EXPERIMENT-01
BFS
graph
'5'
'3'
'7'
'2'
'4'
'8'
}
=
:
:
:
:
:
:
{
['3','7'],
['2', '4'],
['8'],
[],
['8'],
[]
visited = []
queue = []
def bfs(visited, graph, node):
visited.append(node)
queue.append(node)
while queue:
m = queue.pop(0)
print (m, end = " ")
for neighbour in graph[m]:
if neighbour not in visited:
visited.append(neighbour)
queue.append(neighbour)
print("Following is the Breadth-First Search")
bfs(visited, graph, '5')
OUTPUT:
Following is the Breadth-First Search
5 3 7 2 4 8
DFS
graph
'5'
'3'
'7'
'2'
'4'
'8'
}
=
:
:
:
:
:
:
{
['3','7'],
['2', '4'],
['8'],
[],
['8'],
[]
visited = set()
def dfs(visited, graph, node):
if node not in visited:
print (node)
visited.add(node)
for neighbour in graph[node]:
dfs(visited, graph, neighbour)
print("Following is the Depth-First Search")
dfs(visited, graph, '5')
OUTPUT:
Following is the Depth-First Search
5
3
2
4
8
7
EXPERIMENT-02
A* Algorithm
from collections import deque
class Graph:
def __init__(self, adjacency_list):
self.adjacency_list = adjacency_list
def get_neighbors(self, v):
return self.adjacency_list[v]
def h(self, n):
H = {
'A': 1,
'B': 1,
'C': 1,
'D': 1
}
return H[n]
def a_star_algorithm(self, start_node, stop_node):
open_list = set([start_node])
closed_list = set([])
g = {}
g[start_node] = 0
parents = {}
parents[start_node] = start_node
while len(open_list) > 0:
n = None
for v in open_list:
if n == None or g[v] + self.h(v) < g[n] + self.h(n):
n = v
if n == None:
print('Path does not exist!')
return None
if n == stop_node:
reconst_path = []
while parents[n] != n:
reconst_path.append(n)
n = parents[n]
reconst_path.append(start_node)
reconst_path.reverse()
print('Path found: {}'.format(reconst_path))
return reconst_path
for (m, weight) in self.get_neighbors(n):
if m not in open_list and m not in closed_list:
open_list.add(m)
parents[m] = n
g[m] = g[n] + weight
else:
if g[m] > g[n] + weight:
g[m] = g[n] + weight
parents[m] = n
if m in closed_list:
closed_list.remove(m)
open_list.add(m)
open_list.remove(n)
closed_list.add(n)
print('Path does not exist!')
return None
adjacency_list = {
'A': [('B', 1), ('C', 3), ('D', 7)],
'B': [('D', 5)],
'C': [('D', 12)]
}
graph1 = Graph(adjacency_list)
graph1.a_star_algorithm('A', 'D')
OUTPUT:
Path found: ['A', 'B', 'D']
EXPERIMENT-03
Prims algorithm
import sys
class Graph():
def __init__(self, vertices):
self.V = vertices
self.graph = [[0 for column in range(vertices)]
for row in range(vertices)]
def printMST(self, parent):
print("Edge \tWeight")
for i in range(1, self.V):
print(parent[i], "-", i, "\t", self.graph[i][parent[i]])
def minKey(self, key, mstSet):
# Initialize min value
min = sys.maxsize
for v in range(self.V):
if key[v] < min and mstSet[v] == False:
min = key[v]
min_index = v
return min_index
def primMST(self):
key = [sys.maxsize] * self.V
parent = [None] * self.V # Array to store constructed MST
key[0] = 0
mstSet = [False] * self.V
parent[0] = -1 # First node is always the root of
for cout in range(self.V):
u = self.minKey(key, mstSet)
mstSet[u] = True
for v in range(self.V):
if self.graph[u][v] > 0 and mstSet[v] == False
and key[v] > self.graph[u][v]:
key[v] = self.graph[u][v]
parent[v] = u
self.printMST(parent)
if __name__ == '__main__':
g = Graph(5)
g.graph = [[0, 2, 0, 6, 0],
[2, 0, 3, 8, 5],
[0, 3, 0, 0, 7],
[6, 8, 0, 0, 9],
[0, 5, 7, 9, 0]]
g.primMST()
OUTPUT:
Edge Weight
0-1 2
1-2 3
0-3 6
1-4 5
Experiment-04
NQUEEN PROBLEMS
print ("Enter the number of queens")
N = int(input())
board = [[0]*N for _ in range(N)]
def is_attack(i, j):
for k in range(0,N):
if board[i][k]==1 or board[k][j]==1:
return True
for k in range(0,N):
for l in range(0,N):
if (k+l==i+j) or (k-l==i-j):
if board[k][l]==1:
return True
return False
def N_queen(n):
if n==0:
return True
for i in range(0,N):
for j in range(0,N):
'''checking if we can place a queen here or not
queen will not be placed if the place is being attacked
or already occupied'''
if (not(is_attack(i,j))) and (board[i][j]!=1):
board[i][j] = 1
if N_queen(n-1)==True:
return True
board[i][j] = 0
return False
N_queen(N)
for i in board:
print (i)
Output:
Enter the number of queens
8
[1, 0, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 0, 1]
[0, 0, 0, 0, 0, 1, 0, 0]
[0, 0, 1, 0, 0, 0, 0, 0]
[0, 0, 0, 0, 0, 0, 1, 0]
[0, 1, 0, 0, 0, 0, 0, 0]
[0, 0, 0, 1, 0, 0, 0, 0]