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DFS (G, s)

for each vertex u in V[G] //Initialization

color[u] WHITE //mark each vertex as unvisited

parent[u] NIL //Set parent of each vertex to

nil

End for

time 0 //Global time to mark visited/traversed

color[s] GRAY //Mark as visited u

v[s] time //mark visited time of u

for each vertex u in V[G] //start exploring graph

ifcolor[u] WHITE // if vertex is unvisited

DFS-Visit(u) //build a new DFS-tree from u

end if

End for

End DFS (G, s)

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Step 1: Initialization Mark each vertex of graph as unvisited and predecessor

as null and set a global timestamp to zero .

Step 2: Start Exploring from starting vertex Start iterating through each unvisited vertex and its

adjacent vertices until its maximum depth. Mark asvisited.

Step 3: Repeat Recursively Start exploring node and its adjacent.

When maximum depth is reached, backtrack to unvisitednode and start visiting its descendant until all nodes andtheir descendants are visited.

Step 4: Mark the explored nodes as traversed When a node and its adjacent are explored mark it as

traversed and repeat step 3 if applicable.

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DFS (G, s)

for each vertex u in V[G] //Initialization

color[u] WHITE //mark each vertex as unvisited

parent[u] NIL //Set parent of each vertex to nil

End fortime 0 //Global time to mark visited/traversed

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Starting from 0

Parent[u] = nil

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color[s] GRAY //Mark as visited u

v[s] time //mark visited time of u

for each vertexxadjacent to u //explore (u, v)

ifcolor[x] WHITE //if vertex is unvisited

parent[x]u // set parent of v to u

DFS-Visit(x) // Recursively call DFS-Visit(u) until

goal/leaf is found and backtracking starts

end if

End for

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Starting from 0

Parent[u] = nil

Parent[5] = 0

Visited time v[0]=1

v[u] = {0}

t[u] = {}

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DFS-Visit(x)

color[s] GRAY //Mark as visited u

time time + 1 //Add +1 to time to mark u as visited

v[x] time //mark visited time of x

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Starting from 0

Parent[u] = nil

Visited time v[0]=1

Set Parent[5] = 0

Visited time v[5]=2

v[u] = {0,5}

t[u] = {}

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for each vertex vadjacent tox //explore (u, v)

ifcolor[v] WHITE //if vertex is unvisited

parent[v] u // set parent of v to u

DFS-Visit(v) // Recursively call DFS-Visit(u)

until goal/leaf is found and backtracking startsend if

End for

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Starting from 0

Parent[u] = nil

set parent[5]=0

Visited time v[5]=2

Visited time v[0]=1

v[u] = {0,5}

t[u] = {}

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for each vertex vadjacent tox //explore (u, v)

ifcolor[v] WHITE //if vertex is unvisited

parent[v] u // set parent of v to u

DFS-Visit(v) // Recursively call DFS-Visit(u)

until goal/leaf is found and backtracking startsend if

End for

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

v[u] = {0,5,1}

t[u] = {}

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for each vertex vadjacent tox //explore (u, v)

ifcolor[v] WHITE //if vertex is unvisited

parent[v] u // set parent of v to u

DFS-Visit(v) // Recursively call DFS-Visit(u)

until goal/leaf is found and backtracking startsend if

End for

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

v[u] = {0,5,1}

t[u] = {}

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for each vertex vadjacent tox //explore (u, v)

ifcolor[v] WHITE //if vertex is unvisited

parent[v] u // set parent of v to u

DFS-Visit(v) // Recursively call DFS-Visit(u)

until goal/leaf is found and backtracking startsend if

End for

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

Visited time

v[4]=4

v[u] = {0,5,1,4}

t[u] = {}

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for each vertex vadjacent tox //explore (u, v)

ifcolor[v] WHITE //if vertex is unvisited

parent [v] u // set parent of v to u

DFS-Visit(v) // Recursively call DFS-Visit(u)

until goal/leaf is found and backtracking startsend if

End for

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

Visited time

v[4]=4

Visited time

v[3]=5

v[u] = {0,5,1,4,3}

t[u] = {}

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for each vertex vadjacent tox //explore (u, v)

ifcolor[v] WHITE //if vertex is unvisited

parent [v] u // set parent of v to u

DFS-Visit(v) // Recursively call DFS-Visit(u)

until goal/leaf is found and backtracking startsend if

End for

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

Visited time

v[4]=4

Visited time

v[3]=5

Visited time

v[2]=6

v[u] = {0,5,1,4,3,2}

t[u] = {}

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color[u] BLACK // mark u to traversed

time time + 1 // mark traversed time of u

t[u] time // Traversed time of u

End DFS-Visit(u)

