Definition: We define a path in a graph to be short if it contains ≤ 100 edges. Note that we are looking at the number of edges, not the number of vertices. The Problem: •INPUT – An unweighted DAG G = (V, E) – Two specific vertices s, t ∈V •OUTPUT: the number of different short paths in G from s to t. You don’t have to output the actual paths; you just have to figure out how many of them there are. Show a dynamic programming algorithm that solves the above problem in O(|E|) time. You only need to write pseudocode, nothing else. NOTE: a reminder that you can assume in this class that all arithmetic operations (multiplication, addition, etc.) take O(1) time, even if the numbers are very big.

Q: Write a function find_equivalent_matchings that takes a matching and returns all matchings with the…

A: {(2, 3), (0, 5), (4, 7), (1, 6)}{(2, 3), (0, 7), (4, 6), (1, 5)}{(3, 4), (0, 7), (6, 1), (2, 5)}{(4,…

Q: Output For each graph, produce a line listing the weak vertices ordered from least to greatest.…

A: #include<iostream> using namespace std;   //max no of nodes const int n_max=20;   int main(){…

Q: Suppose you have a graph with N vertices. What is the largest number of edges it may have? log N…

A: Below is the answer assuming the graph provided is an undirected graph.

Q: Write code for complete application that includes all the code for computing the shortest paths…

A: Introduction: Dijkstra's algorithm is a shortest path algorithm for finding the shortest path…

Polynomial Time

The problems for which the deterministic polynomial-time algorithm exists belong to the complexity class (p) and it is central in the field of computational complexity theory. According to Cobham’s thesis, polynomial time is a synonym for “feasible”, “fast”, and “efficient”.