1. Presented by-Kapil Kumar Cse-iii rd year kapilkumar0303@gmail.com
TOPIC-ALL PAIR SHORTEST PATH
Floyd – Warshall Alogorithm
Presented by-Kapil Kumar
Cse-iii rd year

2. Graph - Basis A Non linear data structure Set of vertices and edges
Classification According to Direction of edges
Directed Graph
Undirected graph
Classification According to weight on edges
Weighted graph
Unweighted graph
vertex
edge

3. Graph – Basis (continue..)
Representation
Incident matrix
Adjacency matrix
Adjacency list
Path matrix

4. What is Floyd warshall algorithm?
An example of dynamic programming
An algorithm for finding shortest path in a weighted graph with
positive or negative edge weights
No negative weight cycle
Find the length of shortest path between all pair of vertices

5. History Naming Bernard Roy in 1959 Robert Floyd in 1962
Stephen Warshall in 1962
Naming
The Floyd's algorithm
the Roy–Warshall algorithm
the Roy–Floyd algorithm, or
the WFI algorithm

6. Path 3: A -> B -> C -> D = 6
What is shortest path?
There are several paths between A and D: 7 B D 1 2 3
Path 1: A -> B -> D = 9
Path 2: A -> C -> D = 7
Path 3: A -> B -> C -> D = 6 A C 4

7. Floyd Warshall Algorithm
function Floyd(L[l.. n, 1..n]): array [1.. n,1. n]
array D[L..n,1 ..n] Time
D  L (1)
for k  1 to n do (n)
for i  1 to n do (n)
for j  1 to n do 0(n)
D[i,j] min(D[i, j],D[i, k]+D[k,j])
return D

8. Floyd Warshall Algorithm
The running time is O(n3).
The space requirements are O(n2)

9. Example
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10. Application Fast computation of path finder networks. Optimal routing.
Detecting negative-weight cycles in graph.
Shortest paths in directed graphs
Transitive closure of directed graphs.
Inversion of real matrices
Maximum bandwidth paths

11. Any Query ?

12. Thank you