Example 1: prims minimum spanning tree
import math
def empty_tree (n):
lst = []
for i in range(n):
lst.append([0]*n)
return lst
def min_extension (con,graph,n):
min_weight = math.inf
for i in con:
for j in range(n):
if j not in con and 0 < graph[i][j] < min_weight:
min_weight = graph[i][j]
v,w = i,j
return v,w
def min_span(graph):
con = [0]
n = len(graph)
tree = empty_tree(n)
while len(con) < n :
i ,j = min_extension(con,graph,n)
tree[i][j],tree[j][i] = graph[i][j], graph[j][i]
con += [j]
return tree
def find_weight_of_edges(graph):
tree = min_span(graph)
lst = []
lst1 = []
x = 0
for i in tree:
lst += i
for i in lst:
if i not in lst1:
lst1.append(i)
x += i
return x
graph = [[0,1,0,0,0,0,0,0,0],
[1,0,3,4,0,3,0,0,0],
[0,3,0,0,0,4,0,0,0],
[0,4,0,0,2,9,1,0,0],
[0,0,0,2,0,6,0,0,0],
[0,3,4,9,6,0,0,0,6],
[0,0,0,1,0,0,0,2,8],
[0,0,0,0,0,0,2,0,3],
[0,0,0,0,0,6,8,3,0]]
graph1 = [[0,3,5,0,0,6],
[3,0,4,1,0,0],
[5,4,0,4,5,2],
[0,1,4,0,6,0],
[0,0,5,6,0,8],
[6,0,2,0,8,0]]
print(min_span(graph1))
print("Total weight of the tree is: " + str(find_weight_of_edges(graph1)))
Example 2: find the graph is minimal spanig tree or not
#include <iostream>
#include <vector>
#include <utility>
#include <algorithm>
using namespace std;
const int MAX = 1e4 + 5;
int id[MAX], nodes, edges;
pair <long long, pair<int, int> > p[MAX];
void initialize()
{
for(int i = 0;i < MAX;++i)
id[i] = i;
}
int root(int x)
{
while(id[x] != x)
{
id[x] = id[id[x]];
x = id[x];
}
return x;
}
void union1(int x, int y)
{
int p = root(x);
int q = root(y);
id[p] = id[q];
}
long long kruskal(pair<long long, pair<int, int> > p[])
{
int x, y;
long long cost, minimumCost = 0;
for(int i = 0;i < edges;++i)
{
x = p[i].second.first;
y = p[i].second.second;
cost = p[i].first;
if(root(x) != root(y))
{
minimumCost += cost;
union1(x, y);
}
}
return minimumCost;
}
int main()
{
int x, y;
long long weight, cost, minimumCost;
initialize();
cin >> nodes >> edges;
for(int i = 0;i < edges;++i)
{
cin >> x >> y >> weight;
p[i] = make_pair(weight, make_pair(x, y));
}
sort(p, p + edges);
minimumCost = kruskal(p);
cout << minimumCost << endl;
return 0;
}
Example 3: kruskal's algorithm
#include<bits/stdc++.h>
using namespace std;
int main()
{
int n = 9;
int mat[9][9] = {
{100,4,100,100,100,100,100,8,100},
{4,100,8,100,100,100,100,100,100},
{100,8,100,7,100,4,100,100,2},
{100,100,7,100,9,14,100,100,100},
{100,100,100,9,100,10,100,100,100},
{100,100,4,14,10,100,2,100,100},
{100,100,100,100,100,2,100,1,6},
{8,100,100,100,100,100,1,100,7},
{100,100,2,100,100,100,6,7,100}};
int parent[n];
int edges[100][3];
int count = 0;
for(int i=0;i<n;i++)
for(int j=i;j<n;j++)
{
if(mat[i][j] != 100)
{
edges[count][0] = i;
edges[count][1] = j;
edges[count++][2] = mat[i][j];
}
}
for(int i=0;i<count-1;i++)
for(int j=0;j<count-i-1;j++)
if(edges[j][2] > edges[j+1][2])
{
int t1=edges[j][0], t2=edges[j][1], t3=edges[j][2];
edges[j][0] = edges[j+1][0];
edges[j][1] = edges[j+1][1];
edges[j][2] = edges[j+1][2];
edges[j+1][0] = t1;
edges[j+1][1] = t2;
edges[j+1][2] = t3;
}
int mst[n-1][2];
int mstVal = 0;
int l = 0;
cout<<endl;
for(int i=0;i<n;i++)
parent[i] = -1;
cout<<endl;
for(int i=0;i<count;i++)
{
if((parent[edges[i][0]] == -1 && parent[edges[i][1]] == -1))
{
parent[edges[i][0]] = edges[i][0];
parent[edges[i][1]] = edges[i][0];
mst[l][0] = edges[i][0];
mst[l++][1] = edges[i][1];
mstVal += edges[i][2];
}
else if((parent[edges[i][0]] == -1 && parent[edges[i][1]] != -1))
{
parent[edges[i][0]] = parent[edges[i][1]];
mst[l][0] = edges[i][1];
mst[l++][1] = edges[i][0];
mstVal += edges[i][2];
}
else if((parent[edges[i][0]] != -1 && parent[edges[i][1]] == -1))
{
parent[edges[i][1]] = parent[edges[i][0]];
mst[l][0] = edges[i][0];
mst[l++][1] = edges[i][1];
mstVal += edges[i][2];
}
else if(parent[edges[i][0]] != -1 && parent[edges[i][1]] != -1 && parent[edges[i][0]] != parent[edges[i][1]])
{
int p = parent[edges[i][1]];
for(int j=0;j<n;j++)
if(parent[j] == p)
parent[j] = parent[edges[i][0]];
mst[l][0] = edges[i][0];
mst[l++][1] = edges[i][1];
mstVal += edges[i][2];
}
}
for(int i=0;i<l;i++)
cout<<mst[i][0]<<" -> "<<mst[i][1]<<endl;
cout<<endl;
cout<<mstVal<<endl;
return(0);
}