CT_Week4_Loops_While

CT Week 4: While Loops (Iteration)

0. Prerequisites

NOTE

What you need to know:

• Conditionals: True keeps the loop running, False stops it.
• Variable Update: i = i + 1.

Quick Refresher

• Loop: Repeating a block of code multiple times.
• While Loop: Keeps running as long as the condition is True.
• Infinite Loop: A loop that never stops (Bad!).

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1. Core Concepts

1.1 Anatomy of a Loop

1. Initialization: Setting up variables before the loop. (i = 0).
2. Condition: The gatekeeper. (while i < 5).
3. Body: The code to repeat. (Print i).
4. Update: Changing the variable so the condition eventually becomes False. (i = i + 1).

1.2 Flow of Execution

1. Check Condition.
2. If True $\to$ Run Body $\to$ Run Update $\to$ Go back to Step 1.
3. If False $\to$ Exit Loop.

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2. Pattern Analysis & Goated Solutions

Pattern 1: The “Counter” Loop (Standard)

Context: “How many times does this run?” Code:

i = 0
while i < 5:
    Print i
    i = i + 1

TIP

Mental Algorithm (Trace):

1. Init: i=0.
2. Check: $0<5$? Yes. Print 0. Update i=1.
3. Check: $1<5$? Yes. Print 1. Update i=2. …
4. Check: $5<5$? No. Stop.

• Result: Prints 0, 1, 2, 3, 4. (Runs 5 times).

Pattern 2: The “Accumulator” (Summing)

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

i = 1, S = 0
while i <= 3:
    S = S + i
    i = i + 1

TIP

Mental Algorithm:

Step	i	Condition ($i\le 3$)	S ($S+i$)
Init	1	-	0
Loop 1	2	True	$0+1=1$
Loop 2	3	True	$1+2=3$
Loop 3	4	True	$3+3=6$
Stop	4	False	-
Answer: S = 6.

Pattern 3: Infinite Loop Detection

Context: “Does this loop terminate?” Code:

i = 10
while i > 0:
    Print i
    i = i + 1  <-- Mistake!

TIP

Mental Algorithm:

1. Check Direction: Condition is i > 0. We start at 10.
2. Check Update: i increases (11, 12, 13…).
3. Logic: Will increasing numbers ever be less than 0? No.
4. Result: Infinite Loop.

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3. Practice Exercises

1. Trace: i=0. while i < 3: i = i + 2. Final i?
   • Hint: 0 $\to$ 2 $\to$ 4. Stops because $4\nless 3$. Final 4.
2. Logic: while False: …?
   • Hint: Never runs. Body skipped.
3. Count: i=10. while i > 0: i = i - 1. How many runs?
   • Hint: 10, 9, …, 1. Runs 10 times.

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🧠 Level Up: Advanced Practice

Question 1: Loop Termination

Problem: while(A > B) { A = A - 1 }. When does it stop? Logic:

• It stops as soon as A becomes equal to B (assuming integers and A starts > B).
• Trap: If A starts < B, it never runs.
• Trap: If A is float, A == B might be missed due to precision, leading to infinite loop? (In pseudocode usually exact).

Question 2: Infinite Loop Detection

Problem:

X = 0
While (X < 10) {
    Print X
    If (X == 5) { X = X - 1 }
    X = X + 1
}

Trace:

• 0, 1, 2, 3, 4, 5.
• At 5: X becomes 4. Then X becomes 5.
• Loop goes back to 5. X becomes 4. Then 5.
• Result: Infinite Loop oscillating between 4 and 5.

Question 3: Aggregation in Loop

Problem: Calculate average of positive numbers. Logic:

Sum = 0, Count = 0
While (Pile not empty) {
    Read X
    If (X > 0) {
        Sum = Sum + X
        Count = Count + 1
    }
}
Avg = Sum / Count

Trap: Division by zero if Count is 0 (no positive numbers). Always check If Count > 0 before dividing.