Iteration

]

# Week 5: .fancy[Iteration]

### <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M243.4 2.6l-224 96c-14 6-21.8 21-18.7 35.8S16.8 160 32 160v8c0 13.3 10.7 24 24 24H456c13.3 0 24-10.7 24-24v-8c15.2 0 28.3-10.7 31.3-25.6s-4.8-29.9-18.7-35.8l-224-96c-8.1-3.4-17.2-3.4-25.2 0zM128 224H64V420.3c-.6 .3-1.2 .7-1.8 1.1l-48 32c-11.7 7.8-17 22.4-12.9 35.9S17.9 512 32 512H480c14.1 0 26.5-9.2 30.6-22.7s-1.1-28.1-12.9-35.9l-48-32c-.6-.4-1.2-.7-1.8-1.1V224H384V416H344V224H280V416H232V224H168V416H128V224zm128-96c-17.7 0-32-14.3-32-32s14.3-32 32-32s32 14.3 32 32s-14.3 32-32 32z"/></svg> EMSE 4571: Intro to Programming for Analytics
### <svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M272 304h-96C78.8 304 0 382.8 0 480c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32C448 382.8 369.2 304 272 304zM48.99 464C56.89 400.9 110.8 352 176 352h96c65.16 0 119.1 48.95 127 112H48.99zM224 256c70.69 0 128-57.31 128-128c0-70.69-57.31-128-128-128S96 57.31 96 128C96 198.7 153.3 256 224 256zM224 48c44.11 0 80 35.89 80 80c0 44.11-35.89 80-80 80S144 172.1 144 128C144 83.89 179.9 48 224 48z"/></svg> John Paul Helveston
### <svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:white;overflow:visible;position:relative;"><path d="M152 64H296V24C296 10.75 306.7 0 320 0C333.3 0 344 10.75 344 24V64H384C419.3 64 448 92.65 448 128V448C448 483.3 419.3 512 384 512H64C28.65 512 0 483.3 0 448V128C0 92.65 28.65 64 64 64H104V24C104 10.75 114.7 0 128 0C141.3 0 152 10.75 152 24V64zM48 448C48 456.8 55.16 464 64 464H384C392.8 464 400 456.8 400 448V192H48V448z"/></svg> February 16, 2023

]

---

# Quiz 3

## Write your name on the quiz!

## Rules:

- Work alone; no outside help of any kind is allowed.
- No calculators, no notes, no books, no computers, no phones.

]

]

---

# Common problems in homeworks

### .red[Use `almostEqual()` in test cases with numbers]

This could fail:

```r
stopifnot(getTheCents(2.45) == 45)
```

Instead, use:

```r
stopifnot(almostEqual(getTheCents(2.45), 45))
```

---

# Common problems in homeworks

<br>

### .red[Check your full script for errors]

- Restart R and run your whole code from the top
- **Sequence matters**: Have you called a function before defining it?

---

# Read homework feedback on Box

### Go to [box.com](https://box.com/)

### Search for folder named `netID-p4a` (e.g., `jph-p4a`)

---

# Don't copy-paste code!

<br>

## It's easy to catch (I use [this algorithm](https://theory.stanford.edu/~aiken/publications/papers/sigmod03.pdf))

## Everyone involved gets a 0
 
---

# Week 5: .fancy[Iteration]

### 1. for loops
### 2. breaking and skipping

### BREAK

### 3. while loops

---

# Week 5: .fancy[Iteration]

### 1. .orange[for loops]
### 2. breaking and skipping

### BREAK

### 3. while loops

---

# "Flow Control"

### Code that alters the otherwise linear flow of operations in a program.

### Last week:

- `if` statements
- `else` statements

]

### This week:

- `for` loops
- `while` loops
- `break` statements
- `next` statements

]

---

# The `for` loop

### Basic format:

```r
for (item in sequence) {
    # Do stuff with item

# Loop stops after last item
}
```

]]

### Flow chart:

]

---

# Making a sequence

### (Side note: these are vectors...that's next week - read ahead!)

### Two ways to make a sequence:

### 1. Use the `seq()` function

```r
seq(1, 10)
```

```
#>  [1]  1  2  3  4  5  6  7  8  9 10
```

```r
seq(1, 10, by = 2)
```

```
#> [1] 1 3 5 7 9
```

]]

### 2. Use the `:` operator (step size = 1)

```r
1:10
```

```
#>  [1]  1  2  3  4  5  6  7  8  9 10
```

```r
10:1
```

```
#>  [1] 10  9  8  7  6  5  4  3  2  1
```

]]

---

# Quick code tracing

What will this function print?

```r
for (i in 1:5) {
    if ((i %% 2) == 0) {
        cat('--')
    } else if ((i %% 3) == 0) {
        cat('----')
    }
    cat(i, '\n')
}
```

]]

---

# Quick code tracing

What will this function print?

```r
n <- 6
for (i in seq(n)) {
    cat('|')
    for (j in seq(1, n, 2)) {
        cat('*')
    }
    cat('|', '\n')
}
```

]]

---

## Your turn

1) `sumFromMToN(m, n)`: Write a function that sums the total of the integers between `m` and `n`.<br>**Challenge**: Try solving this without a loop!

- `sumFromMToN(5, 10) == (5 + 6 + 7 + 8 + 9 + 10)`
- `sumFromMToN(1, 1) == 1`

2) `sumEveryKthFromMToN(m, n, k)`: Write a function to sum every kth integer from `m` to `n`.

