increment 1

graphs/ArticulationPoints.py

@@ -0,0 +1,44 @@
+# Finding Articulation Points in Undirected Graph
+def computeAP(l):
+    n = len(l)
+    outEdgeCount = 0
+    low = [0] * n
+    visited = [False] * n
+    isArt = [False] * n
+
+    def dfs(root, at, parent, outEdgeCount):
+        if parent == root:
+            outEdgeCount += 1
+        visited[at] = True
+        low[at] = at
+
+        for to in l[at]:
+            if to == parent:
+                pass
+            elif not visited[to]:
+                outEdgeCount = dfs(root, to, at, outEdgeCount)
+                low[at] = min(low[at], low[to])
+
+                # AP found via bridge
+                if at < low[to]:
+                    isArt[at] = True
+                # AP found via cycle
+                if at == low[to]:
+                    isArt[at] = True
+            else:
+                low[at] = min(low[at], to)
+        return outEdgeCount
+
+    for i in range(n):
+        if not visited[i]:
+            outEdgeCount = 0
+            outEdgeCount = dfs(i, i, -1, outEdgeCount)
+            isArt[i] = (outEdgeCount > 1)
+
+    for x in range(len(isArt)):
+        if isArt[x] == True:
+            print(x)
+
+# Adjacency list of graph
+l = {0:[1,2], 1:[0,2], 2:[0,1,3,5], 3:[2,4], 4:[3], 5:[2,6,8], 6:[5,7], 7:[6,8], 8:[5,7]}
+computeAP(l)

graphs/CheckBipartiteGraph_BFS.py

@@ -0,0 +1,43 @@
+# Check whether Graph is Bipartite or Not using BFS
+
+# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
+# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
+# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
+# or u belongs to V and v to U. We can also say that there is no edge that connects
+# vertices of same set.
+def checkBipartite(l):
+    queue = []
+    visited = [False] * len(l)
+    color = [-1] * len(l)
+
+    def bfs():
+        while(queue):
+            u = queue.pop(0)
+            visited[u] = True
+
+            for neighbour in l[u]:
+
+                if neighbour == u:
+                    return False
+
+                if color[neighbour] == -1:
+                    color[neighbour] = 1 - color[u]
+                    queue.append(neighbour)
+
+                elif color[neighbour] == color[u]:
+                    return False
+
+        return True
+
+    for i in range(len(l)):
+        if not visited[i]:
+            queue.append(i)
+            color[i] = 0
+            if bfs() == False:
+                return False
+
+    return True
+
+# Adjacency List of graph
+l = {0:[1,3], 1:[0,2], 2:[1,3], 3:[0,2]}
+print(checkBipartite(l))

graphs/FindingBridges.py

@@ -0,0 +1,31 @@
+# Finding Bridges in Undirected Graph
+def computeBridges(l):
+    id = 0
+    n = len(l) # No of vertices in graph
+    low = [0] * n
+    visited = [False] * n
+
+    def dfs(at, parent, bridges, id):
+        visited[at] = True
+        low[at] = id
+        id += 1
+        for to in l[at]:
+            if to == parent:
+                pass
+            elif not visited[to]:
+                dfs(to, at, bridges, id)
+                low[at] = min(low[at], low[to])
+                if at < low[to]:
+                    bridges.append([at, to])
+            else:
+                # This edge is a back edge and cannot be a bridge
+                low[at] = min(low[at], to)
+
+    bridges = []
+    for i in range(n):
+        if (not visited[i]):
+            dfs(i, -1, bridges, id)
+    print(bridges)
+            
+l = {0:[1,2], 1:[0,2], 2:[0,1,3,5], 3:[2,4], 4:[3], 5:[2,6,8], 6:[5,7], 7:[6,8], 8:[5,7]}
+computeBridges(l)

