|
| 1 | +--- |
| 2 | +comments: true |
| 3 | +difficulty: 简单 |
| 4 | +edit_url: https://github.com/doocs/leetcode/edit/main/solution/3300-3399/3364.Minimum%20Positive%20Sum%20Subarray/README.md |
| 5 | +--- |
| 6 | + |
| 7 | +<!-- problem:start --> |
| 8 | + |
| 9 | +# [3364. 最小正和子数组](https://leetcode.cn/problems/minimum-positive-sum-subarray) |
| 10 | + |
| 11 | +[English Version](/solution/3300-3399/3364.Minimum%20Positive%20Sum%20Subarray/README_EN.md) |
| 12 | + |
| 13 | +## 题目描述 |
| 14 | + |
| 15 | +<!-- description:start --> |
| 16 | + |
| 17 | +<p>给你一个整数数组 <code>nums</code> 和 <strong>两个</strong> 整数 <code>l</code> 和 <code>r</code>。你的任务是找到一个长度在 <code>l</code> 和 <code>r</code> 之间(包含)且和大于 0 的 <strong>子数组</strong> 的 <strong>最小</strong> 和。</p> |
| 18 | + |
| 19 | +<p>返回满足条件的子数组的 <strong>最小</strong> 和。如果不存在这样的子数组,则返回 -1。</p> |
| 20 | + |
| 21 | +<p><strong>子数组</strong> 是数组中的一个连续 <b>非空</b> 元素序列。</p> |
| 22 | + |
| 23 | +<p> </p> |
| 24 | + |
| 25 | +<p><strong class="example">示例 1:</strong></p> |
| 26 | + |
| 27 | +<div class="example-block"> |
| 28 | +<p><strong>输入:</strong> <span class="example-io">nums = [3, -2, 1, 4], l = 2, r = 3</span></p> |
| 29 | + |
| 30 | +<p><strong>输出:</strong> <span class="example-io">1</span></p> |
| 31 | + |
| 32 | +<p><strong>解释:</strong></p> |
| 33 | + |
| 34 | +<p>长度在 <code>l = 2</code> 和 <code>r = 3</code> 之间且和大于 0 的子数组有:</p> |
| 35 | + |
| 36 | +<ul> |
| 37 | + <li><code>[3, -2]</code> 和为 1</li> |
| 38 | + <li><code>[1, 4]</code> 和为 5</li> |
| 39 | + <li><code>[3, -2, 1]</code> 和为 2</li> |
| 40 | + <li><code>[-2, 1, 4]</code> 和为 3</li> |
| 41 | +</ul> |
| 42 | + |
| 43 | +<p>其中,子数组 <code>[3, -2]</code> 的和为 1,是所有正和中最小的。因此,答案为 1。</p> |
| 44 | +</div> |
| 45 | + |
| 46 | +<p><strong class="example">示例 2:</strong></p> |
| 47 | + |
| 48 | +<div class="example-block"> |
| 49 | +<p><strong>输入:</strong> <span class="example-io">nums = [-2, 2, -3, 1], l = 2, r = 3</span></p> |
| 50 | + |
| 51 | +<p><strong>输出:</strong> <span class="example-io">-1</span></p> |
| 52 | + |
| 53 | +<p><strong>解释:</strong></p> |
| 54 | + |
| 55 | +<p>不存在长度在 <code>l</code> 和 <code>r</code> 之间且和大于 0 的子数组。因此,答案为 -1。</p> |
| 56 | +</div> |
| 57 | + |
| 58 | +<p><strong class="example">示例 3:</strong></p> |
| 59 | + |
| 60 | +<div class="example-block"> |
| 61 | +<p><strong>输入:</strong> <span class="example-io">nums = [1, 2, 3, 4], l = 2, r = 4</span></p> |
| 62 | + |
| 63 | +<p><strong>输出:</strong> <span class="example-io">3</span></p> |
| 64 | + |
| 65 | +<p><strong>解释:</strong></p> |
| 66 | + |
| 67 | +<p>子数组 <code>[1, 2]</code> 的长度为 2,和为 3,是所有正和中最小的。因此,答案为 3。</p> |
| 68 | +</div> |
| 69 | + |
| 70 | +<p> </p> |
| 71 | + |
| 72 | +<p><strong>提示:</strong></p> |
| 73 | + |
| 74 | +<ul> |
| 75 | + <li><code>1 <= nums.length <= 100</code></li> |
| 76 | + <li><code>1 <= l <= r <= nums.length</code></li> |
| 77 | + <li><code>-1000 <= nums[i] <= 1000</code></li> |
| 78 | +</ul> |
| 79 | + |
| 80 | +<!-- description:end --> |
| 81 | + |
| 82 | +## 解法 |
| 83 | + |
| 84 | +<!-- solution:start --> |
| 85 | + |
| 86 | +### 方法一:枚举 |
| 87 | + |
| 88 | +我们可以枚举子数组的左端点 $i$,然后在 $[i, n)$ 的区间内从左往右枚举右端点 $j$,计算区间 $[i, j]$ 的和 $s$,如果 $s$ 大于 0 且区间长度在 $[l, r]$ 之间,我们就更新答案。 |
| 89 | + |
