|
| 1 | +--- |
| 2 | +comments: true |
| 3 | +difficulty: 中等 |
| 4 | +edit_url: https://github.com/doocs/leetcode/edit/main/solution/3600-3699/3672.Sum%20of%20Weighted%20Modes%20in%20Subarrays/README.md |
| 5 | +--- |
| 6 | + |
| 7 | +<!-- problem:start --> |
| 8 | + |
| 9 | +# [3672. Sum of Weighted Modes in Subarrays 🔒](https://leetcode.cn/problems/sum-of-weighted-modes-in-subarrays) |
| 10 | + |
| 11 | +[English Version](/solution/3600-3699/3672.Sum%20of%20Weighted%20Modes%20in%20Subarrays/README_EN.md) |
| 12 | + |
| 13 | +## 题目描述 |
| 14 | + |
| 15 | +<!-- description:start --> |
| 16 | + |
| 17 | +<p>You are given an integer array <code>nums</code> and an integer <code>k</code>.</p> |
| 18 | + |
| 19 | +<p>For every <strong>subarray</strong> of length <code>k</code>:</p> |
| 20 | + |
| 21 | +<ul> |
| 22 | + <li>The <strong>mode</strong> is defined as the element with the <strong>highest frequency</strong>. If there are multiple choices for a mode, the <strong>smallest</strong> such element is taken.</li> |
| 23 | + <li>The <strong>weight</strong> is defined as <code>mode * frequency(mode)</code>.</li> |
| 24 | +</ul> |
| 25 | + |
| 26 | +<p>Return the <strong>sum</strong> of the weights of all <strong>subarrays</strong> of length <code>k</code>.</p> |
| 27 | + |
| 28 | +<p><strong>Note:</strong></p> |
| 29 | + |
| 30 | +<ul> |
| 31 | + <li>A <strong>subarray</strong> is a contiguous <strong>non-empty</strong> sequence of elements within an array.</li> |
| 32 | + <li>The <strong>frequency</strong> of an element <code>x</code> is the number of times it occurs in the array.</li> |
| 33 | +</ul> |
| 34 | + |
| 35 | +<p> </p> |
| 36 | +<p><strong class="example">Example 1:</strong></p> |
| 37 | + |
| 38 | +<div class="example-block"> |
| 39 | +<p><strong>Input:</strong> <span class="example-io">nums = [1,2,2,3], k = 3</span></p> |
| 40 | + |
| 41 | +<p><strong>Output:</strong> <span class="example-io">8</span></p> |
| 42 | + |
| 43 | +<p><strong>Explanation:</strong></p> |
| 44 | + |
| 45 | +<p>Subarrays of length <code>k = 3</code> are:</p> |
| 46 | + |
| 47 | +<table border="1" bordercolor="#ccc" cellpadding="5" cellspacing="0" style="border: 1px solid black;"> |
| 48 | + <thead> |
| 49 | + <tr> |
| 50 | + <th style="border: 1px solid black;">Subarray</th> |
| 51 | + <th style="border: 1px solid black;">Frequencies</th> |
| 52 | + <th style="border: 1px solid black;">Mode</th> |
| 53 | + <th style="border: 1px solid black;">Mode<br /> |
| 54 | + Frequency</th> |
| 55 | + <th style="border: 1px solid black;">Weight</th> |
| 56 | + </tr> |
| 57 | + </thead> |
| 58 | + <tbody> |
| 59 | + <tr> |
| 60 | + <td style="border: 1px solid black;">[1, 2, 2]</td> |
| 61 | + <td style="border: 1px solid black;">1: 1, 2: 2</td> |
| 62 | + <td style="border: 1px solid black;">2</td> |
| 63 | + <td style="border: 1px solid black;">2</td> |
| 64 | + <td style="border: 1px solid black;">2 × 2 = 4</td> |
| 65 | + </tr> |
| 66 | + <tr> |
| 67 | + <td style="border: 1px solid black;">[2, 2, 3]</td> |
| 68 | + <td style="border: 1px solid black;">2: 2, 3: 1</td> |
| 69 | + <td style="border: 1px solid black;">2</td> |
| 70 | + <td style="border: 1px solid black;">2</td> |
| 71 | + <td style="border: 1px solid black;">2 × 2 = 4</td> |
| 72 | + </tr> |
| 73 | + </tbody> |
| 74 | +</table> |
| 75 | + |
| 76 | +<p>Thus, the sum of weights is <code>4 + 4 = 8</code>.</p> |
| 77 | +</div> |
| 78 | + |
| 79 | +<p><strong class="example">Example 2:</strong></p> |
| 80 | + |
| 81 | +<div class="example-block"> |
| 82 | +<p><strong>Input:</strong> <span class="example-io">nums = [1,2,1,2], k = 2</span></p> |
| 83 | + |
| 84 | +<p><strong>Output:</strong> <span class="example-io">3</span></p> |
| 85 | + |
| 86 | +<p><strong>Explanation:</strong></p> |
| 87 | + |
| 88 | +<p>Subarrays of length <code>k = 2</code> are:</p> |
| 89 | + |
| 90 | +<table border="1" bordercolor="#ccc" cellpadding="5" cellspacing="0" style="border: 1px solid black;"> |
| 91 | + <thead> |
| 92 | + <tr> |
| 93 | + <th style="border: 1px solid black;">Subarray</th> |
| 94 | + <th style="border: 1px solid black;">Frequencies</th> |
| 95 | + <th style="border: 1px solid black;">Mode</th> |
