Code Complexity Analysis — Loops & Conditions | Analyzing Code Complexity | Selection With Sathi

📚 Code Complexity Analysis — Loops & Conditions | Analyzing Code Complexity
Step-by-step rules for analyzing loops, nested loops, conditions, and logarithmic patterns

📌 Key Formulas:
1. Single Loop Analysis: for i in range(n): body → body runs n times → O(n)
2. Nested Loop Analysis: Outer n × Inner n = n² → O(n²) | Dependent: 0+1+...+(n-1) = n(n-1)/2 = O(n²)
3. Consecutive Statements Rule: T(P1) + T(P2) = max(T(P1), T(P2)) — keep the dominant term
4. If-Then-Else Analysis: if C: block_1 else: block_2 → O(max(block_1, block_2))
5. Logarithmic Loops: i = i * 2 each step → 1,2,4,...,n → log₂(n) iterations → O(log n)

⏱️ Timestamps:
0:00 Introduction
0:49 Single Loop Analysis
1:40 Nested Loop Analysis
2:39 Consecutive Statements Rule
3:36 If-Then-Else Analysis
4:28 Logarithmic Loops
5:36 Dependent Nested Loop — O(n²)
6:29 Square Root Loop — O(√n)
7:20 Mixed Loop — O(n log n)
8:13 GATE Classic — Geometric Series O(n)
9:18 Quick Tips & Tricks | टिप्स
10:20 Summary | सारांश

💡 Quick Tips:
• Dependent inner loop (j ‹ i) still gives O(n²) because the arithmetic sum 0+1+...+(n-1) = n(n-1)/2
• Square root loops appear when the condition is i*i ‹= n — the loop runs √n times
• Don't blindly multiply nested loop counts — trace with a concrete value of n first to verify
• Geometric series 1+2+4+...+n = 2n-1 = O(n) — a classic GATE trick where the answer is NOT O(n log n)

📚 Useful for: GATE CSE, Placements, Interviews and all govt exams

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