Algorithms

Search algorithms

       Linear search. Finding smallest/biggest element in array O(n)

       Binary search. checking for the existance of an element in O(logn)

Math

       Handling extremely big numbers.

       Euler function

       calculate A^N for O(logn) time

        Finding the greatest common divisor of 2 numbers in O(logn).Euclid's algorithm    

        Finding all prime numbers in [1;N] for O(nlogn).the sieve of eratostenes

       Prime factorization

       Greatest common divisor of 2 numbers. Euclid's Algorithm

Dynamic Programming

       LCS(Longest Common Subsequence)

       The number of minimum insertions to make a palindrome out of a string

       Knapsack Problem with 1 parameter

       Knapsack Problem with 2 parameters

       Optimizing the knapsack problem.

       Game 1: 2 players taking items from 2 ends, second one takes the biggest

       Edit Distance (Levanshtein's distance)

Graphs

       What are graphs? 

       Directed and indirected graphs.

       BFS( Breadth First Search) 

       DFS( Depth First Search)

       Segment trees.Finding the sum of a given range in O(logN)

       Finding the longest path in a tree.

       Tries

OTHER

       Finding the next permutation of a sequence

       Josephus Problem

       Minimum operations to form a correct bracket expression