| 96 | + <th style="border: 1px solid black;">Mode<br /> |
| 97 | + Frequency</th> |
| 98 | + <th style="border: 1px solid black;">Weight</th> |
| 99 | + </tr> |
| 100 | + </thead> |
| 101 | + <tbody> |
| 102 | + <tr> |
| 103 | + <td style="border: 1px solid black;">[1, 2]</td> |
| 104 | + <td style="border: 1px solid black;">1: 1, 2: 1</td> |
| 105 | + <td style="border: 1px solid black;">1</td> |
| 106 | + <td style="border: 1px solid black;">1</td> |
| 107 | + <td style="border: 1px solid black;">1 × 1 = 1</td> |
| 108 | + </tr> |
| 109 | + <tr> |
| 110 | + <td style="border: 1px solid black;">[2, 1]</td> |
| 111 | + <td style="border: 1px solid black;">2: 1, 1: 1</td> |
| 112 | + <td style="border: 1px solid black;">1</td> |
| 113 | + <td style="border: 1px solid black;">1</td> |
| 114 | + <td style="border: 1px solid black;">1 × 1 = 1</td> |
| 115 | + </tr> |
| 116 | + <tr> |
| 117 | + <td style="border: 1px solid black;">[1, 2]</td> |
| 118 | + <td style="border: 1px solid black;">1: 1, 2: 1</td> |
| 119 | + <td style="border: 1px solid black;">1</td> |
| 120 | + <td style="border: 1px solid black;">1</td> |
| 121 | + <td style="border: 1px solid black;">1 × 1 = 1</td> |
| 122 | + </tr> |
| 123 | + </tbody> |
| 124 | +</table> |
| 125 | + |
| 126 | +<p>Thus, the sum of weights is <code>1 + 1 + 1 = 3</code>.</p> |
| 127 | +</div> |
| 128 | + |
| 129 | +<p><strong class="example">Example 3:</strong></p> |
| 130 | + |
| 131 | +<div class="example-block"> |
| 132 | +<p><strong>Input:</strong> <span class="example-io">nums = [4,3,4,3], k = 3</span></p> |
| 133 | + |
| 134 | +<p><strong>Output:</strong> <span class="example-io">14</span></p> |
| 135 | + |
| 136 | +<p><strong>Explanation:</strong></p> |
| 137 | + |
| 138 | +<p>Subarrays of length <code>k = 3</code> are:</p> |
| 139 | + |
| 140 | +<table border="1" bordercolor="#ccc" cellpadding="5" cellspacing="0" style="border: 1px solid black;"> |
| 141 | + <thead> |
| 142 | + <tr> |
| 143 | + <th style="border: 1px solid black;">Subarray</th> |
| 144 | + <th style="border: 1px solid black;">Frequencies</th> |
| 145 | + <th style="border: 1px solid black;">Mode</th> |
| 146 | + <th style="border: 1px solid black;">Mode<br /> |
| 147 | + Frequency</th> |
| 148 | + <th style="border: 1px solid black;">Weight</th> |
| 149 | + </tr> |
| 150 | + </thead> |
| 151 | + <tbody> |
| 152 | + <tr> |
| 153 | + <td style="border: 1px solid black;">[4, 3, 4]</td> |
| 154 | + <td style="border: 1px solid black;">4: 2, 3: 1</td> |
| 155 | + <td style="border: 1px solid black;">4</td> |
| 156 | + <td style="border: 1px solid black;">2</td> |
| 157 | + <td style="border: 1px solid black;">2 × 4 = 8</td> |
| 158 | + </tr> |
| 159 | + <tr> |
| 160 | + <td style="border: 1px solid black;">[3, 4, 3]</td> |
| 161 | + <td style="border: 1px solid black;">3: 2, 4: 1</td> |
| 162 | + <td style="border: 1px solid black;">3</td> |
| 163 | + <td style="border: 1px solid black;">2</td> |
| 164 | + <td style="border: 1px solid black;">2 × 3 = 6</td> |
| 165 | + </tr> |
| 166 | + </tbody> |
| 167 | +</table> |
| 168 | + |
| 169 | +<p>Thus, the sum of weights is <code>8 + 6 = 14</code>.</p> |
| 170 | +</div> |
| 171 | + |
| 172 | +<p> </p> |
| 173 | +<p><strong>Constraints:</strong></p> |
| 174 | + |
| 175 | +<ul> |
| 176 | + <li><code>1 <= nums.length <= 10<sup>5</sup></code></li> |
| 177 | + <li><code>1 <= nums[i] <= 10<sup>5</sup></code></li> |
| 178 | + <li><code>1 <= k <= nums.length</code></li> |
| 179 | +</ul> |
| 180 | + |
| 181 | +<!-- description:end --> |
| 182 | + |
| 183 | +## 解法 |
| 184 | + |
| 185 | +<!-- solution:start --> |
| 186 | + |
| 187 | +### 方法一 |
| 188 | + |
| 189 | +<!-- tabs:start --> |
| 190 | + |
| 191 | +#### Python3 |
| 192 | + |
| 193 | +```python |
| 194 | + |
| 195 | +``` |
| 196 | + |
| 197 | +#### Java |
| 198 | + |
| 199 | +```java |
| 200 | + |
| 201 | +``` |
| 202 | + |
| 203 | +#### C++ |
| 204 | + |
| 205 | +```cpp |
| 206 | + |
| 207 | +``` |
| 208 | + |
| 209 | +#### Go |
| 210 | + |
| 211 | +```go |
| 212 | + |
| 213 | +``` |
| 214 | + |
| 215 | +<!-- tabs:end --> |
| 216 | + |
| 217 | +<!-- solution:end --> |
| 218 | + |
| 219 | +<!-- problem:end --> |
0 commit comments