Create problem statement for bracket sequence cost

Added problem statement for regular bracket sequence restoration and cost calculation.

Author: Dheeraj-06

Problems/Data-structures/Day-04/q001.md

@@ -0,0 +1,61 @@
+# PROBLEM STATEMENT :
+
+Monocarp had a regular bracket sequence **s** of length **n** (**n** is even).  
+He even came up with his own way to calculate its **cost**.
+
+In a regular bracket sequence (RBS), each opening bracket is paired with the corresponding closing bracket.  
+The **cost** of an RBS is defined as the **sum of distances** between all corresponding bracket pairs.
+
+For example, consider the RBS **(())()**. It has three bracket pairs:
+
+- Brackets at positions **1** and **4** → distance = **4 − 1 = 3**
+- Brackets at positions **2** and **3** → distance = **3 − 2 = 1**
+- Brackets at positions **5** and **6** → distance = **6 − 5 = 1**
+
+So, the total cost is **3 + 1 + 1 = 5**.
+
+---
+
+Unfortunately, due to data corruption, Monocarp lost all characters on **odd positions**  
+(**s₁, s₃, …, sₙ₋₁**). Only characters on **even positions** remain.
+
+For example:
+(())() → _(_)_)
+
+
+Monocarp wants to restore the string by placing brackets on odd positions such that:
+
+- The resulting string is a **valid regular bracket sequence**
+- The **total cost is minimized**
+
+It is guaranteed that at least one valid restoration exists.
+
+---
+
+## Input
+
+The first line contains a single integer **t**  
+(**1 ≤ t ≤ 5000**) — the number of test cases.
+
+For each test case:
+
+- The first line contains an even integer **n**  
+  (**2 ≤ n ≤ 2 · 10⁵**) — the length of the string.
+- The second line contains a string **s** of length **n**, where:
+  - Characters at **odd positions** are `'_'`
+  - Characters at **even positions** are `'('` or `')'`
+
+Additional constraints:
+
+- The sum of **n** over all test cases does not exceed **2 · 10⁵**
+- The string can always be restored to at least one valid RBS
+
+---
+
+## Output
+
+For each test case, print a single integer —  
+the **minimum possible cost** of a regular bracket sequence that can be obtained.
+
+
+[PROBLEM LINK](https://codeforces.com/problemset/problem/1997/C)