Update valid_checking_lru/README.md

Author: mellivorandy

valid_checking_lru/README.md

@@ -107,72 +107,72 @@ Move it to the front (MRU).
 
 ### Lookup (Hit/Miss Checking)
 
-- Using HashMap<tag, Node>, checking if a block is present takes `O(1)`.
+- Using `HashMap<tag, Node>`, checking if a block is present takes $O(1)$.
 
 <br>
 
 ### Insert New Block (On Miss)
 
 Two scenarios for handling a miss:
 
-1. Use an invalid block: O(N), worst-case requires searching all set entries.
-<br>
-2. Evict LRU block (if all are valid): O(1).
+1. Use an invalid block: $O(N)$, worst-case requires searching all set entries.
+
+2. Evict LRU block (if all are valid): $O(1)$.
 <br><br>
 
 **Case 1**: Use an invalid block
-Search for a valid=false block: O(N) (N = set_degree, worst case is that all blocks are valid).
-Update block's tag and set valid=true: O(1).
-Move block to head (most recently used): O(1).
+Search for a valid=false block: $O(N)$ (N = set_degree, worst case is that all blocks are valid).
+Update block's tag and set valid=true: $O(1)$.
+Move block to head (most recently used): $O(1)$.
 
-Overall: O(N) + O(1) + O(1) = `O(N)`
+Overall: $O(N) + O(1) + O(1) = O(N)$
 (Worst case: scanning all blocks in the set to find an invalid one.)
 
 <br>
 
 **Case 2**: Evict LRU block (All blocks are valid=true)
-Find LRU block (always at the tail): O(1).
-Replace with new block, update tag, set valid=true: O(1).
-Move to head (most recently used): O(1).
+Find LRU block (always at the tail): $O(1)$.
+Replace with new block, update tag, set valid=true: $O(1)$.
+Move to head (most recently used): $O(1)$.
 
-Overall: O(1) + O(1) + O(1) = `O(1)`
+Overall: $O(1) + O(1) + O(1) = O(1)$
 
 <br>
 
 ### Move Block to Head (On Hit)
 
-- Find in HashMap: O(1).
+- Find in HashMap: $O(1)$.
 
-- Remove from current position: O(1).
+- Remove from current position: $O(1)$.
 
-- Insert at the front: O(1).
+- Insert at the front: $O(1)$.
 
-Overall: O(1) + O(1) + O(1) = `O(1)`.
+Overall: $O(1) + O(1) + O(1) = O(1)$.
 
 <br>
 
 ### Eviction (When the set is full)
 
-- Identify LRU block (always at the tail): O(1).
+- Identify LRU block (always at the tail): $O(1)$.
 
-- Remove from doubly linked list: O(1).
+- Remove from doubly linked list: $O(1)$.
 
-- Remove from HashMap: O(1).
+- Remove from HashMap: $O(1)$.
 
-- Insert new block at head: O(1).
+- Insert new block at head: $O(1)$.
 
-Overall: O(1) + O(1) + O(1) + O(1) = `O(1)`.
+Overall: $O(1) + O(1) + O(1) + O(1) = O(1)$.
 
 <br>
 
 ### Summary
 
 |   Operation   |  Complexity  |
 |---------------|--------------|
-|Lookup	        |     O(1)     |
-|Insert 	    |     O(N)     |
-|Move to Head 	|     O(1)     |
-|Eviction       |	  O(1)     |
+|Lookup	        |    $O(1)$    |
+|Insert 	    |    $O(N)$    |
+|Move to Head 	|    $O(1)$    |
+|Eviction       |	 $O(1)$    |
 
 <br>
 
@@ -187,8 +187,11 @@ Overall: O(1) + O(1) + O(1) + O(1) = `O(1)`.
 ### Prerequisites
 
 - [Rust](https://www.rust-lang.org/) (recommended 1.84.1 or higher)
+
 - A terminal or command prompt to run `cargo`
-<br><br>
+
+<br>
+
 ---
 
 ### Building and Running