# Exercises

## Dynamic programming

### Pascal triangle

Write a function that returns the nth row of the Pascal triangle as a list.

### Knight

Let's say that you have a knight on the chessboard. Calculate how many steps does it take to optimally reach the other places on the board.

Write a function knight(x,y) where the parameters are the x, y coordinates of the initial place. Return an 8-by-8 table of integers containing the minimum number of steps to reach that position. For example the initial state should have 0 on it.

Use a dynamic programming table!

### Paint Bucket Tool

Save the following "text" as a list of lists in python!

```.....................................
...#######################...........
...#.....................#...........
...#.....................#...........
...#.....................#...........
...#.....................#...........
...#.....................#...........
...#.....................#######.....
...###.................##......#.....
...#..##.............##........#.....
...#....##.........##..........#.....
...#......##.....##............#.....
...#........#####..............#.....
...#........#..................#.....
...#.......##..................#.....
...#.....##....................#.....
...#...##......................#.....
...#############################.....
.....................................
.....................................
.....................................
.....................................
```

Write a function fill(x,y) which fills a territory starting with the given coordinates, like the bucket tool in Paint.

Starting from the (x, y) coordinate replace . with #, if you encounter a # then stop. Do this recursively for every neighbor of the given point. This will fill out an enclosed territory.

## Finite-state machine

### Parenthesis

Given a string, replace the enclosed parts of the string with a \$ character. A formula is enclosed if it is surrounded by parenthesis. For example:

```(xc)aa(c(b)) -> \$\$\$\$aa\$\$\$\$\$\$
```

Note that the parenthesis can be enclosed into each other.

### Keystrokes

This file contains keystroke data when someone was typing. The interesting part starts from the 5th line:

• The first column is an event: keydown or keyup (others are irrelevant now)
• The next three numbers encode the key, actually the second one is important (third column).
• The fourth column refers to capital or lowercase, but thats also irrelevant now.
• The last one is a timestamp, the number of milliseconds elapsed since January 1st, 1970.

The exercise is to process the keystrokes and reconstruct the typed text. Mind that there is a SHIFT key in the data.

Hint:

• Store a dictionary of keys which are pressed at a given time.
• if a key is released, and it was in the dictionary, then that letter was entered.
• in this case, erase that key from the dictionary.
• store the state of the SHIFT key (up or down)
• There is also a BACKSPACE key!