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| 1 | +--- |
| 2 | +title: 3652.按策略买卖股票的最佳时机:滑动窗口 |
| 3 | +date: 2025-12-18 18:45:15 |
| 4 | +tags: [题解, LeetCode, 中等, 数组, 前缀和, 滑动窗口] |
| 5 | +categories: [题解, LeetCode] |
| 6 | +--- |
| 7 | + |
| 8 | +# 【LetMeFly】3652.按策略买卖股票的最佳时机:滑动窗口 |
| 9 | + |
| 10 | +力扣题目链接:[https://leetcode.cn/problems/best-time-to-buy-and-sell-stock-using-strategy/](https://leetcode.cn/problems/best-time-to-buy-and-sell-stock-using-strategy/) |
| 11 | + |
| 12 | +<p>给你两个整数数组 <code>prices</code> 和 <code>strategy</code>,其中:</p> |
| 13 | + |
| 14 | +<ul> |
| 15 | + <li><code>prices[i]</code> 表示第 <code>i</code> 天某股票的价格。</li> |
| 16 | + <li><code>strategy[i]</code> 表示第 <code>i</code> 天的交易策略,其中: |
| 17 | + <ul> |
| 18 | + <li><code>-1</code> 表示买入一单位股票。</li> |
| 19 | + <li><code>0</code> 表示持有股票。</li> |
| 20 | + <li><code>1</code> 表示卖出一单位股票。</li> |
| 21 | + </ul> |
| 22 | + </li> |
| 23 | +</ul> |
| 24 | + |
| 25 | +<p>同时给你一个 <strong>偶数 </strong>整数 <code>k</code>,你可以对 <code>strategy</code> 进行 <strong>最多一次 </strong>修改。一次修改包括:</p> |
| 26 | + |
| 27 | +<ul> |
| 28 | + <li>选择 <code>strategy</code> 中恰好 <code>k</code> 个 <strong>连续 </strong>元素。</li> |
| 29 | + <li>将前 <code>k / 2</code> 个元素设为 <code>0</code>(持有)。</li> |
| 30 | + <li>将后 <code>k / 2</code> 个元素设为 <code>1</code>(卖出)。</li> |
| 31 | +</ul> |
| 32 | + |
| 33 | +<p><strong>利润 </strong>定义为所有天数中 <code>strategy[i] * prices[i]</code> 的 <strong>总和 </strong>。</p> |
| 34 | + |
| 35 | +<p>返回你可以获得的 <strong>最大 </strong>可能利润。</p> |
| 36 | + |
| 37 | +<p><strong>注意:</strong> 没有预算或股票持有数量的限制,因此所有买入和卖出操作均可行,无需考虑过去的操作。</p> |
| 38 | + |
| 39 | +<p> </p> |
| 40 | + |
| 41 | +<p><strong class="example">示例 1:</strong></p> |
| 42 | + |
| 43 | +<div class="example-block"> |
| 44 | +<p><strong>输入:</strong> <span class="example-io">prices = [4,2,8], strategy = [-1,0,1], k = 2</span></p> |
| 45 | + |
| 46 | +<p><strong>输出:</strong> <span class="example-io">10</span></p> |
| 47 | + |
| 48 | +<p><strong>解释:</strong></p> |
| 49 | + |
| 50 | +<table style="border: 1px solid black;"> |
| 51 | + <thead> |
| 52 | + <tr> |
| 53 | + <th style="border: 1px solid black;">修改</th> |
| 54 | + <th style="border: 1px solid black;">策略</th> |
| 55 | + <th style="border: 1px solid black;">利润计算</th> |
| 56 | + <th style="border: 1px solid black;">利润</th> |
| 57 | + </tr> |
| 58 | + </thead> |
| 59 | + <tbody> |
| 60 | + <tr> |
| 61 | + <td style="border: 1px solid black;">原始</td> |
| 62 | + <td style="border: 1px solid black;">[-1, 0, 1]</td> |
| 63 | + <td style="border: 1px solid black;">(-1 × 4) + (0 × 2) + (1 × 8) = -4 + 0 + 8</td> |