| 90 | +最后,如果答案仍然是初始值,说明没有找到符合条件的子数组,返回 $-1$,否则返回答案。 |
| 91 | + |
| 92 | +时间复杂度 $O(n^2)$,其中 $n$ 是数组 $\textit{nums}$ 的长度。空间复杂度 $O(1)$。 |
| 93 | + |
| 94 | +<!-- tabs:start --> |
| 95 | + |
| 96 | +#### Python3 |
| 97 | + |
| 98 | +```python |
| 99 | +class Solution: |
| 100 | + def minimumSumSubarray(self, nums: List[int], l: int, r: int) -> int: |
| 101 | + n = len(nums) |
| 102 | + ans = inf |
| 103 | + for i in range(n): |
| 104 | + s = 0 |
| 105 | + for j in range(i, n): |
| 106 | + s += nums[j] |
| 107 | + if l <= j - i + 1 <= r and s > 0: |
| 108 | + ans = min(ans, s) |
| 109 | + return -1 if ans == inf else ans |
| 110 | +``` |
| 111 | + |
| 112 | +#### Java |
| 113 | + |
| 114 | +```java |
| 115 | +class Solution { |
| 116 | + public int minimumSumSubarray(List<Integer> nums, int l, int r) { |
| 117 | + int n = nums.size(); |
| 118 | + final int inf = Integer.MAX_VALUE; |
| 119 | + int ans = inf; |
| 120 | + for (int i = 0; i < n; ++i) { |
| 121 | + int s = 0; |
| 122 | + for (int j = i; j < n; ++j) { |
| 123 | + s += nums.get(j); |
| 124 | + int k = j - i + 1; |
| 125 | + if (k >= l && k <= r && s > 0) { |
| 126 | + ans = Math.min(ans, s); |
| 127 | + } |
| 128 | + } |
| 129 | + } |
| 130 | + return ans == inf ? -1 : ans; |
| 131 | + } |
| 132 | +} |
| 133 | +``` |
| 134 | + |
| 135 | +#### C++ |
| 136 | + |
| 137 | +```cpp |
| 138 | +class Solution { |
| 139 | +public: |
| 140 | + int minimumSumSubarray(vector<int>& nums, int l, int r) { |
| 141 | + int n = nums.size(); |
| 142 | + const int inf = INT_MAX; |
| 143 | + int ans = inf; |
| 144 | + for (int i = 0; i < n; ++i) { |
| 145 | + int s = 0; |
| 146 | + for (int j = i; j < n; ++j) { |
| 147 | + s += nums[j]; |
| 148 | + int k = j - i + 1; |
| 149 | + if (k >= l && k <= r && s > 0) { |
| 150 | + ans = min(ans, s); |
| 151 | + } |
| 152 | + } |
| 153 | + } |
| 154 | + return ans == inf ? -1 : ans; |
| 155 | + } |
| 156 | +}; |
| 157 | +``` |
| 158 | +
|
| 159 | +#### Go |
| 160 | +
|
| 161 | +```go |
| 162 | +func minimumSumSubarray(nums []int, l int, r int) int { |
| 163 | + const inf int = 1 << 30 |
| 164 | + ans := inf |
| 165 | + for i := range nums { |
| 166 | + s := 0 |
| 167 | + for j := i; j < len(nums); j++ { |
| 168 | + s += nums[j] |
| 169 | + k := j - i + 1 |
| 170 | + if k >= l && k <= r && s > 0 { |
| 171 | + ans = min(ans, s) |
| 172 | + } |
| 173 | + } |
| 174 | + } |
| 175 | + if ans == inf { |
| 176 | + return -1 |
| 177 | + } |
| 178 | + return ans |
| 179 | +} |
| 180 | +``` |
| 181 | + |
| 182 | +#### TypeScript |
| 183 | + |
| 184 | +```ts |
| 185 | +function minimumSumSubarray(nums: number[], l: number, r: number): number { |
| 186 | + const n = nums.length; |
| 187 | + let ans = Infinity; |
| 188 | + for (let i = 0; i < n; ++i) { |
| 189 | + let s = 0; |
| 190 | + for (let j = i; j < n; ++j) { |
| 191 | + s += nums[j]; |
| 192 | + const k = j - i + 1; |
| 193 | + if (k >= l && k <= r && s > 0) { |
| 194 | + ans = Math.min(ans, s); |
| 195 | + } |
| 196 | + } |
| 197 | + } |
| 198 | + return ans == Infinity ? -1 : ans; |
| 199 | +} |
| 200 | +``` |
| 201 | + |
| 202 | +<!-- tabs:end --> |
| 203 | + |
| 204 | +<!-- solution:end --> |
| 205 | + |
| 206 | +<!-- problem:end --> |
0 commit comments