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Sainnhe Park 2023-02-10 12:08:26 +08:00
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- [背包问题](./knapsack.md)
- [打家劫舍](./house-robber.md)
- [股票问题](./stock.md)
- [子序列问题](./subsequence.md)
# STL

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# 子序列问题
## [300. 最长递增子序列](https://leetcode.cn/problems/longest-increasing-subsequence/)
- `dp[i]` 表示以 `nums[i]` 结尾的最长递增子序列的长度
- 遍历 `j``0``i`, `if (nums[i] > nums[j]) dp[i] = max(dp[i], dp[j] + 1)`
- `dp[i] = 1`
- 外层遍历 `i` 内层遍历 `j`,都是从前往后
## [674. 最长连续递增序列](https://leetcode.cn/problems/longest-continuous-increasing-subsequence/)
- `dp[i]` 表示以 `nums[i]` 结尾的最长连续递增子序列的长度
- 递推公式:
- `if (nums[i] > nums[i - 1]) dp[i] = dp[i - 1] + 1`
- `if (nums[i] <= nums[i - 1]) dp[i] = 1`
- `dp[0] = 1`
- 从前往后
## [718. 最长重复子数组](https://leetcode.cn/problems/maximum-length-of-repeated-subarray/)
- `dp[i][j]` 表示以 `i` 为下标结尾的 A 和以 `j` 为下标结尾的 B 的最长重复子数组
- `if (nums1[i] == nums2[j]) dp[i][j] = dp[i - 1][j - 1] + 1` 否则为 `0`
- 初始化:
- `if (nums1[i] == nums2[0]) dp[i][0] = 1` 否则为 `0`
- `if (nums1[0] == nums2[j]) dp[0][j] = 1` 否则为 `0`
- 其它都初始化为 `0`
- 都从前往后遍历,下标从 `1` 开始
## [1143. 最长公共子序列](https://leetcode.cn/problems/longest-common-subsequence/)
- `dp[i][j]` 表示以 `i` 为下标结尾的 text1 和以 `j` 为下标结尾的 text2 的最长公共子序列
- 递推公式
- `if (text1[i] == text2[j]) dp[i][j] = dp[i - 1][j - 1] + 1`
- `else dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])`
- 只需要初始化三个:
- `dp[0][0]`
- `dp[1][0]`
- `dp[0][1]`