序列的最大长度是 2 ,所以 answer[0] = 2 。 |
| 24 | +- 子序列 [4,5,1] 的和小于或等于 10 。可以证明满足题目要求的子序列的最大长度是 3 ,所以 answer[1] = 3 。 |
| 25 | +- 子序列 [4,5,2,1] 的和小于或等于 21 。可以证明满足题目要求的子序列的最大长度是 4 ,所以 answer[2] = 4 。 |
| 26 | +</pre> |
| 27 | + |
| 28 | +<p><strong>示例 2:</strong></p> |
| 29 | + |
| 30 | +<pre> |
| 31 | +<strong>输入:</strong>nums = [2,3,4,5], queries = [1] |
| 32 | +<strong>输出:</strong>[0] |
| 33 | +<strong>解释:</strong>空子序列是唯一一个满足元素和小于或等于 1 的子序列,所以 answer[0] = 0 。</pre> |
| 34 | + |
| 35 | +<p> </p> |
| 36 | + |
| 37 | +<p><strong>提示:</strong></p> |
| 38 | + |
| 39 | +<ul> |
| 40 | + <li><code>n == nums.length</code></li> |
| 41 | + <li><code>m == queries.length</code></li> |
| 42 | + <li><code>1 <= n, m <= 1000</code></li> |
| 43 | + <li><code>1 <= nums[i], queries[i] <= 10<sup>6</sup></code></li> |
| 44 | +</ul> |
| 45 | + |
| 46 | +## 解法 |
| 47 | + |
| 48 | +<!-- 这里可写通用的实现逻辑 --> |
| 49 | + |
| 50 | +**方法一:排序 + 前缀和 + 二分查找** |
| 51 | + |
| 52 | +将 `nums` 排序,对于每个 `queries[i]`,求出 `nums` 中所有元素之和小于等于 `queries[i]` 的子序列的最大长度。 |
| 53 | + |
| 54 | +时间复杂度 $O(n\log n + m\log n)$。其中 $n$ 为 `nums` 的长度,$m$ 为 `queries` 的长度。 |
| 55 | + |
| 56 | +<!-- tabs:start --> |
| 57 | + |
| 58 | +### **Python3** |
| 59 | + |
| 60 | +<!-- 这里可写当前语言的特殊实现逻辑 --> |
| 61 | + |
| 62 | +```python |
| 63 | +class Solution: |
| 64 | + def answerQueries(self, nums: List[int], queries: List[int]) -> List[int]: |
| 65 | + nums.sort() |
| 66 | + s = list(accumulate(nums)) |
| 67 | + return [bisect_right(s, v) for v in queries] |
| 68 | +``` |
| 69 | + |
| 70 | +### **Java** |
| 71 | + |
| 72 | +<!-- 这里可写当前语言的特殊实现逻辑 --> |
| 73 | + |
| 74 | +```java |
| 75 | +class Solution { |
| 76 | + public int[] answerQueries(int[] nums, int[] queries) { |
| 77 | + Arrays.sort(nums); |
| 78 | + int n = nums.length; |
| 79 | + int[] s = new int[n + 1]; |
| 80 | + for (int i = 0; i < n; ++i) { |
| 81 | + s[i + 1] = s[i] + nums[i]; |
| 82 | + } |
| 83 | + int m = queries.length; |
| 84 | + int[] ans = new int[m]; |
| 85 | + for (int i = 0; i < m; ++i) { |
| 86 | + ans[i] = search(s, queries[i]); |
| 87 | + } |
| 88 | + return ans; |
| 89 | + } |
| 90 | + |
| 91 | + private int search(int[] s, int v) { |
| 92 | + int left = 1, right = s.length; |
| 93 | + while (left < right) { |
| 94 | + int mid = (left + right) >> 1; |
| 95 | + if (s[mid] > v) { |
| 96 | + right = mid; |
| 97 | + } else { |
| 98 | + left = mid + 1; |
| 99 | + } |
| 100 | + } |
| 101 | + return left - 1; |
| 102 | + } |
| 103 | +} |
| 104 | +``` |
| 105 | + |
| 106 | +### **C++** |
| 107 | + |
| 108 | +```cpp |
| 109 | +class Solution { |
| 110 | +public: |
| 111 | + vector<int> answerQueries(vector<int>& nums, vector<int>& queries) { |
| 112 | + sort(nums.begin(), nums.end()); |
| 113 | + int n = nums.size(), m = queries.size(); |
| 114 | + vector<int> s(n + 1); |
| 115 | + for (int i = 0; i < n; ++i) { |
| 116 | + s[i + 1] = s[i] + nums[i]; |
| 117 | + } |
| 118 | + vector<int> ans(m); |
| 119 | + for (int i = 0; i < m; ++i) { |
| 120 | + ans[i] = upper_bound(s.begin() + 1, s.end(), queries[i]) - s.begin() - 1; |
| 121 | + } |
| 122 | + return ans; |
| 123 | + } |
| 124 | +}; |
| 125 | +``` |
| 126 | +
|
| 127 | +### **Go** |
| 128 | +
|
| 129 | +```go |
| 130 | +func answerQueries(nums []int, queries []int) []int { |
| 131 | + sort.Ints(nums) |
| 132 | + n, m := len(nums), len(queries) |
| 133 | + s := make([]int, n+1) |
| 134 | + for i, v := range nums { |
| 135 | + s[i+1] = s[i] + v |
| 136 | + } |
| 137 | + ans := make([]int, m) |
| 138 | + for i, v := range queries { |
| 139 | + left, right := 1, len(s) |
| 140 | + for left < right { |
| 141 | + mid := (left + right) >> 1 |
| 142 | + if s[mid] > v { |
| 143 | + right = mid |
| 144 | + } else { |
| 145 | + left = mid + 1 |
| 146 | + } |
| 147 | + } |
| 148 | + ans[i] = left - 1 |
| 149 | + } |
| 150 | + return ans |
| 151 | +} |
| 152 | +``` |
| 153 | + |
| 154 | +### **TypeScript** |
| 155 | + |
| 156 | +```ts |
| 157 | + |
| 158 | +``` |
| 159 | + |
| 160 | +### **...** |
| 161 | + |
| 162 | +``` |
| 163 | +
|
| 164 | +
|
| 165 | +``` |
| 166 | + |
| 167 | +<!-- tabs:end --> |
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