CS1010 AY24/25 S1 Lecture 5

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# Lecture 5

### 9 September 2024

**Admin Matters**<br>
**Unit 11:** Loops<br>
**Unit 12:** Loop Invariants<br>

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### Programming Exercises

- Exercise 1 due today

- Exercise 2 released today

- Past year PE questions released

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.fit[![meme](figures/meme/pe-is-coming.jpg)]

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### Practical Exam 0

- **Date**: 1 October 2024 (Tuesday)
- **Time**: 6 - 9 PM
- **Duration**: 2 hours
- **Venue**: Programming labs in AS6/COM1/COM4
- **10%** of your grade
- `ssh` into restricted PE hosts with special exam account using lab PCs

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- **Scope:** Units 1 - 12 / Exercises 0 - 2

- **Open Book** (printed/written notes only)

- Past year questions on Canvas

- File a ticket if you have a clash

- More details in upcoming announcements

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### Warning

Pay attention to exam regulations.  Disciplinary actions will be taken against violators.

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# Loops

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.fit[![max](../notes/figures/loops/loops-pdf-6.png)]

max(L,k)

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.fit[![max](../notes/figures/loops/loops-pdf-7.png)]

Loop body: what we do repeatedly

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.fit[![max](../notes/figures/loops/loops-pdf-8.png)]

Terminating condition: when to stop repeating?

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.fit[![max](../notes/figures/loops/loops-pdf-9.png)]

Loop update: what changes from one iteration to the next?

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.fit[![max](../notes/figures/loops/loops-pdf-10.png)]

Loop initialization: what do we need to setup before entering the loop?

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.fit[![max](../notes/figures/max-flowchart/max-flowchart-pdf-9.png)]

Finding factorial recursively

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.fit[![max](../notes/figures/loops/loops-pdf-3.png)]

Finding factorial with a loop

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.fit70[![max](../notes/figures/loops/loops-pdf-3.png)]
.fit70[![max](../notes/figures/loops/loops-pdf-2.png)]

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.fit80[![max](../notes/figures/loops/loops-pdf-2.png)]

.small[
```C
for (initialize; condition; update) {
   body;
}
```
]

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.fit80[![max](../notes/figures/loops/loops-pdf-2.png)]

.small[
```C
initialize;
while (condition) {
   body and update;
}
```
]

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.fit[![meme](figures/meme/for-while-the-same.jpg)]

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.fit80[![max](../notes/figures/loops/loops-pdf-4.png)]

.small[
```C
initialize;
do {
   body and update;
} while (condition);
```
]

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### Demo: Number Guessing Game

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.fit[![max](../notes/figures/loops/loops-pdf-5.png)]

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## Infinite Loop

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### For a Loop to Terminate

Starting from an initial state, every update must move the state towards the termination state.

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## Assertion

```
// { ... }
```

A logical expression that must be true at a given point in a program.

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Does this correctly compute factorial of $n$?

.small[
```C
long factorial(long n)
{
  long product = 1;
  long i = 1;
  while (i < n) {
    i += 1;
    product *= i;
  }
  return product;
}

```
]

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```C
while (cond) {
   // ??
   :
   :
}
// ??
```

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```C
while (cond) {
   // { cond } <-- always true
   :
   :
}
// { !cond } <-- always true
```

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```C
while (cond A) {
   // ?? 
   :
   :
   // { cond B }
}
//  ??
```

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```C
while (cond A) {
   // { A && B }
   :
   :
   // { cond B }
}
// { !A && B }
```

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```C
// { cond B }
while (..) {
   //  ??
   :
   :
}
//  ??
```

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```C
// { cond B }
while (..) {
   // B ❌ <-- only 1st loop
   :
   :
}
// B ❌ <-- only if loop is not entered
```

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```C
// ??
while (cond A) {
   // ??
   :
   :
   // ??
}
// { cond B } <-- if we want this 
// where else must this be true?
```

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```C
// { cond B } <-- must be true here
while (cond A) {
   
   :
   :
   // { cond B } <-- and here
}
// { cond B } <-- to guarantee that 
// 	           B is true here.
```

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### Loop Invariant

An assertion that holds

- before the loop; 
- at the end of each iteration of the loop;
- after the loop;

(but may be temporarily false during the loop)

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### Loop Invariant

.fit[![max](../notes/figures/loops/loops-pdf-2.png)]

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### Loop Invariant

An assertion that holds

- before the loop; 
- at the end of 1st iteration
- at the end of 2nd iteration
- at the end of 3rd iteration
		  :
- after the loop;

(but may be temporarily false during the loop)

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### Loop Invariant

An assertion that holds

- before the loop; 
- at the end of 1st iteration
- if holds at the end of $(k-1)$-th iteration, then also holds at the end of $k$-th iteration
- after the loop;

(but may be temporarily false during the loop)

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### Loop Invariant

An assertion that holds

- before the loop; 
- at the end of 1st iteration
- if holds at the beginning of $k$-th iteration, then also holds at the end of $k$-th iteration
- after the loop;

(but may be temporarily false during the loop)

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Show that `i >= 1` is a loop invariant.

.small[
```C
  long product = 1;
  long i = 1;
  //
  while (i < n) {
    // 
    i += 1;
    product *= i;
	// 
  }
  //
```
]

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Show that `product >= 1` is a loop invariant.

.small[
```C
  long product = 1;
  long i = 1;
  // 
  while (i < n) {
    //
    i += 1;
    product *= i;
	//
  }
  //
```
]

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Show that `product == i!` is a loop invariant.

.small[
```C
  long product = 1;
  long i = 1;
  // 
  while (i < n) {
    // 
    i += 1;
    // 
    product *= i;
    // 
  }
  // 
```
]

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### Homework

- Self-Diagnostic Quiz for Lecture 5

- Exercise 2

- Problem Sets 11 and 12

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