of 8
8/19/2019 Prims Algorithm.ppt
1/17
Prim's Algorithm
on minimum spanningtree
Submitted by:Humayon Tahir (22)
M.Mudassar (56)
M.Sanwal (23)Akif Malik (17)Hafiz sman Tahir (5!3)
"#$ar%m#n% of &om$u%#r S'i#n'#
ni#rsi%y of Sar*odha +ahor# &am$us.
,%h S#m#s%#r S#' A S#ssion- 21,/10
8/19/2019 Prims Algorithm.ppt
2/17
What is Minimum Spanning Tree
• Given a connected, undirected graph, a
spanning tree of that graph is asubgraph which is a tree and connectsall the vertices together.
• A single graph can have many dierent
spanning trees.• A minimum spanning tree is then
a spanning tree with weight lessthan or equal to the weight of
every other spanning tree.
8/19/2019 Prims Algorithm.ppt
3/17
graph G
Spanning Tree from Graph G
2
4
1
2
3
1
4 5
1
8/19/2019 Prims Algorithm.ppt
4/17
Algorithm for finding
Minimum Spanning Tree
• The Prim's Algorithm
8/19/2019 Prims Algorithm.ppt
5/17
About Prim’s AlgorithmTh# al*ori%hm was dis'o#r#d in 1!3 y
ma%h#ma%i'ian o%#'h 4arnik and la%#r ind#$#nd#n%ly
y 'om$u%#r s'i#n%is% o#r% &. rim in 1!57.
Th# al*ori%hm 'on%inuously in'r#as#s %h# siz# of a
%r## s%ar%in* wi%h a sin*l# #r%# un%il i% s$ans all %h#
#r%i'#s.
rim8s al*ori%hm is fas%#r on d#ns#
*ra$hs.
rim8s al*ori%hm runs in 9(n:n)
;u% %h# runnin* %im# 'an # r#du'#usin* a sim$l# inary h#a$ da%a s%ru'%ur#
and an ada'#n'y lis% r#$r#s#n%a%ion
8/19/2019 Prims Algorithm.ppt
6/17
• Prim's algorithm for finding a minimal spanningtree parallels closely the depth- and breadth-first
traversal algorithms !"st as these algorithmsmaintained a closed list of nodes and the pathsleading to them# Prim's algorithm maintains aclosed list of nodes and the edges that lin$ them
into the minimal spanning tree• %hereas the depth-first algorithm "sed a stac$
as its data str"ct"re to maintain the list of opennodes and the breadth-first traversal "sed a
&"e"e# Prim's "ses a priority &"e"e
8/19/2019 Prims Algorithm.ppt
7/17
8/19/2019 Prims Algorithm.ppt
8/17
ets( At first )e declare an array named* closed list
And consider the open list as a priority &"e"e
)ith min-heap
Adding a node and its edge to the closed list
indicates that )e have fo"nd an edge that lin$sthe node into the minimal spanning
tree As a node is added to the
closed list# its s"ccessors
+immediately ad,acent nodesare e.amined and added to a
priority &"e"e of open nodes
8/19/2019 Prims Algorithm.ppt
9/17
/pen ist* d0lose ist*
Total Cost: 0
8/19/2019 Prims Algorithm.ppt
10/17
/pen ist* a, f, e, b
0lose ist* d
Total Cost: 0
8/19/2019 Prims Algorithm.ppt
11/17
/pen ist* f, e, b
0lose ist* d, a
Total Cost: 5
8/19/2019 Prims Algorithm.ppt
12/17
/pen ist* b, e, g
0lose ist* d, a, f
Total Cost: 11
8/19/2019 Prims Algorithm.ppt
13/17
/pen ist* e, g, c
0lose ist* d, a, f, b
Total Cost: 18
8/19/2019 Prims Algorithm.ppt
14/17
/pen ist* c, g
0lose ist* d, a, f, b, e
Total Cost: 25
8/19/2019 Prims Algorithm.ppt
15/17
/pen ist* g
0lose ist* d, a, f, b, e, c
Total Cost: 30
8/19/2019 Prims Algorithm.ppt
16/17
/pen ist*
0lose ist* d, a, f, b, e, c
Total Cost: 39
8/19/2019 Prims Algorithm.ppt
17/17
Than$ yo" for being )ith "s(
Any