| 64 | + <td style="border: 1px solid black;">4</td> |
| 65 | + </tr> |
| 66 | + <tr> |
| 67 | + <td style="border: 1px solid black;">修改 [0, 1]</td> |
| 68 | + <td style="border: 1px solid black;">[0, 1, 1]</td> |
| 69 | + <td style="border: 1px solid black;">(0 × 4) + (1 × 2) + (1 × 8) = 0 + 2 + 8</td> |
| 70 | + <td style="border: 1px solid black;">10</td> |
| 71 | + </tr> |
| 72 | + <tr> |
| 73 | + <td style="border: 1px solid black;">修改 [1, 2]</td> |
| 74 | + <td style="border: 1px solid black;">[-1, 0, 1]</td> |
| 75 | + <td style="border: 1px solid black;">(-1 × 4) + (0 × 2) + (1 × 8) = -4 + 0 + 8</td> |
| 76 | + <td style="border: 1px solid black;">4</td> |
| 77 | + </tr> |
| 78 | + </tbody> |
| 79 | +</table> |
| 80 | + |
| 81 | +<p>因此,最大可能利润是 10,通过修改子数组 <code>[0, 1]</code> 实现。</p> |
| 82 | +</div> |
| 83 | + |
| 84 | +<p><strong class="example">示例 2:</strong></p> |
| 85 | + |
| 86 | +<div class="example-block"> |
| 87 | +<p><strong>输入:</strong> <span class="example-io">prices = [5,4,3], strategy = [1,1,0], k = 2</span></p> |
| 88 | + |
| 89 | +<p><strong>输出:</strong> <span class="example-io">9</span></p> |
| 90 | + |
| 91 | +<p><strong>解释:</strong></p> |
| 92 | + |
| 93 | +<div class="example-block"> |
| 94 | +<table style="border: 1px solid black;"> |
| 95 | + <thead> |
| 96 | + <tr> |
| 97 | + <th style="border: 1px solid black;">修改</th> |
| 98 | + <th style="border: 1px solid black;">策略</th> |
| 99 | + <th style="border: 1px solid black;">利润计算</th> |
| 100 | + <th style="border: 1px solid black;">利润</th> |
| 101 | + </tr> |
| 102 | + </thead> |
| 103 | + <tbody> |
| 104 | + <tr> |
| 105 | + <td style="border: 1px solid black;">原始</td> |
| 106 | + <td style="border: 1px solid black;">[1, 1, 0]</td> |
| 107 | + <td style="border: 1px solid black;">(1 × 5) + (1 × 4) + (0 × 3) = 5 + 4 + 0</td> |
| 108 | + <td style="border: 1px solid black;">9</td> |
| 109 | + </tr> |
| 110 | + <tr> |
| 111 | + <td style="border: 1px solid black;">修改 [0, 1]</td> |
| 112 | + <td style="border: 1px solid black;">[0, 1, 0]</td> |
| 113 | + <td style="border: 1px solid black;">(0 × 5) + (1 × 4) + (0 × 3) = 0 + 4 + 0</td> |
| 114 | + <td style="border: 1px solid black;">4</td> |
| 115 | + </tr> |
| 116 | + <tr> |
| 117 | + <td style="border: 1px solid black;">修改 [1, 2]</td> |
| 118 | + <td style="border: 1px solid black;">[1, 0, 1]</td> |
| 119 | + <td style="border: 1px solid black;">(1 × 5) + (0 × 4) + (1 × 3) = 5 + 0 + 3</td> |
| 120 | + <td style="border: 1px solid black;">8</td> |
| 121 | + </tr> |
