Analyse the running time of the following algorithm in big-O notation. You may use either the exact summation method, or the rules of thumb. An undirected weighted graph G = (V, E) with n vertices (|V| = n). An n times n matrix containing the length of the shortest path between each pair of vertices, D = a n times n matrix of minimum distances initialized to infinity for each vertex v do D[v][v] = 0 for each edge (u, v) do D[u][v] = D[v][u] = w(u, v) (w(u, v) is the weight of edge (u, v)) for k = 1 to n do for I = 1 to n do for j = 1 to n do if D[i][j] > D[i][k] + D[k][j], then D[i][j] = D[i][k] + D[k][j] return D
Solution
Answer is O(n 3 )
Explanation to answer:
-------------------------------
Each for loop will iterate for (n+1) times.
So.. in given algorithm there are three for loops which are placed inside each other.
So the total steps are..
for each verted v do ---------> (n+1) times
D[v][v] = 0
for each edge {u,v} do ---------> (n+1) times
D[u][v] = D[e][u] = w{u,v}{w{u,v} is the weight of edge {u,v}}
for k=1 to n do ---------> (n+1) times
for i=1 to n do ---------> (n+1) times
for j=1 to n do ---------> (n+1) times
So totally..
(n+1) + (n+1) + (n+1)*(n+1)*(n+1)
2n + 2 + (n 2 + 2n + 1) * (n+1)
==> 2n + 2 + n 3 + 3n 2 + 3n + 1
For complexity we will consider highest degree... so O(n 3 )
.
Z Score,T Score, Percential Rank and Box Plot Graph
Analyse the running time of the following algorithm in big-O notation-.docx
1. Analyse the running time of the following algorithm in big-O notation. You may use either the
exact summation method, or the rules of thumb. An undirected weighted graph G = (V, E) with n
vertices (|V| = n). An n times n matrix containing the length of the shortest path between each
pair of vertices, D = a n times n matrix of minimum distances initialized to infinity for each
vertex v do D[v][v] = 0 for each edge (u, v) do D[u][v] = D[v][u] = w(u, v) (w(u, v) is the weight
of edge (u, v)) for k = 1 to n do for I = 1 to n do for j = 1 to n do if D[i][j] > D[i][k] + D[k][j],
then D[i][j] = D[i][k] + D[k][j] return D
Solution
Answer is O(n 3 )
Explanation to answer:
-------------------------------
Each for loop will iterate for (n+1) times.
So.. in given algorithm there are three for loops which are placed inside each other.
So the total steps are..
for each verted v do ---------> (n+1) times
D[v][v] = 0
for each edge {u,v} do ---------> (n+1) times
D[u][v] = D[e][u] = w{u,v}{w{u,v} is the weight of edge {u,v}}
for k=1 to n do ---------> (n+1) times
for i=1 to n do ---------> (n+1) times
for j=1 to n do ---------> (n+1) times
So totally..
(n+1) + (n+1) + (n+1)*(n+1)*(n+1)
2n + 2 + (n 2
+ 2n + 1) * (n+1)
==> 2n + 2 + n 3
+ 3n 2
+ 3n + 1
For complexity we will consider highest degree... so O(n 3 )
![Analyse the running time of the following algorithm in big-O notation. You may use either the
exact summation method, or the rules of thumb. An undirected weighted graph G = (V, E) with n
vertices (|V| = n). An n times n matrix containing the length of the shortest path between each
pair of vertices, D = a n times n matrix of minimum distances initialized to infinity for each
vertex v do D[v][v] = 0 for each edge (u, v) do D[u][v] = D[v][u] = w(u, v) (w(u, v) is the weight
of edge (u, v)) for k = 1 to n do for I = 1 to n do for j = 1 to n do if D[i][j] > D[i][k] + D[k][j],
then D[i][j] = D[i][k] + D[k][j] return D
Solution
Answer is O(n 3 )
Explanation to answer:
-------------------------------
Each for loop will iterate for (n+1) times.
So.. in given algorithm there are three for loops which are placed inside each other.
So the total steps are..
for each verted v do ---------> (n+1) times
D[v][v] = 0
for each edge {u,v} do ---------> (n+1) times
D[u][v] = D[e][u] = w{u,v}{w{u,v} is the weight of edge {u,v}}
for k=1 to n do ---------> (n+1) times
for i=1 to n do ---------> (n+1) times
for j=1 to n do ---------> (n+1) times
So totally..
(n+1) + (n+1) + (n+1)*(n+1)*(n+1)
2n + 2 + (n 2
+ 2n + 1) * (n+1)
==> 2n + 2 + n 3
+ 3n 2
+ 3n + 1
For complexity we will consider highest degree... so O(n 3 )](https://image.slidesharecdn.com/analysetherunningtimeofthefollowingalgorithminbig-onotation-230204001623-af5ac82f/85/Analyse-the-running-time-of-the-following-algorithm-in-big-O-notation-docx-1-320.jpg)
