Table of Contents

- 1 What is the time complexity of adjacency list?
- 2 What is the time complexity of following operation in adjacency list and Adjacency Matrix?
- 3 What is adjacency multi list?
- 4 What is the purpose of running a BFS on a graph?
- 5 How is an edge found in an adjacency list?
- 6 Why do we need an adjacency matrix and list?

## What is the time complexity of adjacency list?

Therefore the complexity is O(|V|2). There are two pointers in adjacency list first points to the front node and the other one points to the rear node. Thus insertion of a vertex can be done directly in O(1) time. To add an edge say from i to j, matrix[i][j] = 1 which requires O(1) time.

## What is the time complexity of following operation in adjacency list and Adjacency Matrix?

Time/Space complexity of adjacency matrix and adjacency list. I am reading “Algorithms Design” By Eva Tardos and in chapter 3 it is mentioned that adjacency matrix has the complexity of O(n^2) while adjacency list has O(m+n) where m is the total number of edges and n is the total number of nodes.

**What is the running time of BFS that works on a graph represented by an Adjacency Matrix?**

4 Answers. The complexity of BFS implemented using an Adjacency Matrix will be O(|V|²) . And that when implemented by an Adjacency List is O(|V| + |E|) .

**What is the time complexity of DFS using adjacency list?**

For a directed graph, the sum of the sizes of the adjacency lists of all the nodes is E. So, the time complexity in this case is O(V) + O(E) = O(V + E). For an undirected graph, each edge appears twice. Once in the adjacency list of either end of the edge.

### What is adjacency multi list?

Adjacency Multi list. An edge in an undirected graph is represented by two nodes in adjacency list representation. Adjacency Multi lists lists in which nodes may be shared among several lists.

### What is the purpose of running a BFS on a graph?

Breadth-first search (BFS) is an important graph search algorithm that is used to solve many problems including finding the shortest path in a graph and solving puzzle games (such as Rubik’s Cubes). Many problems in computer science can be thought of in terms of graphs.

**What is the time and space complexity of an adjacency matrix?**

Time and Space Complexity Assuming the graph has vertices, the time complexity to build such a matrix is . The space complexity is also . Given a graph, to build the adjacency matrix, we need to create a square matrix and fill its values with 0 and 1. It costs us space.

**How to calculate the time and space complexity of a list?**

Time and Space Complexity If is the number of edges in a graph, then the time complexity of building such a list is . The space complexity is . But, in the worst case of a complete graph, which contains edges, the time and space complexities reduce to .

## How is an edge found in an adjacency list?

In a complete graph with vertices, for every vertex the element of would contain element, as every vertex is connected with every other vertex in such a graph. Therefore, the time complexity checking the presence of an edge in the adjacency list is .

## Why do we need an adjacency matrix and list?

Each element is also a list and contains all the vertices, adjacent to the current vertex . By choosing an adjacency list as a way to store the graph in memory, this may save us space. For instance, in the Depth-First Search algorithm, there is no need to store the adjacency matrix.

**What is the time complexity of an adjacency matrix?**

In an adjacency list every vertex is associated with a list of adjacent vertices. For a given graph, in order to check for an edge we need to check for vertices adjacent to given vertex. A vertex can have at most O(|V|) neighbours and in worst can we would have to check for every adjacent vertex. Therefore, time complexity is O(|V|).

In a complete graph with vertices, for every vertex the element of would contain element, as every vertex is connected with every other vertex in such a graph. Therefore, the time complexity checking the presence of an edge in the adjacency list is .

Time and Space Complexity If is the number of edges in a graph, then the time complexity of building such a list is . The space complexity is . But, in the worst case of a complete graph, which contains edges, the time and space complexities reduce to .

**How to insert a vertex in an adjacency list?**

Therefore the complexity is O (|V|2). There are two pointers in adjacency list first points to the front node and the other one points to the rear node.Thus insertion of a vertex can be done directly in O (1) time. To add an edge say from i to j, matrix [i] [j] = 1 which requires O (1) time.