graphs/KahnsAlgorithm_long.py

@@ -0,0 +1,30 @@
+# Finding longest distance in Directed Acyclic Graph using KahnsAlgorithm
+def longestDistance(l):
+    indegree = [0] * len(l)
+    queue = []
+    longDist = [1] * len(l)
+
+    for key, values in l.items():
+        for i in values:
+            indegree[i] += 1
+
+    for i in range(len(indegree)):
+        if indegree[i] == 0:
+            queue.append(i)
+
+    while(queue):
+        vertex = queue.pop(0)
+        for x in l[vertex]:
+            indegree[x] -= 1
+
+            if longDist[vertex] + 1 > longDist[x]:
+                longDist[x] =  longDist[vertex] + 1
+
+            if indegree[x] == 0:
+                queue.append(x)
+
+    print(max(longDist))
+
+# Adjacency list of Graph
+l = {0:[2,3,4], 1:[2,7], 2:[5], 3:[5,7], 4:[7], 5:[6], 6:[7], 7:[]}
+longestDistance(l)

graphs/KahnsAlgorithm_topo.py

@@ -0,0 +1,32 @@
+# Kahn's Algorithm is used to find Topological ordering of Directed Acyclic Graph using BFS
+def topologicalSort(l):
+    indegree = [0] * len(l)
+    queue = []
+    topo = []
+    cnt = 0
+
+    for key, values in l.items():
+        for i in values:
+            indegree[i] += 1
+
+    for i in range(len(indegree)):
+        if indegree[i] == 0:
+            queue.append(i)
+
+    while(queue):
+        vertex = queue.pop(0)
+        cnt += 1
+        topo.append(vertex)
+        for x in l[vertex]:
+            indegree[x] -= 1
+            if indegree[x] == 0:
+                queue.append(x)
+
+    if cnt != len(l):
+        print("Cycle exists")
+    else:
+        print(topo)
+
+# Adjacency List of Graph
+l = {0:[1,2], 1:[3], 2:[3], 3:[4,5], 4:[], 5:[]}
+topologicalSort(l)

graphs/MinimumSpanningTree_Prims.py

@@ -0,0 +1,111 @@
+import sys
+from collections import defaultdict
+
+def PrimsAlgorithm(l):
+
+    nodePosition = []
+    def getPosition(vertex):
+        return nodePosition[vertex]
+
+    def setPosition(vertex, pos):
+        nodePosition[vertex] = pos
+
+    def topToBottom(heap, start, size, positions):
+        if start > size // 2 - 1:
+            return
+        else:
+            if 2 * start + 2 >= size:
+                m = 2 * start + 1
+            else:
+                if heap[2 * start + 1] < heap[2 * start + 2]:
+                    m = 2 * start + 1
+                else:
+                    m = 2 * start + 2
+            if heap[m] < heap[start]:
+                temp, temp1 = heap[m], positions[m]
+                heap[m], positions[m] = heap[start], positions[start]
+                heap[start], positions[start] = temp, temp1
+
+                temp = getPosition(positions[m])
+                setPosition(positions[m], getPosition(positions[start]))
+                setPosition(positions[start], temp)
+
+                topToBottom(heap, m, size, positions)
+
+    # Update function if value of any node in min-heap decreases
+    def bottomToTop(val, index, heap, position):
+        temp = position[index]
+
+        while(index != 0):
+            if index % 2 == 0:
+                parent = int( (index-2) / 2 )
+            else:
+                parent = int( (index-1) / 2 )
+
+            if val < heap[parent]:
+                heap[index] = heap[parent]
+                position[index] = position[parent]
+                setPosition(position[parent], index)
+            else:
+                heap[index] = val
+                position[index] = temp
+                setPosition(temp, index)
+                break
+            index = parent
+        else:
+            heap[0] = val
+            position[0] = temp
+            setPosition(temp, 0)
+
+    def heapify(heap, positions):
+        start = len(heap) // 2 - 1
+        for i in range(start, -1, -1):
+            topToBottom(heap, i, len(heap), positions)
+
+    def deleteMinimum(heap, positions):
+        temp = positions[0]
+        heap[0] = sys.maxsize
+        topToBottom(heap, 0, len(heap), positions)
+        return temp
+
+    visited = [0 for i in range(len(l))]
+    Nbr_TV  = [-1 for i in range(len(l))] # Neighboring Tree Vertex of selected vertex
+    # Minimum Distance of explored vertex with neighboring vertex of partial tree formed in graph
+    Distance_TV = [] # Heap of Distance of vertices from their neighboring vertex
+    Positions = []
+
+    for x in range(len(l)):
+        p = sys.maxsize
+        Distance_TV.append(p)
+        Positions.append(x)
+        nodePosition.append(x)
+
+    TreeEdges = []
+    visited[0] = 1
+    Distance_TV[0] = sys.maxsize
+    for x in l[0]:
+        Nbr_TV[ x[0] ] = 0
+        Distance_TV[ x[0] ] = x[1]
+    heapify(Distance_TV, Positions)
+
+    for i in range(1, len(l)):
+        vertex = deleteMinimum(Distance_TV, Positions)
+        if visited[vertex] == 0:
+            TreeEdges.append((Nbr_TV[vertex], vertex))
+            visited[vertex] = 1
+            for v in l[vertex]:
+                if visited[v[0]] == 0 and v[1] < Distance_TV[ getPosition(v[0]) ]:
+                    Distance_TV[ getPosition(v[0]) ] = v[1]
+                    bottomToTop(v[1], getPosition(v[0]), Distance_TV, Positions)
+                    Nbr_TV[ v[0] ] = vertex
+    return TreeEdges
+
+# < --------- Prims Algorithm --------- >
+n = int(raw_input("Enter number of vertices: "))
+e = int(raw_input("Enter number of edges: "))
+adjlist = defaultdict(list)
+for x in range(e):
+    l = [int(x) for x in input().split()]
+    adjlist[l[0]].append([ l[1], l[2] ])
+    adjlist[l[1]].append([ l[0], l[2] ])
+print(PrimsAlgorithm(adjlist))

