From ed62e1dd7100a1e0ccba5c1f86813b376608f845 Mon Sep 17 00:00:00 2001
From: Sainnhe Park <i@sainnhe.dev>
Date: Fri, 10 Feb 2023 12:08:26 +0800
Subject: [PATCH] Add subsequence

---
 notes/src/SUMMARY.md     |  1 +
 notes/src/subsequence.md | 38 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 39 insertions(+)
 create mode 100644 notes/src/subsequence.md

diff --git a/notes/src/SUMMARY.md b/notes/src/SUMMARY.md
index 62de650..abfc0f3 100644
--- a/notes/src/SUMMARY.md
+++ b/notes/src/SUMMARY.md
@@ -58,6 +58,7 @@
 - [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
 
diff --git a/notes/src/subsequence.md b/notes/src/subsequence.md
new file mode 100644
index 0000000..0f315e4
--- /dev/null
+++ b/notes/src/subsequence.md
@@ -0,0 +1,38 @@
+# 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` 从 `0` 到 `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]`