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

Visited time

v[4]=4

Visited time

v[3]=5

Visited time

v[2]=6

v[u] = {0,5,1,4,3,2}

t[u] = {2,3,4}

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color[u] BLACK // mark u to traversed

time time + 1 // mark traversed time of u

t[u] time // Traversed time of u

End DFS-Visit(u)

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

Visited time

v[4]=4

Visited time

v[3]=5

Visited time

v[2]=6

v[u] = {0,5,1,4,3,2}

t[u] = {2,3,4}

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color[u] BLACK // mark u to traversed

time time + 1 // mark traversed time of u

t[u] time // Traversed time of u

End DFS-Visit(u)

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

Visited time

v[4]=4

Visited time

v[3]=5

Visited time

v[2]=6

v[u] = {0,5,1,4,3,2}

t[u] = {2,3,4,1}

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color[u] BLACK // mark u to traversed

time time + 1 // mark traversed time of u

t[u] time // Traversed time of u

End DFS-Visit(u)

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

Visited time

v[4]=4

Visited time

v[3]=5

Visited time

v[2]=6

Visited time v[7]=7

v[u] = {0,5,1,4,3,2,7}

t[u] = {2,3,4,1,5,0}

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color[u] BLACK // mark u to traversed

time time + 1 // mark traversed time of u

t[u] time // Traversed time of u

End DFS-Visit(u)

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

Visited time

v[4]=4

Visited time

v[3]=5

Visited time

v[2]=6

Visited time v[7]=7

v[u] = {0,5,1,4,3,2,7,6}

t[u] = {2,3,4,1,5,0,7}

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color[u] BLACK // mark u to traversed

time time + 1 // mark traversed time of u

t[u] time // Traversed time of u

End DFS-Visit(u)

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Starting from 0

Parent[u] = nil

Mark as white and

set parent[u]=0

Visited time v[5]=2

Visited time v[0]=1

Visited time

v[1]=3

Visited time

v[4]=4

Visited time

v[3]=5

Visited time

v[2]=6

Visited time v[7]=7

v[u] = {0,5,1,4,3,2,7,6}

t[u] = {2,3,4,1,5,0,7,6}

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BFS(G, s)

for each vertex u in V[G] //Initialization

color[u] := WHITE //Mark as unvisited

d[u] := infinity //set visited order to infinity

p[u] := null //set parent to null

end for

color[s] := GRAY //Mark Source vertex s as visitedd[s] := 1 //visited/discovery time of s is 1

ENQUEUE(Q, s) //insert s into Queue (Q)

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while (Q != ) //While Q is not empty

U = DEQUEUE(Q) //pick the element from head

for each vertex v in Adj[u] //loop through each adjacent of u as v

if (color[v] = WHITE) //if unvisited

color[v] = GRAY //mark as visited

d[u] = d[u] + 1 //add +1 in visited order timed[v] = d[u] //set visited time of v to d[u]

p[v] = u //set previous of v to u

ENQUEUE(Q, v) insert v into Queue Q

end for

color[u] := BLACK //mark u as traversed

end while

End BFS(G, s)

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Step1: Initialization Loop through each vertex of Graph G and mark each vertex as

unvisited, previous/parent of each vertex as null, anddiscovery/visited time to infinity.

Step2: Start exploring from starting vertex Mark source/starting vertex s as visited and visited time of s

as 1 and insert s into the Queue Q.

Step3: Loop through each vertexs Adjacent until Queue isempty Start looping from starting vertex and visit its adjacent first.

Step4: Repeat step 3 until Queue is empty

Repeat loop for adjacent vertex first and then each adjacentdescendents until Queue Q is empty.