graphs/Multi_Hueristic_Astar.py

@@ -0,0 +1,266 @@
+from __future__ import print_function
+import heapq
+import numpy as np
+
+try:
+    xrange          # Python 2
+except NameError:
+    xrange = range  # Python 3
+
+
+class PriorityQueue:
+	def __init__(self):
+		self.elements = []
+		self.set = set()
+
+	def minkey(self):
+		if not self.empty():
+			return self.elements[0][0]
+		else:
+			return float('inf')
+	
+	def empty(self):
+		return len(self.elements) == 0
+
+	def put(self, item, priority):
+		if item not in self.set:
+			heapq.heappush(self.elements, (priority, item))
+			self.set.add(item)
+		else:
+			# update
+			# print("update", item)
+			temp = []
+			(pri, x) = heapq.heappop(self.elements)
+			while x != item:
+				temp.append((pri, x))
+				(pri, x) = heapq.heappop(self.elements)
+			temp.append((priority, item))
+			for (pro, xxx) in temp:
+				heapq.heappush(self.elements, (pro, xxx))
+
+	def remove_element(self, item):
+		if item in self.set:
+			self.set.remove(item)
+			temp = []
+			(pro, x) = heapq.heappop(self.elements)
+			while x != item:
+				temp.append((pro, x))
+				(pro, x) = heapq.heappop(self.elements)
+			for (prito, yyy) in temp:
+				heapq.heappush(self.elements, (prito, yyy))
+	
+	def top_show(self):
+		return self.elements[0][1]
+	
+	def get(self):
+		(priority, item) = heapq.heappop(self.elements)
+		self.set.remove(item)
+		return (priority, item)
+
+def consistent_hueristic(P, goal):
+	# euclidean distance
+	a = np.array(P)
+	b = np.array(goal)
+	return np.linalg.norm(a - b)
+
+def hueristic_2(P, goal):
+	# integer division by time variable
+	return consistent_hueristic(P, goal) // t 
+
+def hueristic_1(P, goal):
+	# manhattan distance
+	return abs(P[0] - goal[0]) + abs(P[1] - goal[1])
+
+def key(start, i, goal, g_function):
+	ans = g_function[start] + W1 * hueristics[i](start, goal)
+	return ans
+	
+def do_something(back_pointer, goal, start):
+	grid = np.chararray((n, n))
+	for i in range(n):
+		for j in range(n):
+			grid[i][j] = '*'
+	
+	for i in range(n):
+		for j in range(n):
+			if (j, (n-1)-i) in blocks:
+				grid[i][j] = "#"
+
+	grid[0][(n-1)] = "-"
+	x = back_pointer[goal]
+	while x != start:
+		(x_c, y_c) = x
+		# print(x)
+		grid[(n-1)-y_c][x_c] = "-"
+		x = back_pointer[x]
+	grid[(n-1)][0] = "-"
+	
+
+	for i in xrange(n):
+		for j in range(n):
+			if (i, j) == (0, n-1):
+				print(grid[i][j], end=' ')
+				print("<-- End position", end=' ')
+			else:
+				print(grid[i][j], end=' ')
+		print()
+	print("^")
+	print("Start position")
+	print()
+	print("# is an obstacle")
+	print("- is the path taken by algorithm")
+	print("PATH TAKEN BY THE ALGORITHM IS:-")
+	x = back_pointer[goal]
+	while x != start:
+		print(x, end=' ') 
+		x = back_pointer[x]
+	print(x)
+	quit()
+
+def valid(p):
+	if p[0] < 0 or p[0] > n-1:
+		return False
+	if p[1] < 0 or p[1] > n-1:
+		return False
+	return True
+
+def expand_state(s, j, visited, g_function, close_list_anchor, close_list_inad,  open_list, back_pointer):
+	for itera in range(n_hueristic):
+		open_list[itera].remove_element(s)
+	# print("s", s)
+	# print("j", j)
+	(x, y) = s
+	left = (x-1, y)
+	right = (x+1, y)
+	up = (x, y+1)
+	down = (x, y-1)
+
+	for neighbours in [left, right, up, down]:
+		if neighbours not in blocks:
+			if valid(neighbours) and neighbours not in visited:
+				# print("neighbour", neighbours)
+				visited.add(neighbours)
+				back_pointer[neighbours] = -1
+				g_function[neighbours] = float('inf')
+
