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Write a program that plays Hangman as good as possible. For example you can use a large dictionary like this and select the letter that excludes most words that are still possible solutions. Try to make the program as efficient as possible, i.e. don’t scan the whole dictionary in every turn.000
Write a Tetris clone000
Write a Memory game.000
Write a program that displays a bouncing ball.000
Given a set of d-dimensional rectangular boxes, write a program that computes the volume of their union. Start with 2D and work your way up.000
Implement a van Emde Boas tree. Compare it with your previous search tree implementations.000
Write a function that multiplies two matrices together. Make it as efficient as you can and compare the performance to a polished linear algebra library for your language. You might want to read about Strassen’s algorithm and the effects CPU caches have. Try out different matrix layouts and see what happens.000
Given two strings, write a program that outputs the shortest sequence of character insertions and deletions that turn one string into the other.000
Given an array with numbers, write a program that efficiently answers queries of the form: “Which is the nearest larger value for the number at position i?”, where distance is the difference in array indices. For example in the array [1,4,3,2,5,7], the nearest larger value for 4 is 5. After linear time preprocessing you should be able to answer queries in constant time.000
Given two strings, write a program that efficiently finds the longest common subsequence.000
Compare the performance of insertion, deletion and search on your unbalanced search tree with your balanced search tree and a sorted list. Think about good input sequences. If you implemented an (a,b)-tree, think about good values of a and b.000
Implement a balanced binary search tree of your choice. I like (a,b)-trees best.000
Implement an unbalanced binary search tree.000
Implement a binary heap. Once using a list as the base data structure and once by implementing a pointer-linked binary tree. Use it for implementing heap-sort.000
If you chose your growth right in the previous problem, you typically won’t allocate very often. However, adding to a big list sometimes consumes considerable time. That might be problematic in some applications. Instead try allocating new chunks of memory for new items. So when your list is full and the user wants to add something, allocate a new chunk of 100 elements instead of copying all elements over to a new large chunk. Think about where to do the book-keeping about which chunks you have. Different book keeping strategies can quite dramatically change the performance characteristics of your list.000
Improve your previous implementation such that an arbitrary number of elements can be stored in your list. You can for example allocate bigger and bigger chunks of memory as your list grows, copy the old elements over and release the old storage. You should probably also release this memory eventually if your list shrinks enough not to need it anymore. Think about how much bigger the new chunk of memory should be so that your performance won’t be killed by allocations. Increasing the size by 1 element for example is a bad idea.000
Implement your list interface using a fixed chunk of memory, say an array of size 100. If the user wants to add more stuff to your list than fits in your memory you should produce some kind of error, for example you can throw an exception if your language supports that.000
Think of a good interface for a list. What operations do you typically need? You might want to investigate the list interface in your language and in some other popular languages for inspiration.000
Write a program that finds the longest palindromic substring of a given string. Try to be as efficient as possible!000
Write a program that automatically converts English text to Morse code and vice versa.000
Write a program that automatically generates essays for you.000
Write a function that generates a DOT representation of a graph.000
Implement a data structure for graphs that allows modification (insertion, deletion). It should be possible to store values at edges and nodes. It might be easiest to use a dictionary of (node, edgelist) to do this.000
Write a program that takes the duration of a year (in fractional days) for an imaginary planet as an input and produces a leap-year rule that minimizes the difference to the planet’s solar year.000
Write a program that outputs all possibilities to put + or - or nothing between the numbers 1,2,…,9 (in this order) such that the result is 100. For example 1 + 2 + 3 - 4 + 5 + 6 + 78 + 9 = 100.000
Write function that translates a text to Pig Latin and back. English is translated to Pig Latin by taking the first letter of every word, moving it to the end of the word and adding ‘ay’. “The quick brown fox” becomes “Hetay uickqay rownbay oxfay”.000
Write a function that takes a list of strings an prints them, one per line, in a rectangular frame. For example the list ["Hello", "World", "in", "a", "frame"] gets printed as: ********* * Hello * * World * * in * * a * * frame * *********000
Implement binary search.000
Implement the following sorting algorithms: Selection sort, Insertion sort, Merge sort, Quick sort, Stooge Sort. Check Wikipedia for descriptions.000
Write a function that takes a list of numbers, a starting base b1 and a target base b2 and interprets the list as a number in base b1 and converts it into a number in base b2 (in the form of a list-of-digits). So for example [2,1,0] in base 3 gets converted to base 10 as [2,1].000
Write functions that add, subtract, and multiply two numbers in their digit-list representation (and return a new digit list). If you’re ambitious you can implement Karatsuba multiplication. Try different bases. What is the best base if you care about speed? If you couldn’t completely solve the prime number exercise above due to the lack of large numbers in your language, you can now use your own library for this task.000
Write a function that takes a number and returns a list of its digits. So for 2342 it should return [2,3,4,2].000
Write a function that computes the list of the first 100 Fibonacci numbers. The first two Fibonacci numbers are 1 and 1. The n+1-st Fibonacci number can be computed by adding the n-th and the n-1-th Fibonacci number. The first few are therefore 1, 1, 1+1=2, 1+2=3, 2+3=5, 3+5=8.000
Write a function that rotates a list by k elements. For example [1,2,3,4,5,6] rotated by two becomes [3,4,5,6,1,2]. Try solving this without creating a copy of the list. How many swap or move operations do you need?000
Write a function that merges two sorted lists into a new sorted list. [1,4,6],[2,3,5] → [1,2,3,4,5,6]. You can do this quicker than concatenating them followed by a sort.000
Write a function that combines two lists by alternatingly taking elements, e.g. [a,b,c], [1,2,3] → [a,1,b,2,c,3].000
Write a function that concatenates two lists. [a,b,c], [1,2,3] → [a,b,c,1,2,3]000
Write a function on_all that applies a function to every element of a list. Use it to print the first twenty perfect squares. The perfect squares can be found by multiplying each natural number with itself. The first few perfect squares are 1*1= 1, 2*2=4, 3*3=9, 4*4=16. Twelve for example is not a perfect square because there is no natural number m so that m*m=12. (This question is tricky if your programming language makes it difficult to pass functions as arguments.)000
Write three functions that compute the sum of the numbers in a list: using a for-loop, a while-loop and recursion. (Subject to availability of these constructs in your language of choice.)000
Write a function that tests whether a string is a palindrome.000
Write a function that computes the running total of a list.000
Write a function that returns the elements on odd positions in a list.000
Write a function that checks whether an element occurs in a list.000
Write function that reverses a list, preferably in place.000
Write a function that returns the largest element in a list.000
Write a program that computes 4\cdot \sum_{k=1}^{10^6} \frac{(-1)^{k+1}}{2k-1} = 4\cdot(1-1/3+1/5-1/7+1/9-1/11\ldots).000
Write a program that prints the next 20 leap years000
Write a guessing game where the user has to guess a secret number. After every guess the program tells the user whether their number was too large or too small. At the end the number of tries needed should be printed. It counts only as one try if they input the same number multiple times consecutively.000
Write a program that prints all prime numbers. (Note: if your programming language does not support arbitrary size numbers, printing all primes up to the largest number you can easily represent is fine too.)000
Write a program that prints a multiplication table for numbers up to 12.001
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