Step5: Mark explored vertex as traversed Mark each vertex traversed after exploring its adjacent or

siblings and its descendents.

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for each vertex u in V[G] //Initialization

color[u] = WHITE //Mark as unvisited

d[u] = infinity //set visited order to infinity

p[u] = null //set parent to null

end for

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d[0] = infinity

p[0] = null

d[5] = infinity

P[5] = null

d[2] = infinityp[2] = null

d[7] = infinity

p[7] = null

d[6] = infinityp[6] = null

d[4] = infinity

p[4] = null

d[3] = infinityp[3] = null

d[1] = infinity

d[1] = null

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color[s] = GRAY //Mark Source vertex s as visited

d[s] = 1 //visited/discovery time of s is 1

ENQUEUE(Q, s) //insert s into Queue (Q)

0Q

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d[0] = 1

p[0] = null

d[5] = infinity

P[5] = null

d[2] = infinity

p[2] = null

d[7] = infinity

p[7] = null

d[6] = infinityp[6] = null

d[4] = infinity

p[4] = null

d[3] = infinity

p[3] = null

d[1] = infinity

d[1] = null

Q

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while (Q != ) //While Q is not empty

U = DEQUEUE(Q) //pick the element from head

Q

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d[0] = 1

p[0] = null

d[5] = infinity

P[5] = null

d[2] = infinity

p[2] = null

d[7] = infinity

p[7] = null

d[6] = infinityp[6] = null

d[4] = infinity

p[4] = null

d[3] = infinity

p[3] = null

d[1] = infinity

d[1] = null

0Q

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for each vertex v in Adj[u] //loop through each adjacent of u as v

if (color[v] = WHITE) //if unvisited

color[v] = GRAY //mark as visited

d[u] = d[u] + 1 //add +1 in visited order time

d[v] = d[u] //set visited time of v to d[u]

p[v] = u //set previous of v to uENQUEUE(Q, v) //insert v into Queue Q

end for

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d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = infinity

p[2] = null

d[7] = 2

p[7] = 0

d[6] = infinityp[6] = null

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

7 5 3Q

d[1] = infinity

d[1] = null

0Q

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color[u] := BLACK //mark u as traversed

end while

End BFS(G, s)

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d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = infinity

p[2] = null

d[7] = 2

p[7] = 0

d[6] = infinityp[6] = null

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

7 5 3Q

d[1] = infinity

d[1] = null

0Q

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while (Q != ) //While Q is not empty

U = DEQUEUE(Q) //pick the element from head

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d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = infinity

p[2] = null

d[7] = 2

p[7] = 0

d[6] = infinityp[6] = null

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

5 3Q

d[1] = infinity

d[1] = null

0 7Q

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for each vertex v in Adj[u] //loop through each adjacent of u as v

if (color[v] = WHITE) //if unvisited

color[v] = GRAY //mark as visited

d[u] = d[u] + 1 //add +1 in visited order time

d[v] = d[u] //set visited time of v to d[u]

p[v] = u //set previous of v to uENQUEUE(Q, v) //insert v into Queue Q

end for

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d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = infinity

p[2] = null

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

5 3 6Q

d[1] = 5

d[1] = 7

0 7Q

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color[u] := BLACK //mark u as traversed

end while

End BFS(G, s)

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d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = infinity

p[2] = null

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

5 3 6Q

d[1] = 5

d[1] = 7

0 7Q

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while (Q != ) //While Q is not empty

U = DEQUEUE(Q) //pick the element from head

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d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = infinity

p[2] = null

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

3 6Q

d[1] = 5

d[1] = 7

0 7 5Q

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for each vertex v in Adj[u] //loop through each adjacent of u as v

if (color[v] = WHITE) //if unvisited

color[v] = GRAY //mark as visited

d[u] = d[u] + 1 //add +1 in visited order time

d[v] = d[u] //set visited time of v to d[u]

p[v] = u //set previous of v to uENQUEUE(Q, v) //insert v into Queue Q

end for

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d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

3 6 2Q

d[1] = 5

d[1] = 7

0 7 5Q

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color[u] := BLACK //mark u as traversed

end while

End BFS(G, s)

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1

5

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d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

3 6 2Q

d[1] = 5

d[1] = 7

0 7 5Q

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while (Q != ) //While Q is not empty

