What is the depth first search(DFS)? Write the pseudo code for DFS traversal and write its time and space complexity. How to represent sparse matrix in arrays. explain in details. code example

Example 1: dfs python

###############
#The Algorithm (In English):

# 1) Pick any node. 
# 2) If it is unvisited, mark it as visited and recur on all its 
#    adjacent nodes. 
# 3) Repeat until all the nodes are visited, or the node to be 
#    searched is found.


# The graph below (declared as a Python dictionary)
# is from the linked website and is used for the sake of
# testing the algorithm. Obviously, you will have your own
# graph to iterate through.
graph = {
    'A' : ['B','C'],
    'B' : ['D', 'E'],
    'C' : ['F'],
    'D' : [],
    'E' : ['F'],
    'F' : []
}

visited = set() # Set to keep track of visited nodes.


##################
# The Algorithm (In Code)

def dfs(visited, graph, node):
    if node not in visited:
        print (node)
        visited.add(node)
        for neighbour in graph[node]:
            dfs(visited, graph, neighbour)
            
# Driver Code to test in python yourself.
# Note that when calling this, you need to
# call the starting node. In this case it is 'A'.
dfs(visited, graph, 'A')

# NOTE: There are a few ways to do DFS, depending on what your
# variables are and/or what you want returned. This specific
# example is the most fleshed-out, yet still understandable,
# explanation I could find.

Example 2: depth first search

# HAVE USED ADJACENY LIST
class Graph:
    def __init__(self,lst=None):
        self.lst=dict()
        if lst is None:
            pass
        else:
            self.lst=lst
    def find_path(self,start,end):
        self.checklist={}
        for i in self.lst.keys():
            self.checklist[i]=False
        self.checklist[start]=True
        store,extra=(self.explore(start,end))
        if store==False:
            print('No Path Found')
        else:
            print(extra)
    def explore(self,start,end):
        while True:
            q=[]        
            #print(self.checklist,q)
            q.append(start)
            flag=False            
            for i in self.lst[start]:
                if i==end:
                    q.append(i)
                    return True,q
                if self.checklist[i]:
                    pass
                else:
                    flag=True
                    self.checklist[i]=True
                    q.append(i)
                    break   
            if flag:
                store,extra=self.explore(q[-1],end) 
                if store==False:
                    q.pop()
                    if len(q)==0:return False
                    return self.explore(q[-1],end)
                elif store==None:
                    pass
                elif store==True:
                    q.pop()
                    q.extend(extra)
                    return True,q
            else:
                return False,None
    def __str__(self):return str(self.lst)
if __name__=='__main__':
    store={1: [2, 3, 4], 2: [3, 1], 3: [2, 1], 4: [5, 8, 1], 5: [4, 6, 7], 6: [5, 7, 9, 8], 7: [5, 6], 8: [4, 6, 9], 9: [6, 8, 10], 10: [9],11:[12,13]}
    a=Graph(store)
    a.find_path(1,11) # No Path Found 
    a.find_path(1,6)# [1, 4, 5, 6]    
    a.find_path(3,10)   # [3, 2, 1, 4, 5, 6, 9, 10] 
    a.find_path(4,10)# [4, 5, 6, 9, 10]
    print(a) #

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Cpp Example