+			if valid(neighbours) and g_function[neighbours] > g_function[s] + 1:
+				g_function[neighbours] = g_function[s] + 1
+				back_pointer[neighbours] = s
+				if neighbours not in close_list_anchor:
+					open_list[0].put(neighbours, key(neighbours, 0, goal, g_function))
+					if neighbours not in close_list_inad:
+						for var in range(1,n_hueristic):
+							if key(neighbours, var, goal, g_function) <= W2 * key(neighbours, 0, goal, g_function):
+								# print("why not plssssssssss")
+								open_list[j].put(neighbours, key(neighbours, var, goal, g_function))
+			
+
+	# print
+
+def make_common_ground():
+	some_list = []
+	# block 1
+	for x in range(1, 5):
+		for y in range(1, 6):
+			some_list.append((x, y))
+
+	# line
+	for x in range(15, 20):
+		some_list.append((x, 17))
+
+	# block 2 big
+	for x in range(10, 19):
+		for y in range(1, 15):
+			some_list.append((x, y))
+
+	# L block
+	for x in range(1, 4):
+		for y in range(12, 19):
+			some_list.append((x, y))
+	for x in range(3, 13):
+		for y in range(16, 19):
+			some_list.append((x, y))
+	return some_list
+
+hueristics = {0: consistent_hueristic, 1: hueristic_1, 2: hueristic_2}
+
+blocks_blk = [(0, 1),(1, 1),(2, 1),(3, 1),(4, 1),(5, 1),(6, 1),(7, 1),(8, 1),(9, 1),(10, 1),(11, 1),(12, 1),(13, 1),(14, 1),(15, 1),(16, 1),(17, 1),(18, 1), (19, 1)]
+blocks_no = []
+blocks_all = make_common_ground()
+
+
+
+
+blocks = blocks_blk
+# hyper parameters
+W1 = 1
+W2 = 1
+n = 20
+n_hueristic = 3 # one consistent and two other inconsistent
+
+# start and end destination
+start = (0, 0)
+goal = (n-1, n-1)
+
+t = 1
+def multi_a_star(start, goal, n_hueristic):
+	g_function = {start: 0, goal: float('inf')}
+	back_pointer = {start:-1, goal:-1}
+	open_list = []
+	visited = set()
+
+	for i in range(n_hueristic):
+		open_list.append(PriorityQueue())
+		open_list[i].put(start, key(start, i, goal, g_function))
+	
+	close_list_anchor = []
+	close_list_inad = []
+	while open_list[0].minkey() < float('inf'):
+		for i in range(1, n_hueristic):
+			# print("i", i)
+			# print(open_list[0].minkey(), open_list[i].minkey())
+			if open_list[i].minkey() <= W2 * open_list[0].minkey():
+				global t
+				t += 1
+				# print("less prio")
+				if g_function[goal] <= open_list[i].minkey():
+					if g_function[goal] < float('inf'):
+						do_something(back_pointer, goal, start)
+				else:
+					_, get_s = open_list[i].top_show()
+					visited.add(get_s)
+					expand_state(get_s, i, visited, g_function, close_list_anchor, close_list_inad, open_list, back_pointer)
+					close_list_inad.append(get_s)
+			else:
+				# print("more prio")
+				if g_function[goal] <= open_list[0].minkey():
+					if g_function[goal] < float('inf'):
+						do_something(back_pointer, goal, start)
+				else:
+					# print("hoolla")
+					get_s = open_list[0].top_show()
+					visited.add(get_s)
+					expand_state(get_s, 0, visited, g_function, close_list_anchor, close_list_inad, open_list, back_pointer)
+					close_list_anchor.append(get_s)
+	print("No path found to goal")
+	print()
+	for i in range(n-1,-1, -1):
+		for j in range(n):
+			if (j, i) in blocks:
+				print('#', end=' ')
+			elif (j, i) in back_pointer:
+				if (j, i) == (n-1, n-1):
+					print('*', end=' ')
+				else:
+					print('-', end=' ')
+			else:
+				print('*', end=' ')
+			if (j, i) == (n-1, n-1):
+				print('<-- End position', end=' ')
+		print()
+	print("^")
+	print("Start position")
+	print()
+	print("# is an obstacle")
+	print("- is the path taken by algorithm")
+multi_a_star(start, goal, n_hueristic)