| 122 | + </tbody> |
| 123 | +</table> |
| 124 | + |
| 125 | +<p>因此,最大可能利润是 9,无需任何修改即可达成。</p> |
| 126 | +</div> |
| 127 | +</div> |
| 128 | + |
| 129 | +<p> </p> |
| 130 | + |
| 131 | +<p><strong>提示:</strong></p> |
| 132 | + |
| 133 | +<ul> |
| 134 | + <li><code>2 <= prices.length == strategy.length <= 10<sup>5</sup></code></li> |
| 135 | + <li><code>1 <= prices[i] <= 10<sup>5</sup></code></li> |
| 136 | + <li><code>-1 <= strategy[i] <= 1</code></li> |
| 137 | + <li><code>2 <= k <= prices.length</code></li> |
| 138 | + <li><code>k</code> 是偶数</li> |
| 139 | +</ul> |
| 140 | + |
| 141 | + |
| 142 | + |
| 143 | +## 解题方法:滑动窗口 |
| 144 | + |
| 145 | +既然修改范围是定长的,并且最多修改1次,那么就从前往后将每一种修改可能都试试呗。 |
| 146 | + |
| 147 | +初始先计算原数组不修改时收益,再从前往后依次尝试修改区间,取收益最大的一个作为答案。 |
| 148 | + |
| 149 | +如何从一个区间快速计算出下一个区间呢?变化的有3个:(变化前的)区间起点、区间中点、区间终点,把这三个位置的值更新一下就好了。 |
| 150 | + |
| 151 | ++ 时间复杂度$O(len(prices))$ |
| 152 | ++ 空间复杂度$O(1)$ |
| 153 | + |
| 154 | +### AC代码 |
| 155 | + |
| 156 | +#### C++ |
| 157 | + |
| 158 | +```cpp |
| 159 | +/* |
| 160 | + * @LastEditTime: 2025-12-18 18:42:50 |
| 161 | + */ |
| 162 | +typedef long long ll; |
| 163 | +class Solution { |
| 164 | +public: |
| 165 | + ll maxProfit(vector<int>& prices, vector<int>& strategy, int k) { |
| 166 | + ll ans = 0; |
| 167 | + int n = prices.size(); |
| 168 | + for (int i = 0; i < n; i++) { |
| 169 | + ans += strategy[i] * prices[i]; |
| 170 | + } |
| 171 | + |
| 172 | + ll now = ans; |
| 173 | + for (int i = 0; i < k / 2; i++) { |
| 174 | + now += (0 - strategy[i]) * prices[i]; |
| 175 | + } |
| 176 | + for (int i = k / 2; i < k; i++) { |
| 177 | + now += (1 - strategy[i]) * prices[i]; |
| 178 | + } |
| 179 | + ans = max(ans, now); |
| 180 | + |
| 181 | + for (int i = 1; i + k <= n; i++) { |
| 182 | + // i-1: 0->original |
| 183 | + // i+k/2-1: 1->0 |
| 184 | + // i+k-1: original->1 |
| 185 | + now += (strategy[i - 1] - 0) * prices[i - 1] + (0 - 1) * prices[i + k/2 - 1] + (1 - strategy[i + k - 1]) * prices[i + k - 1]; |
| 186 | + ans = max(ans, now); |
| 187 | + } |
| 188 | + return ans; |
| 189 | + } |
| 190 | +}; |
| 191 | +``` |
| 192 | + |
| 193 | +> 同步发文于[CSDN](https://letmefly.blog.csdn.net/article/details/156061117)和我的[个人博客](https://blog.letmefly.xyz/),原创不易,转载经作者同意后请附上[原文链接](https://blog.letmefly.xyz/2025/12/18/LeetCode%203652.%E6%8C%89%E7%AD%96%E7%95%A5%E4%B9%B0%E5%8D%96%E8%82%A1%E7%A5%A8%E7%9A%84%E6%9C%80%E4%BD%B3%E6%97%B6%E6%9C%BA/)哦~ |
| 194 | +> |
| 195 | +> 千篇源码题解[已开源](https://github.com/LetMeFly666/LeetCode) |
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