Example 1: prims c++
using namespace std;
const int MAX = 1e4 + 5;
typedef pair<long long, int> PII;
bool marked[MAX];
vector <PII> adj[MAX];
long long prim(int x)
{
priority_queue<PII, vector<PII>, greater<PII> > Q;
int y;
long long minimumCost = 0;
PII p;
Q.push(make_pair(0, x));
while(!Q.empty())
{
// Select the edge with minimum weight
p = Q.top();
Q.pop();
x = p.second;
// Checking for cycle
if(marked[x] == true)
continue;
minimumCost += p.first;
marked[x] = true;
for(int i = 0;i < adj[x].size();++i)
{
y = adj[x][i].second;
if(marked[y] == false)
Q.push(adj[x][i]);
}
}
return minimumCost;
}
int main()
{
int nodes, edges, x, y;
long long weight, minimumCost;
cin >> nodes >> edges;
for(int i = 0;i < edges;++i)
{
cin >> x >> y >> weight;
adj[x].push_back(make_pair(weight, y));
adj[y].push_back(make_pair(weight, x));
}
// Selecting 1 as the starting node
minimumCost = prim(1);
cout << minimumCost << endl;
return 0;
}
Example 2: 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)))