From 8092f49a57721d87542de7abba09dd7fceff00b8 Mon Sep 17 00:00:00 2001
From: ShusenTang <tangshusen@pku.edu.cn>
Date: Tue, 27 Dec 2022 22:52:05 +0800
Subject: [PATCH] add 97

---
 README.md                            |  1 +
 solutions/97. Interleaving String.md | 47 ++++++++++++++++++++++++++++
 2 files changed, 48 insertions(+)
 create mode 100644 solutions/97. Interleaving String.md

diff --git a/README.md b/README.md
index cc1493f..743e2c0 100644
--- a/README.md
+++ b/README.md
@@ -96,6 +96,7 @@ My LeetCode solutions with Chinese explanation. 我的LeetCode中文题解。
 | 94 |[Binary Tree Inorder Traversal](https://leetcode.com/problems/binary-tree-inorder-traversal/)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/94.%20Binary%20Tree%20Inorder%20Traversal.md)|Medium|  |
 | 95 |[Unique Binary Search Trees II](https://leetcode.com/problems/unique-binary-search-trees-ii/)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/95.%20Unique%20Binary%20Search%20Trees%20II.md)|Medium|  |
 | 96 |[Unique Binary Search Trees](https://leetcode.com/problems/unique-binary-search-trees/)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/96.%20Unique%20Binary%20Search%20Trees.md)|Medium|  |
+| 97 |[Interleaving String](https://leetcode.cn/problems/interleaving-string/)|[C++](solutions/97.%20Interleaving%20String.md)|Medium|  |
 | 98 |[Validate Binary Search Tree](https://leetcode.com/problems/validate-binary-search-tree/)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/98.%20Validate%20Binary%20Search%20Tree.md)|Medium|  |
 | 100 |[Same Tree](https://leetcode.com/problems/same-tree)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/100.%20Same%20Tree.md)|Easy|  |
 | 101 |[Symmetric Tree](https://leetcode.com/problems/symmetric-tree)|[C++](https://github.com/ShusenTang/LeetCode/blob/master/solutions/101.%20Symmetric%20Tree.md)|Easy|  |
diff --git a/solutions/97. Interleaving String.md b/solutions/97. Interleaving String.md
new file mode 100644
index 0000000..84d7392
--- /dev/null
+++ b/solutions/97. Interleaving String.md	
@@ -0,0 +1,47 @@
+# [97. Interleaving String](https://leetcode.cn/problems/interleaving-string/)
+
+# 思路
+仔细分析问题不难发现会涉及到大量子问题，所以我们考虑用动态规划求解。我们定义 dp[i][j] 表示 s1 的前 i 个元素和 s2 的前 j 个元素是否能交错组成 s3 的前 i + j 个元素。可得到初始状态和状态转移方程为：
+```
+初始态（即都为空串）：dp[0][0] = true
+转移方程：dp[i][j] = (dp[i-1][j] && s3[i+j-1] == s1[i-1]) || (dp[i][j-1] && s3[i+j-1] == s2[j-1])
+```
+再考虑下边界条件就不难写出代码。另外由于 dp[i][j] 只和左上元素有关，故可以考虑使用滚动数组优化空间复杂度为O(s2.size())。
+
+
+
+# C++
+``` C++
+class Solution {
+public:
+    bool isInterleave(string s1, string s2, string s3) {
+        if(s1.size() + s2.size() != s3.size()) return false;
+        int n1 = s1.size(), n2 = s2.size(), n3 = s3.size();
+        if(n1 == 0) return s2 == s3;
+        if(n2 == 0) return s1 == s3;
+        
+        // vector<vector<bool>>dp(n1 + 1, vector<bool>(n2 + 1, false));
+        // for(int i = 0; i <= n1; i++){
+        //     for(int j = 0; j <= n2; j++){
+        //         if(i == 0 && j == 0) dp[i][j] = true;
+        //         else if(i > 0 && dp[i-1][j] && s3[i+j-1] == s1[i-1]) dp[i][j] = true;
+        //         else if(j > 0 && dp[i][j-1] && s3[i+j-1] == s2[j-1]) dp[i][j] = true;
+        //         // else dp[i][j] = false; 
+        //     }
+        // }
+        // return dp[n1][n2];
+
+        // 滚动数组空间优化
+        vector<bool>dp(n2 + 1, false);
+        for(int i = 0; i <= n1; i++){
+            for(int j = 0; j <= n2; j++){
+                if(i == 0 && j == 0) dp[j] = true;
+                else if(i > 0 && dp[j] && s3[i+j-1] == s1[i-1]) dp[j] = true;
+                else if(j > 0 && dp[j-1] && s3[i+j-1] == s2[j-1]) dp[j] = true;
+                else dp[j] = false; // 注意这里需重置成false, 因为dp[i-1][j]可能等于true
+            }
+        }
+        return dp[n2];
+    }
+};
+``` 
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