Cs6515 algorithms - Study guides, Class notes & Summaries

Equivalence - ANSWER-"x ≡ y (mod N) means that x/N and y/N have the same remainder a ≡ b (mod N) and c ≡ d (mod N) then: a + c ≡ a + d ≡ b + c ≡ b + d (mod N) a - c ≡ a - d ≡ b - c ≡ b - d (mod N) a ** c ≡ a ** d ≡ b ** c ≡ b ** d (mod N) ka ≡ kb (mod N) for any integer k ak ≡ bk (mod N) for any natural number k a + k ≡ b + k (mod N) for any integer k a + b = c, then a (mod N) + b (mod N) ≡ c (mod N) a ** b = c, then a (mod N) ** b (mod N) ≡ c (mod N)...

Steps to solve a Dynamic Programming Problem - ANSWER-1. Define the Input and Output. 2. Define entries in table, i.e. T(i) or T(i, j) is... 3. Define a Recurrence relationship - Based on a subproblem to the main problem. (hint: use a prefix of the original input 1 < i < n). 4. Define the Pseudocode. 5. Define the Runtime of the algorithm. Use Time Function notation here => T(n) = T(n/2) + 1... DP: Types of Subproblems (4) - ANSWER-Input = x1, x2, ..., xn 1) Subproblem = x1, x2...

DFS outputs - ANSWER-pre array, post array, ccnum array, prev array BFS outputs - ANSWER-dist array, prev array Explore outputs - ANSWER-visited array. When to use Dijkstra's? - ANSWER-Works for both directed and undirected graphs. Must have only non-negative edge weights. Dijkstra's outputs - ANSWER-dist array, prev array Dijkstra's runtime? - ANSWER-O((n+m) log n) log n is from using the min heap (to get the lowest cost weight) When to use Bellman Ford? - ANSWER-Use when there is a ...