graphs/a_star.py

@@ -0,0 +1,102 @@
+from __future__ import print_function
+
+grid = [[0, 1, 0, 0, 0, 0],
+        [0, 1, 0, 0, 0, 0],#0 are free path whereas 1's are obstacles
+        [0, 1, 0, 0, 0, 0],
+        [0, 1, 0, 0, 1, 0],
+        [0, 0, 0, 0, 1, 0]]
+
+'''
+heuristic = [[9, 8, 7, 6, 5, 4],
+             [8, 7, 6, 5, 4, 3],
+             [7, 6, 5, 4, 3, 2],
+             [6, 5, 4, 3, 2, 1],
+             [5, 4, 3, 2, 1, 0]]'''
+
+init = [0, 0]
+goal = [len(grid)-1, len(grid[0])-1] #all coordinates are given in format [y,x] 
+cost = 1
+
+#the cost map which pushes the path closer to the goal
+heuristic = [[0 for row in range(len(grid[0]))] for col in range(len(grid))]
+for i in range(len(grid)):    
+    for j in range(len(grid[0])):            
+        heuristic[i][j] = abs(i - goal[0]) + abs(j - goal[1])
+        if grid[i][j] == 1:
+            heuristic[i][j] = 99 #added extra penalty in the heuristic map
+
+
+#the actions we can take
+delta = [[-1, 0 ], # go up
+         [ 0, -1], # go left
+         [ 1, 0 ], # go down
+         [ 0, 1 ]] # go right
+
+
+#function to search the path
+def search(grid,init,goal,cost,heuristic):
+
+    closed = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]# the referrence grid
+    closed[init[0]][init[1]] = 1
+    action = [[0 for col in range(len(grid[0]))] for row in range(len(grid))]#the action grid
+
+    x = init[0]
+    y = init[1]
+    g = 0
+    f = g + heuristic[init[0]][init[0]]
+    cell = [[f, g, x, y]]
+
+    found = False  # flag that is set when search is complete
+    resign = False # flag set if we can't find expand
+
+    while not found and not resign:
+        if len(cell) == 0:
+            resign = True
+            return "FAIL"
+        else:
+            cell.sort()#to choose the least costliest action so as to move closer to the goal
+            cell.reverse()
+            next = cell.pop()
+            x = next[2]
+            y = next[3]
+            g = next[1]
+            f = next[0]
+
+            
+            if x == goal[0] and y == goal[1]:
+                found = True
+            else:
+                for i in range(len(delta)):#to try out different valid actions
+                    x2 = x + delta[i][0]
+                    y2 = y + delta[i][1]
+                    if x2 >= 0 and x2 < len(grid) and y2 >=0 and y2 < len(grid[0]):
+                        if closed[x2][y2] == 0 and grid[x2][y2] == 0:
+                            g2 = g + cost
+                            f2 = g2 + heuristic[x2][y2]
+                            cell.append([f2, g2, x2, y2])
+                            closed[x2][y2] = 1
+                            action[x2][y2] = i
+    invpath = []
+    x = goal[0]
+    y = goal[1]
+    invpath.append([x, y])#we get the reverse path from here
+    while x != init[0] or y != init[1]:
+        x2 = x - delta[action[x][y]][0]
+        y2 = y - delta[action[x][y]][1]
+        x = x2
+        y = y2
+        invpath.append([x, y])
+
+    path = []
+    for i in range(len(invpath)):
+    	path.append(invpath[len(invpath) - 1 - i])
+    print("ACTION MAP")
+    for i in range(len(action)):
+        print(action[i])
+                  
+    return path
+    
+a = search(grid,init,goal,cost,heuristic)
+for i in range(len(a)):
+	print(a[i]) 
+

