|
| 1 | +--- |
| 2 | +comments: true |
| 3 | +difficulty: 中等 |
| 4 | +edit_url: https://github.com/doocs/leetcode/edit/main/solution/3500-3599/3511.Make%20a%20Positive%20Array/README.md |
| 5 | +--- |
| 6 | + |
| 7 | +<!-- problem:start --> |
| 8 | + |
| 9 | +# [3511. 构造正数组 🔒](https://leetcode.cn/problems/make-a-positive-array) |
| 10 | + |
| 11 | +[English Version](/solution/3500-3599/3511.Make%20a%20Positive%20Array/README_EN.md) |
| 12 | + |
| 13 | +## 题目描述 |
| 14 | + |
| 15 | +<!-- description:start --> |
| 16 | + |
| 17 | +<p>给定一个数组 <code>nums</code>。一个数组被认为是 <strong>正</strong> 的,如果每个包含 <strong>超过两个</strong> 元素的 <strong><span data-keyword="subarray">子数组</span></strong> 的所有数字之和都是正数。</p> |
| 18 | + |
| 19 | +<p>您可以执行以下操作任意多次:</p> |
| 20 | + |
| 21 | +<ul> |
| 22 | + <li>用 -10<sup>18</sup> 和 10<sup>18 </sup>之间的任意整数替换 <code>nums</code> 中的 <strong>一个</strong> 元素。</li> |
| 23 | +</ul> |
| 24 | + |
| 25 | +<p>找到使 <code>nums</code> 变为正数组所需的最小操作数。</p> |
| 26 | + |
| 27 | +<p> </p> |
| 28 | + |
| 29 | +<p><strong class="example">示例 1:</strong></p> |
| 30 | + |
| 31 | +<div class="example-block"> |
| 32 | +<p><span class="example-io"><b>输入:</b>nums = [-10,15,-12]</span></p> |
| 33 | + |
| 34 | +<p><span class="example-io"><b>输出:</b>1</span></p> |
| 35 | + |
| 36 | +<p><strong>解释:</strong></p> |
| 37 | + |
| 38 | +<p>唯一有超过 2 个元素的子数组是这个数组本身。所有元素的和是 <code>(-10) + 15 + (-12) = -7</code>。通过将 <code>nums[0]</code> 替换为 0,新的和变为 <code>0 + 15 + (-12) = 3</code>。因此,现在数组是正的。</p> |
| 39 | +</div> |
| 40 | + |
| 41 | +<p><strong class="example">示例 2:</strong></p> |
| 42 | + |
| 43 | +<div class="example-block"> |
| 44 | +<p><span class="example-io"><b>输入:</b>nums = [-1,-2,3,-1,2,6]</span></p> |
| 45 | + |
| 46 | +<p><strong>输出:</strong><span class="example-io">1</span></p> |
| 47 | + |
| 48 | +<p><strong>解释:</strong></p> |
| 49 | + |
| 50 | +<p>具有 2 个以上元素且和非正的子数组是:</p> |
| 51 | + |
| 52 | +<table style="border: 1px solid black;"> |
| 53 | + <tbody> |
| 54 | + <tr> |
| 55 | + <th style="border: 1px solid black;">子数组下标</th> |
| 56 | + <th style="border: 1px solid black;">子数组</th> |
| 57 | + <th style="border: 1px solid black;">和</th> |
| 58 | + <th style="border: 1px solid black;">替换后的子数组(令 nums[1] = 1)</th> |
| 59 | + <th style="border: 1px solid black;">新的和</th> |
| 60 | + </tr> |
| 61 | + <tr> |
| 62 | + <td style="border: 1px solid black;">nums[0...2]</td> |
| 63 | + <td style="border: 1px solid black;">[-1, -2, 3]</td> |
| 64 | + <td style="border: 1px solid black;">0</td> |
| 65 | + <td style="border: 1px solid black;">[-1, 1, 3]</td> |
| 66 | + <td style="border: 1px solid black;">3</td> |
| 67 | + </tr> |
| 68 | + <tr> |
| 69 | + <td style="border: 1px solid black;">nums[0...3]</td> |
| 70 | + <td style="border: 1px solid black;">[-1, -2, 3, -1]</td> |
| 71 | + <td style="border: 1px solid black;">-1</td> |
| 72 | + <td style="border: 1px solid black;">[-1, 1, 3, -1]</td> |
| 73 | + <td style="border: 1px solid black;">2</td> |
| 74 | + </tr> |
| 75 | + <tr> |
| 76 | + <td style="border: 1px solid black;">nums[1...3]</td> |
| 77 | + <td style="border: 1px solid black;">[-2, 3, -1]</td> |
| 78 | + <td style="border: 1px solid black;">0</td> |
| 79 | + <td style="border: 1px solid black;">[1, 3, -1]</td> |
| 80 | + <td style="border: 1px solid black;">3</td> |
| 81 | + </tr> |
| 82 | + </tbody> |
| 83 | +</table> |
| 84 | + |
| 85 | +<p>因此,<code>nums</code> 在一次操作后是正的。</p> |
| 86 | +</div> |
| 87 | + |
| 88 | +<p><strong class="example">示例 3:</strong></p> |
| 89 | + |
| 90 | +<div class="example-block"> |
| 91 | +<p><span class="example-io"><b>输入:</b>nums = [1,2,3]</span></p> |
| 92 | + |
| 93 | +<p><span class="example-io"><b>输出:</b>0</span></p> |
| 94 | + |
| 95 | +<p><strong>解释:</strong></p> |
| 96 | + |
| 97 | +<p>数组已经是正的,所以不需要操作。</p> |
| 98 | +</div> |
| 99 | + |
| 100 | +<p> </p> |
| 101 | + |
| 102 | +<p><strong>提示:</strong></p> |
| 103 | + |
| 104 | +<ul> |
| 105 | + <li><code>3 <= nums.length <= 10<sup>5</sup></code></li> |
| 106 | + <li><code>-10<sup>9</sup> <= nums[i] <= 10<sup>9</sup></code></li> |
| 107 | +</ul> |
| 108 | + |
| 109 | +<!-- description:end --> |
| 110 | + |
| 111 | +## 解法 |
| 112 | + |
| 113 | +<!-- solution:start --> |
| 114 | + |
| 115 | +### 方法一 |
| 116 | + |
| 117 | +<!-- tabs:start --> |
| 118 | + |
| 119 | +#### Python3 |
| 120 | + |
| 121 | +```python |
| 122 | + |
| 123 | +``` |
| 124 | + |
| 125 | +#### Java |
| 126 | + |
| 127 | +```java |
| 128 | + |
| 129 | +``` |
| 130 | + |
| 131 | +#### C++ |
| 132 | + |
| 133 | +```cpp |
| 134 | + |
| 135 | +``` |
| 136 | + |
| 137 | +#### Go |
| 138 | + |
| 139 | +```go |
| 140 | + |
| 141 | +``` |
| 142 | + |
| 143 | +<!-- tabs:end --> |
| 144 | + |
| 145 | +<!-- solution:end --> |
| 146 | + |
| 147 | +<!-- problem:end --> |
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