- `sumEveryKthFromMToN(1, 10, 2) == (1 + 3 + 5 + 7 + 9)`
- `sumEveryKthFromMToN(5, 20, 7) == (5 + 12 + 19)`
- `sumEveryKthFromMToN(0, 0, 1) == 0`

3) `sumOfOddsFromMToN(m, n)`: Write a function that sums every _odd_ integer between `m` and `n`.<br>**Challenge**: Try solving this without a loop!

- `sumOfOddsFromMToN(4, 10) == (5 + 7 + 9)`
- `sumOfOddsFromMToN(5, 9) == (5 + 7 + 9)`

]

---

# Week 5: .fancy[Iteration]

### BREAK

### 3. while loops
]

---

# Breaking out of a loop

Force a loop to stop with `break`

**Note**: `break` doesn't require `()`

```r
for (val in 1:5) {
    if (val == 3) {
        break
    }
    cat(val, '\n')
}
```

```
1
2
```

]]

---

# Quick code tracing

What will this code print?

```r
for (i in 1:3) {
    cat('|')
    for (j in 1:5) {
        if (j == 3) {
            break
        }
        cat('*')
    }
    cat('|', '\n')
}
```

]]

---

# Skipping iterations

Skip to the next iteration in a loop with `next`

**Note**: `next` doesn't require `()`

```r
for (val in 1:5) {
    if (val == 3) {
        next
    }
    cat(val, '\n')
}
```

```
1
2
4
5
```

]]

---

# Quick code tracing

What will this code print?

```r
for (i in 1:3) {
    cat('|')
    for (j in 1:5) {
        if (j == 3) {
            next
        }
        cat('*')
    }
    cat('|', '\n')
}
```

]]

---

## Your turn

`sumOfOddsFromMToNMax(m, n, max)`: Write a function that sums every _odd_ integer from `m` to `n` up until the sum is less than or equal to the value `max`.

Your solution **must** use both `break` and `next` statements.

- `sumOfOddsFromMToNMax(1, 5, 4) == (1 + 3)`
- `sumOfOddsFromMToNMax(1, 5, 3) == (1)`
- `sumOfOddsFromMToNMax(1, 5, 10) == (1 + 3 + 5)`

---

# .fancy[Break]

---

# Week 5: .fancy[Iteration]

### BREAK

### 3. .orange[while loops]
]

A friend calls her programmer roommate and said, "_while_ you're out, buy some milk"...

...she never returned home.

<img src="images/laugh_emoji.png" width="100">
]

---

# The `while` loop

### Basic format:

```r
while (CONDITION) {
    # Do stuff here

# Update condition
}
```

]]

Here's the general idea:

]

---

# Quick code tracing

Consider this function:

```r
f <- function(x) {
    n <- 1
    while (n < x) {
        cat(n, '\n')
        n <- 2*n
    }
}
```

]]

What will this code print?

```r
f(5)
f(10)
f(50)
f(60)
f(64)
```

]]

---

## `for` vs. `while`

### Use `for` loops when the number of iterations is **_known_**.

1. Build the sequence
2. Iterate over it

```r
*for (i in 1:5) { # Define the sequence
    cat(i, '\n')
}
```

```
#> 1 
#> 2 
#> 3 
#> 4 
#> 5
```

]

### Use `while` loops when the number of iterations is **_unknown_**.

1. Define stopping condition
2. Iterate until condition is met

```r
i <- 1
*while (i <= 5) { # Set stopping condition
    cat(i, '\n')
*   i <- i + 1 # Update condition
}
```

```
#> 1 
#> 2 
#> 3 
#> 4 
#> 5
```

]

---

## Your turn: Write functions

The function `isMultipleOf4Or7(n)` returns `TRUE` if `n` is a multiple of 4 or 7 and `FALSE` otherwise.

- `isMultipleOf4Or7(0) == FALSE`
- `isMultipleOf4Or7(1) == FALSE`
- `isMultipleOf4Or7(4) == TRUE`
- `isMultipleOf4Or7(7) == TRUE`
- `isMultipleOf4Or7(28) == TRUE`

]

Your job is to write `nthMultipleOf4Or7(n)`:

A function that returns the nth positive integer that is a multiple of either 4 or 7.

- `nthMultipleOf4Or7(1) == 4`
- `nthMultipleOf4Or7(2) == 7`
- `nthMultipleOf4Or7(3) == 8`
- `nthMultipleOf4Or7(4) == 12`
- `nthMultipleOf4Or7(5) == 14`
- `nthMultipleOf4Or7(6) == 16`

]

---

## Your turn

`isPrime(n)`: Write a function that takes a non-negative integer, `n`, and returns `TRUE` if it is a prime number and `FALSE` otherwise. Here's some test cases:

- `isPrime(1) == FALSE`
- `isPrime(2) == TRUE`
- `isPrime(7) == TRUE`
- `isPrime(13) == TRUE`
- `isPrime(14) == FALSE`

]

`nthPrime(n)`: Write a function that takes a non-negative integer, `n`, and returns the nth prime number, where `nthPrime(1)` returns the first prime number (2). Hint: use the function `isPrime(n)` as a helper function!

- `nthPrime(1) == 2`
- `nthPrime(2) == 3`
- `nthPrime(3) == 5`
- `nthPrime(4) == 7`
- `nthPrime(7) == 17`

]

---

# [HW 5](https://p4a.seas.gwu.edu/2023-Spring/hw/5-iteration.html)

- ## Trickier turtles

- ## Read about [Happy Numbers](https://en.wikipedia.org/wiki/Happy_number)