graphs/basic-graphs.py

@@ -0,0 +1,281 @@
+from __future__ import print_function
+
+try:
+    raw_input          # Python 2
+except NameError:
+    raw_input = input  # Python 3
+
+try:
+    xrange             # Python 2
+except NameError:
+    xrange = range     # Python 3
+
+# Accept No. of Nodes and edges
+n, m = map(int, raw_input().split(" "))
+
+# Initialising Dictionary of edges
+g = {}
+for i in xrange(n):
+    g[i + 1] = []
+
+"""
+--------------------------------------------------------------------------------
+    Accepting edges of Unweighted Directed Graphs
+--------------------------------------------------------------------------------
+"""
+for _ in xrange(m):
+    x, y = map(int, raw_input().split(" "))
+    g[x].append(y)
+
+"""
+--------------------------------------------------------------------------------
+    Accepting edges of Unweighted Undirected Graphs
+--------------------------------------------------------------------------------
+"""
+for _ in xrange(m):
+    x, y = map(int, raw_input().split(" "))
+    g[x].append(y)
+    g[y].append(x)
+
+"""
+--------------------------------------------------------------------------------
+    Accepting edges of Weighted Undirected Graphs
+--------------------------------------------------------------------------------
+"""
+for _ in xrange(m):
+    x, y, r = map(int, raw_input().split(" "))
+    g[x].append([y, r])
+    g[y].append([x, r])
+
+"""
+--------------------------------------------------------------------------------
+    Depth First Search.
+        Args :  G - Dictionary of edges
+                s - Starting Node
+        Vars :  vis - Set of visited nodes
+                S - Traversal Stack
+--------------------------------------------------------------------------------
+"""
+
+
+def dfs(G, s):
+    vis, S = set([s]), [s]
+    print(s)
+    while S:
+        flag = 0
+        for i in G[S[-1]]:
+            if i not in vis:
+                S.append(i)
+                vis.add(i)
+                flag = 1
+                print(i)
+                break
+        if not flag:
+            S.pop()
+
+
+"""
+--------------------------------------------------------------------------------
+    Breadth First Search.
+        Args :  G - Dictionary of edges
+                s - Starting Node
+        Vars :  vis - Set of visited nodes
+                Q - Traveral Stack
+--------------------------------------------------------------------------------
+"""
+from collections import deque
+
+
+def bfs(G, s):
+    vis, Q = set([s]), deque([s])
+    print(s)
+    while Q:
+        u = Q.popleft()
+        for v in G[u]:
+            if v not in vis:
+                vis.add(v)
+                Q.append(v)
+                print(v)
+
+
+"""
+--------------------------------------------------------------------------------
+    Dijkstra's shortest path Algorithm
+        Args :  G - Dictionary of edges
+                s - Starting Node
+        Vars :  dist - Dictionary storing shortest distance from s to every other node
+                known - Set of knows nodes
+                path - Preceding node in path
+--------------------------------------------------------------------------------
+"""
+
+
+def dijk(G, s):
+    dist, known, path = {s: 0}, set(), {s: 0}
+    while True:
+        if len(known) == len(G) - 1:
+            break
+        mini = 100000
+        for i in dist:
+            if i not in known and dist[i] < mini:
+                mini = dist[i]
+                u = i
+        known.add(u)
+        for v in G[u]:
+            if v[0] not in known:
+                if dist[u] + v[1] < dist.get(v[0], 100000):
+                    dist[v[0]] = dist[u] + v[1]
+                    path[v[0]] = u
+    for i in dist:
+        if i != s:
+            print(dist[i])
+
+
+"""
+--------------------------------------------------------------------------------
+    Topological Sort
+--------------------------------------------------------------------------------
+"""
+from collections import deque
+
+
