From da941d8cdf1cfad3e2d7d46c69bd24ff7a926618 Mon Sep 17 00:00:00 2001
From: fergalhennessy <fergalhennessy@berkeley.edu>
Date: Thu, 11 Jan 2024 14:24:16 -0600
Subject: [PATCH] changed notes

---
 docs/_notes/Public/Merge K Lists.md           |  2 +-
 ...bstring With Concatenation Of All Words.md | 71 +++++++++++++++++++
 2 files changed, 72 insertions(+), 1 deletion(-)
 create mode 100644 docs/_notes/Public/Substring With Concatenation Of All Words.md

diff --git a/docs/_notes/Public/Merge K Lists.md b/docs/_notes/Public/Merge K Lists.md
index 8653b9e9..4536e5fa 100644
--- a/docs/_notes/Public/Merge K Lists.md	
+++ b/docs/_notes/Public/Merge K Lists.md	
@@ -24,7 +24,7 @@ You are given an array of k linked-lists `lists`, where each linked list is sort
 ```
 
 #### Examples:
-lists = $[[1, 4, 5], [1, 3, 4], [2, 6]]$ -->  $[1, 1, 2, 3, 4, 4, 5, 6]$
+lists = `[[1, 4, 5], [1, 3, 4], [2, 6]]` -->  $[1, 1, 2, 3, 4, 4, 5, 6]$
 lists = $[]$ --> $[]$
 lists = $[[]]$
 
diff --git a/docs/_notes/Public/Substring With Concatenation Of All Words.md b/docs/_notes/Public/Substring With Concatenation Of All Words.md
new file mode 100644
index 00000000..2992cb71
--- /dev/null
+++ b/docs/_notes/Public/Substring With Concatenation Of All Words.md	
@@ -0,0 +1,71 @@
+---
+title: Substring With Concatenation Of All Words
+feed: show
+date: 2024/01/11
+tags: hard hashmap sliding-window
+leetcode: 30
+---
+
+## Substring With Concatenation Of All Words
+
+You are given a string `s`, and an array of strings `words`. All the strings of words are **of the same length** 
+
+A **concatenated substring** in `s` is a substring that contains all the strings of any permutation of `words` concatenated. Essentially, if all the words in `words` appear exactly once consecutively, then the substring is a concatenated substring.
+
+*Return the starting indices of the concatenated substrings in* `s`. You can return the answer in **any order.**
+
+## Examples
+
+**Input: ** `s = "barfoothefoobarman", words = ["foo, bar"]` --> `[0, 9]`
+**Input: ** `s = "wordgoodgoodgoodbestword", words = ["word", "good", "best", "word"]` --> `[]`
+
+### Solution 1: Brute Force Hashmap Comparison
+
+Let the size of `s` be `n`, let the number of elements in `words` be `m`, let the length of a word in `words` be `w`. It follows that every concatenated substring will have length `m * w`. We can brute force a solution as follows:
+1. load all `words` into a hashmap `total`
+2. For each length `m * w` substring of `s`, split into length `w` pieces, add the pieces to a new hashmap `prospect` and check `prospect == total`
+3. Return a vector of all the indices where step 2 is true.
+Putting these steps into code, we get this solution:
+
+```
+class Solution{
+public:
+	vector<int> findSubstring(string s, vector<string>& words){
+		vector<int> res;
+		if(words.size() == 0) return res;
+		unordered_map<string, int> total;
+		for(string& word: words){
+			total[word]++;
+		}
+		int m = words.size();
+		int w = words[0].size();
+		for(int i = 0; i < s.size() - (m*w) + 1; ++i){
+			unordered_map<string, int> prospect;
+			int j = i;
+			while(j < i + (m*w)){
+				string word = s.substr(j, w);
+				prospect[word] += 1;
+				j+= w;
+			}
+			if(prospect == total) res.push_back(i);
+		}
+		return res;
+	}
+};
+```
+
+##### Runtime Analysis:
+1. Building `total`: `O(1) * m = O(m)`
+2. Building `prospect` and comparing with `total`: `O(m*w)`  (There are `(m*w)` characters in both maps)
+3. Iterating through `s`: `O(n)`
+Total Runtime: `O(m) + O(n * m * w) = O(n * m* w)`
+
+##### Space Analysis:
+1. `total`: `O(m*w)`
+2. `prospect`: `O(m*w)` (`n` times)
+Space complexity is also `O(m*n*w)`
+
+Both space and time are cubic: can we do better? Looking at this solution, we do a lot of duplicate comparisons. if we create a map `prospect` and check all the internals against `total`, then discard it, we waste a lot of comparisons that we could have saved for future iterations...
+
+### Solution 2: Sliding Window Hashmap Comparison
+