1️⃣ What Is a Constraint? (Absolute Beginner)
A constraint is a rule or limit given in a problem that tells you:
- How large input can be
- How fast your solution must run
- How much memory you can use
Simple Line:
Constraints define the limits of a problem.
Example
1 ≤ n ≤ 10^5
Meaning:
-
nwill never exceed100,000 - Your code must work efficiently for this size
2️⃣ Why Constraints Exist (VERY IMPORTANT)
Constraints exist to:
- Stop brute-force solutions
- Force efficient thinking
- Separate beginners from problem solvers
📌 Interviewers don’t test coding — they test constraint handling.
3️⃣ Types of Constraints (YOU MUST IDENTIFY THESE)
🔹 1. Input Size Constraints
1 ≤ n ≤ 10^5
1 ≤ arr[i] ≤ 10^9
Used to decide:
- Loop limits
- Data structures
- Data types (
int,long,long long)
🔹 2. Time Constraints
Usually:
- 1 second
- 2 seconds
🧠 Rule of thumb:
1 second ≈ 10^7 – 10^8 operations
🔹 3. Space Constraints
Example:
Memory limit = 256 MB
Limits:
- Array sizes
- Recursion depth
- Extra data structures
4️⃣ What Happens If You Ignore Constraints?
| Mistake | Result |
|---|---|
| O(n²) for large n | ❌ TLE |
| Deep recursion | ❌ Stack overflow |
| Extra arrays | ❌ MLE |
| Wrong data type | ❌ Wrong Answer |
5️⃣ The Most Important Truth in DSA
You NEVER choose an algorithm first.Constraints choose the algorithm for you.
6️⃣ Input Size vs Maximum Allowed Time Complexity (CORE TABLE)
🧠 MASTER TABLE (MEMORIZE THIS)
| Input Size (n) | Max Allowed Time Complexity |
|---|---|
| n ≤ 10 | O(n!), O(2ⁿ) |
| n ≤ 20 | O(2ⁿ) |
| n ≤ 100 | O(n³) |
| n ≤ 1,000 | O(n²) |
| n ≤ 10⁵ | O(n log n) |
| n ≤ 10⁶ | O(n) |
| n ≥ 10⁷ | O(log n) / O(1) |
📌 This table automatically filters wrong solutions.
7️⃣ Understanding Time Complexity (Easy Language)
| Complexity | Meaning | Example |
|---|---|---|
| O(1) | Constant | Array access |
| O(log n) | Divide by half | Binary search |
| O(n) | One loop | Sum array |
| O(n log n) | Sort + loop | Merge sort |
| O(n²) | Two loops | Pair checking |
| O(2ⁿ) | All subsets | Backtracking |
| O(n!) | All permutations | Arrangements |
8️⃣ Why O(n²) Is Dangerous
If:
n = 100,000
Then:
n² = 10^10 operations ❌
But computer can only do:
~10^8 operations/sec
➡️ Guaranteed TLE
9️⃣ Space Complexity (From Zero)
What Is Space Complexity?
Extra memory used by your algorithm.
Common Space Usage
| Structure | Space |
|---|---|
| Array of size n | O(n) |
| HashMap | O(n) |
| Recursion stack | O(depth) |
| 2D matrix | O(n²) |
🔟 Why Space Constraints Matter
- Memory is limited
- Online judges are strict
- Stack overflow crashes programs
📌 Sometimes:
- Time is fine
- Space fails
1️⃣1️⃣ Data Type Constraints (VERY IMPORTANT)
| Constraint | Use |
|---|---|
| ≤ 10⁹ | int |
| ≤ 10¹⁸ | long / long long |
| Large sum | long |
❌ Using int for large values → Wrong Answer
1️⃣2️⃣ How Constraints Decide the Algorithm (REAL CASES)
Case 1
1 ≤ n ≤ 10^5
❌ Nested loops
❌ Brute force
✅ Sorting
✅ HashMap
✅ Two pointers
Case 2
1 ≤ n ≤ 20
✅ Backtracking
✅ Bitmasking
✅ Recursion
Case 3
Queries ≤ 10^5
❌ Loop for each query
✅ Prefix sum
✅ Segment tree
✅ Fenwick tree
1️⃣3️⃣ Keywords → Algorithm Mapping
| Keyword | Use |
|---|---|
| Subarray | Prefix sum |
| Continuous | Sliding window |
| Max / Min | Greedy |
| Count ways | DP |
| Optimal value | Binary search |
| Frequency | HashMap |
1️⃣4️⃣ How to Analyze Any Question FAST (INTERVIEW METHOD)
STEP 1: Read Constraints First
Ignore story.
STEP 2: Identify Max n
- Small n → brute force?
- Large n → optimized needed
STEP 3: Match with Complexity Table
STEP 4: Choose Data Structure
| Problem Type | DS |
|---|---|
| Search | Binary search |
| Range queries | Prefix sum |
| Ordering | Sorting |
| Min/Max | Heap |
1️⃣5️⃣ How to Understand Problems Faster
Technique 1: Small Dry Run
Try:
n = 3 or 4
Technique 2: Ask These Questions
- What is varying?
- What is fixed?
- What is being optimized?
1️⃣6️⃣ Constraint → Algorithm Cheat Table
| Constraint Clue | Best Approach |
|---|---|
| Large n | O(n log n) |
| Sorted input | Binary search |
| Continuous window | Sliding window |
| Repeated queries | Preprocessing |
| Limited choices | Greedy |
1️⃣7️⃣ Common Beginner Mistakes
❌ Ignoring constraints
❌ Writing code first
❌ Nested loops blindly
❌ Wrong data types
❌ Overusing recursion
1️⃣8️⃣ Golden Rules (INTERVIEW GOLD)
1️⃣ Constraints decide complexity
2️⃣ Complexity decides algorithm
3️⃣ Algorithm decides DS
4️⃣ Code comes LAST
1️⃣9️⃣ Interview Checklist (SAVE THIS)
✔ Max input size
✔ Time complexity safe
✔ Space safe
✔ Edge cases handled
✔ Worst case covered
🔥 FINAL MONSTER-LEVEL TRUTH
Constraints are the hidden solution.If you read them carefully,half the problem is already solved.
📌 How to Use This in Interviews & Exams
- Mention constraints before approach
- Reject brute force verbally
- Justify your algorithm using constraints
- Interviewers LOVE this thinking
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