+def topo(G, ind=None, Q=[1]):
+    if ind is None:
+        ind = [0] * (len(G) + 1) 		# SInce oth Index is ignored
+        for u in G:
+            for v in G[u]:
+                ind[v] += 1
+        Q = deque()
+        for i in G:
+            if ind[i] == 0:
+                Q.append(i)
+    if len(Q) == 0:
+        return
+    v = Q.popleft()
+    print(v)
+    for w in G[v]:
+        ind[w] -= 1
+        if ind[w] == 0:
+            Q.append(w)
+    topo(G, ind, Q)
+
+
+"""
+--------------------------------------------------------------------------------
+    Reading an Adjacency matrix
+--------------------------------------------------------------------------------
+"""
+
+
+def adjm():
+    n, a = raw_input(), []
+    for i in xrange(n):
+        a.append(map(int, raw_input().split()))
+    return a, n
+
+
+"""
+--------------------------------------------------------------------------------
+    Floyd Warshall's algorithm
+        Args :  G - Dictionary of edges
+                s - Starting Node
+        Vars :  dist - Dictionary storing shortest distance from s to every other node
+                known - Set of knows nodes
+                path - Preceding node in path
+
+--------------------------------------------------------------------------------
+"""
+
+
+def floy(A_and_n):
+    (A, n) = A_and_n
+    dist = list(A)
+    path = [[0] * n for i in xrange(n)]
+    for k in xrange(n):
+        for i in xrange(n):
+            for j in xrange(n):
+                if dist[i][j] > dist[i][k] + dist[k][j]:
+                    dist[i][j] = dist[i][k] + dist[k][j]
+                    path[i][k] = k
+    print(dist)
+
+
+"""
+--------------------------------------------------------------------------------
+    Prim's MST Algorithm
+        Args :  G - Dictionary of edges
+                s - Starting Node
+        Vars :  dist - Dictionary storing shortest distance from s to nearest node
+                known - Set of knows nodes
+                path - Preceding node in path
+--------------------------------------------------------------------------------
+"""
+
+
+def prim(G, s):
+    dist, known, path = {s: 0}, set(), {s: 0}
+    while True:
+        if len(known) == len(G) - 1:
+            break
+        mini = 100000
+        for i in dist:
+            if i not in known and dist[i] < mini:
+                mini = dist[i]
+                u = i
+        known.add(u)
+        for v in G[u]:
+            if v[0] not in known:
+                if v[1] < dist.get(v[0], 100000):
+                    dist[v[0]] = v[1]
+                    path[v[0]] = u
+
+
+"""
+--------------------------------------------------------------------------------
+    Accepting Edge list
+        Vars :  n - Number of nodes
+                m - Number of edges
+        Returns : l - Edge list
+                n - Number of Nodes
+--------------------------------------------------------------------------------
+"""
+
+
+def edglist():
+    n, m = map(int, raw_input().split(" "))
+    l = []
+    for i in xrange(m):
+        l.append(map(int, raw_input().split(' ')))
+    return l, n
+
+
+"""
+--------------------------------------------------------------------------------
+    Kruskal's MST Algorithm
+        Args :  E - Edge list
+                n - Number of Nodes
+        Vars :  s - Set of all nodes as unique disjoint sets (initially)
+--------------------------------------------------------------------------------
+"""
+
+
+def krusk(E_and_n):
+    # Sort edges on the basis of distance
+    (E, n) = E_and_n
+    E.sort(reverse=True, key=lambda x: x[2])
+    s = [set([i]) for i in range(1, n + 1)]
+    while True:
+        if len(s) == 1:
+            break
+        print(s)
+        x = E.pop()
+        for i in xrange(len(s)):
+            if x[0] in s[i]:
+                break
+        for j in xrange(len(s)):
+            if x[1] in s[j]:
+                if i == j:
+                    break
+                s[j].update(s[i])
+                s.pop(i)
+                break

