CT_Week5_Loops_For

CT Week 5: For Loops & Nested Loops

0. Prerequisites

NOTE

What you need to know:

• While Loops: The basic concept of iteration.
• Lists: Knowing that a list contains multiple items.

Quick Refresher

• For Loop: Iterates over a sequence (like a list or range).
• Nested Loop: A loop inside another loop.
  • Analogy: Clock. Outer loop is Hour hand, Inner loop is Minute hand.

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1. Core Concepts

1.1 For Loop Syntax

• Pseudocode:

  For each X in List L:
      Print X
  

• Range: For i = 1 to 5 (Runs for 1, 2, 3, 4, 5).

1.2 Nested Loops (The Multiplier Effect)

• Structure:

  For i = 1 to 3:       (Outer)
      For j = 1 to 2:   (Inner)
          Print i, j
  

• Execution:
  • Outer starts ($i=1$).
  • Inner runs completely ($j=1,j=2$).
  • Outer moves ($i=2$).
  • Inner runs completely again ($j=1,j=2$).
• Total Runs: Outer Count $\times$ Inner Count.

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2. Pattern Analysis & Goated Solutions

Pattern 1: Tracing Nested Loops

Context: “What is the final value of C?” Code:

C = 0
For i = 1 to 3:
    For j = 1 to 2:
        C = C + 1

TIP

Mental Algorithm:

1. Identify Counts:
   • Outer ($i$): 1, 2, 3 (3 times).
   • Inner ($j$): 1, 2 (2 times).
2. Multiply: Total Iterations = $3\times 2=6$.
3. Action: C increases by 1 each time.
4. Result: $C=6$.

Pattern 2: Dependent Inner Loop (Triangle Pattern)

Context: “Inner loop depends on Outer variable.” Code:

S = 0
For i = 1 to 3:
    For j = 1 to i:  <-- Depends on i
        S = S + 1

TIP

Mental Algorithm (Trace):

1. i = 1: Inner runs 1 to 1 (1 time). S becomes 1.
2. i = 2: Inner runs 1 to 2 (2 times). S becomes 1+2=3.
3. i = 3: Inner runs 1 to 3 (3 times). S becomes 3+3=6. Answer: S = 6.

Pattern 3: Finding Pairs (Combinations)

Context: “Find pairs (A, B) such that A+B = 10.” Code:

List L = [2, 5, 8]
Count = 0
For each A in L:
    For each B in L:
        If A + B == 10:
            Count = Count + 1

TIP

Mental Algorithm:

1. Grid: Compare every item with every item.
2. Pairs:
   • (2, 2)=4, (2, 5)=7, (2, 8)=10 (Hit!)
   • (5, 2)=7, (5, 5)=10 (Hit!), (5, 8)=13
   • (8, 2)=10 (Hit!), (8, 5)=13, (8, 8)=16
3. Total: 3 Hits.

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3. Practice Exercises

1. Basic: For i = 1 to 5. How many times?
   • Hint: 5 times.
2. Nested: Outer 10 times, Inner 5 times. Total?
   • Hint: $10\times 5=50$.
3. Logic: For X in [1, 2, 3]: S = S + X. Final S?
   • Hint: $1+2+3=6$.

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🧠 Level Up: Advanced Practice

Question 1: All-Pairs Comparison

Problem: Find pair of students with same marks. Logic:

For each student A in Class:
    For each student B in Class:
        If (A.Name != B.Name) AND (A.Marks == B.Marks):
            Print "Pair found"

Efficiency: This checks each pair twice (A,B and B,A). Optimization: Inner loop should start from next student. For B from A+1 to End.

Question 2: Nested Loop Trace

Problem:

Count = 0
For i = 1 to 3:
    For j = 1 to i:
        Count = Count + 1

Trace:

• i=1: j=1. Count=1.
• i=2: j=1, 2. Count=1+2=3.
• i=3: j=1, 2, 3. Count=3+3=6. Answer: 6.

Question 3: Break vs Continue

Problem: Stop processing if a “Fail” grade is found. Logic:

• If Grade == "Fail" then Break. (Exits loop completely).
• If Grade == "Fail" then Continue. (Skips this student, moves to next). Context: If calculating “Class Average”, use Continue (maybe exclude failures?). If checking “All Pass?”, use Break.