Lecture 4: Problem Solving

class: center, middle, inverse, title-slide

.title[
# Lecture 4: Problem Solving
]
.author[
### Robin Liu
]
.institute[
### UCSB
]
.date[
### 2022-06-26
]

---

# Problem Solving
## Today we will tackle some possibly challenging coding problems.

These problems can all be solved using the simple techniques we have learned so far.

During a job interview, you will be asked to solve problems far more challenging
than what I have here.

Some of these problems were inspired by what I found on leetcode.

https://leetcode.com

To get a coding job you **must** grind leetcode problems.
---
# Problem Solving
I will describe a coding problem which involves writing
a function taking certain arguments.

The output of your function should match some provided **test cases**.

---
# Remove element
You are given a numeric vector `v` and a number `target`.
Create a function `remove_elt` that returns a vector containing
elements of `v` but with `target` removed.

```r
remove_elt <- function(v, target) {
  # Your code here
}
```

```r
remove_elt(c(2, 3, 3, 5), 3)
```

```
## [1] 2 5
```

```r
remove_elt(c(14, 14, 7, 7, 14, 10), 14)
```

```
## [1]  7  7 10
```

<div class="countdown" id="timer_62b89e21" style="right:0;bottom:0;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">05</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>
---
# Print Square
Write a function `print_square(n)`. `n` is a nonnegative integer and 
`print_square(n)` prints a square of `*` of dimension `n` by `n`.

```r
print_square <- function(n) {
  # Your code here
}
```

```r
print_square(2)
```

```
## [1] "*" "*"
## [1] "*" "*"
```

```r
print_square(5)
```

```
## [1] "*" "*" "*" "*" "*"
## [1] "*" "*" "*" "*" "*"
## [1] "*" "*" "*" "*" "*"
## [1] "*" "*" "*" "*" "*"
## [1] "*" "*" "*" "*" "*"
```

<div class="countdown" id="timer_62b89ed9" style="right:0;bottom:0;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">05</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>
---
# Print Triangle
Write a function `print_triangle(n)` that prints a triangle of side length `n`.

```r
print_triangle <- function(n) {
  # Your code here
}
```

```r
print_triangle(3)
```

```
## [1] "*"
## [1] "*" "*"
## [1] "*" "*" "*"
```

```r
print_triangle(5)
```

```
## [1] "*"
## [1] "*" "*"
## [1] "*" "*" "*"
## [1] "*" "*" "*" "*"
## [1] "*" "*" "*" "*" "*"
```

<div class="countdown" id="timer_62b89e77" style="right:0;bottom:0;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">05</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>
---
# Max vector
You are given two integer vectors `nums1` and `nums2`, and an integer `n`
representing the number of elements in `nums1` and `nums2`, which have the same length.

Write a function `max_vec` that
returns a vector of the element-wise maximum of `nums` and `nums2`.

```r
max_vec <- function(nums1, nums2, n) {
  result <- vector(length = n) # this initializes an "empty" vector with length n
  # Your code here
  return(result)
}
```

```r
max_vec(1:4, c(0, 27, -5, 19), 4)
```

```
## [1]  1 27  3 19
```
<div class="countdown" id="timer_62b89fc8" style="right:0;bottom:0;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">08</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>
---
# Small Count Simple
Write a function `small_count_simple(v, target)`
that takes a numeric vector `v`, a number `target`, and returns how many
elements of `v` are less than `target`

```r
small_count_simple <- function(v, target) {
  # Your code here
}
```

```r
small_count_simple(c(10, 15, -2, 5), 11)
```

```
## [1] 3
```

```r
small_count_simple(c(0, 0, -2, 5), 4)
```

```
## [1] 3
```

*Hint*: Use a *recycling* comparison and the numeric value of logicals.
Review Lecture 2 slides if necessary.

---
# Small Count
Write a function `small_count(v)` that takes a vector `v`
and returns, for each element `v[i]`, how many elements of `v` are less than `v[i]`.

```r
small_count <- function(v) {
  result <- vector(length = length(v))
  # Your code here
  return(result)
}
```

```r
small_count(c(12, 100, -3))
```

```
## [1] 1 2 0
```

```r
small_count(c(12, 100, -3, -12))
```

```
## [1] 2 3 1 0
```

---
# Two Sum
Write a function `two_sum` that takes a vector `v` and a number `target`
and returns two *indices* of numbers in `v` that add up to `target`.
The two indices cannot be equal.

.pull-left[

```r
two_sum <- function(v, target) {
  i <- 0
  j <- 0
  # Your code here
  # Hint: one way is to use two for loops
}
```
]
.pull-right[

```r
two_sum(c(2, 7, 11, 15), 9)
```

```
## [1] 2 1
```

```r
two_sum(c(3, 2, 4), 6)
```

```
## [1] 3 2
```

```r
two_sum(c(3, 3), 6)
```

```
## [1] 2 1
```
]

---
# Which
This is an important function.
`which` takes a logical vector and returns a vector of indices of TRUE entries.

```r
which(c(T, F, F, T, T))
```

```
## [1] 1 4 5
```

Write a function `first_even` that takes a numeric vector `v`
and returns the first element of `v` that is an even number.

```r
first_even(c(1, 3, 5, 6, 7, 8))
```

```
## [1] 6
```

```r
first_even(c(-1, -4, 0, 2))
```

```
## [1] -4
```

---
# Last Negative
Write a function `last_negative` that takes a numeric vector `v`
and returns the last element that is less than zero.

```r
last_negative(c(1, -9, 0, 6, -7, 0))
```

```
## [1] -7
```

```r
last_negative(c(-1, -4, 0, 2))
```

```
## [1] -4
```

---
# any and all
These functions are usful. They take a logical vector and return a single logical:

```r
any(c(F, F, T, F, F))
```

```
## [1] TRUE
```

```r
all(c(F, F, T, F, F))
```

```
## [1] FALSE
```

```r
all(c(T, T, T))
```

```
## [1] TRUE
```

Write an expression that tests if a vector contains all negative elements.

<div class="countdown" id="timer_62b89e13" style="right:0;bottom:0;" data-warnwhen="0">
<code class="countdown-time"><span class="countdown-digits minutes">01</span><span class="countdown-digits colon">:</span><span class="countdown-digits seconds">00</span></code>
</div>
---
# Vectorized Two Sum

```r
two_sum <- function(v, target) {
  pairs <- combn(seq_along(v), 2)
  w <- v[pairs[1, ]] + v[pairs[2, ]] == target
  pairs[, which(w)]
}
```