U = DEQUEUE(Q) //pick the element from head

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7

1

5

4

3

2

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d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

6 2Q

d[1] = 5

d[1] = 7

0 7 5 3Q

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for each vertex v in Adj[u] //loop through each adjacent of u as v

if (color[v] = WHITE) //if unvisited

color[v] = GRAY //mark as visited

d[u] = d[u] + 1 //add +1 in visited order time

d[v] = d[u] //set visited time of v to d[u]

p[v] = u //set previous of v to uENQUEUE(Q, v) //insert v into Queue Q

end for

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7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

6 2Q

d[1] = 5

d[1] = 7

0 7 5 3Q

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color[u] := BLACK //mark u as traversed

end while

End BFS(G, s)

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

6 2Q

d[1] = 5

d[1] = 7

0 7 5 3Q

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while (Q != ) //While Q is not empty

U = DEQUEUE(Q) //pick the element from head

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

6 2Q

d[1] = 5

d[1] = 7

0 7 5 3Q

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for each vertex v in Adj[u] //loop through each adjacent of u as v

if (color[v] = WHITE) //if unvisited

color[v] = GRAY //mark as visited

d[u] = d[u] + 1 //add +1 in visited order time

d[v] = d[u] //set visited time of v to d[u]

p[v] = u //set previous of v to uENQUEUE(Q, v) //insert v into Queue Q

end for

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = 8

p[4] = 1

d[3] = 4

p[3] = 0

6 2 4Q

d[1] = 5

d[1] = 7

0 7 5 3Q

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color[u] := BLACK //mark u as traversed

end while

End BFS(G, s)

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

6 2 4Q

d[1] = 5

d[1] = 7

0 7 5 3Q

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while (Q != ) //While Q is not empty

U = DEQUEUE(Q) //pick the element from head

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

2 4Q

d[1] = 5

d[1] = 7

0 7 5 3 6Q

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for each vertex v in Adj[u] //loop through each adjacent of u as v

if (color[v] = WHITE) //if unvisited

color[v] = GRAY //mark as visited

d[u] = d[u] + 1 //add +1 in visited order time

d[v] = d[u] //set visited time of v to d[u]

p[v] = u //set previous of v to uENQUEUE(Q, v) //insert v into Queue Q

end for

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

2 4Q

d[1] = 5

d[1] = 7

0 7 5 3 6Q

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color[u] := BLACK //mark u as traversed

end while

End BFS(G, s)

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7

p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

2 4Q

d[1] = 5

d[1] = 7

0 7 5 3 6Q

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while (Q != ) //While Q is not empty

U = DEQUEUE(Q) //pick the element from head

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

4Q

d[1] = 5

d[1] = 7

0 7 5 3 6 2Q

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color[u] := BLACK //mark u as traversed

end while

End BFS(G, s)

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

4Q

d[1] = 5

d[1] = 7

0 7 5 3 6 2Q

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while (Q != ) //While Q is not empty

U = DEQUEUE(Q) //pick the element from head

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

Q

d[1] = 5

d[1] = 7

0 7 5 3 6 2 4Q

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for each vertex v in Adj[u] //loop through each adjacent of u as v

if (color[v] = WHITE) //if unvisited

color[v] = GRAY //mark as visited

d[u] = d[u] + 1 //add +1 in visited order time

d[v] = d[u] //set visited time of v to d[u]

p[v] = u //set previous of v to uENQUEUE(Q, v) //insert v into Queue Q

end for

0

7

1

5

4

3

2

6

d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7p[2] = 8

d[7] = 2

p[7] = 0

d[6] = 6p[6] = 7

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

Q

d[1] = 5

d[1] = 7

0 7 5 3 6 2 4Q

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color[u] := BLACK //mark u as traversed

end while

End BFS(G, s)

0

7

1

5

4

3

2d[0] = 1

p[0] = null

d[5] = 3

P[5] = 0

d[2] = 7p[2] = 8

d[7] = 2

p[7] = 0

d[4] = infinity

p[4] = null

d[3] = 4

p[3] = 0

Q

d[1] = 5

d[1] = 7

0 7 5 3 6 2 4Q