graphs/minimum_spanning_tree_kruskal.py

@@ -0,0 +1,32 @@
+from __future__ import print_function
+num_nodes, num_edges = list(map(int,raw_input().split()))
+
+edges = []
+
+for i in range(num_edges):
+	node1, node2, cost = list(map(int,raw_input().split()))
+	edges.append((i,node1,node2,cost))
+
+edges = sorted(edges, key=lambda edge: edge[3])
+
+parent = [i for i in range(num_nodes)]
+
+def find_parent(i):
+	if(i != parent[i]):
+		parent[i] = find_parent(parent[i])
+	return parent[i]
+
+minimum_spanning_tree_cost = 0
+minimum_spanning_tree = []
+
+for edge in edges:
+	parent_a = find_parent(edge[1])
+	parent_b = find_parent(edge[2])
+	if(parent_a != parent_b):
+		minimum_spanning_tree_cost += edge[3]
+		minimum_spanning_tree.append(edge)
+		parent[parent_a] = parent_b
+
+print(minimum_spanning_tree_cost)
+for edge in minimum_spanning_tree:
+	print(edge)

graphs/scc_kosaraju.py

@@ -0,0 +1,46 @@
+from __future__ import print_function
+# n - no of nodes, m - no of edges
+n, m = list(map(int,raw_input().split()))
+
+g = [[] for i in range(n)] #graph
+r = [[] for i in range(n)] #reversed graph
+# input graph data (edges)
+for i in range(m):
+    u, v = list(map(int,raw_input().split()))
+    g[u].append(v)
+    r[v].append(u)
+
+stack = []
+visit = [False]*n
+scc = []
+component = []
+
+def dfs(u):
+    global g, r, scc, component, visit, stack
+    if visit[u]: return
+    visit[u] = True
+    for v in g[u]:
+        dfs(v)
+    stack.append(u)
+
+def dfs2(u):
+    global g, r, scc, component, visit, stack
+    if visit[u]: return
+    visit[u] = True
+    component.append(u)
+    for v in r[u]:
+        dfs2(v)
+
+def kosaraju():
+    global g, r, scc, component, visit, stack
+    for i in range(n):
+        dfs(i)
+    visit = [False]*n
+    for i in stack[::-1]:
+        if visit[i]: continue
+        component = []
+        dfs2(i)
+        scc.append(component)
+    return scc
+
+print(kosaraju())

graphs/tarjans_scc.py

@@ -0,0 +1,78 @@
+from collections import deque
+
+
+def tarjan(g):
+    """
+    Tarjan's algo for finding strongly connected components in a directed graph
+
+    Uses two main attributes of each node to track reachability, the index of that node within a component(index),
+    and the lowest index reachable from that node(lowlink).
+
+    We then perform a dfs of the each component making sure to update these parameters for each node and saving the
+    nodes we visit on the way.
+
+    If ever we find that the lowest reachable node from a current node is equal to the index of the current node then it
+    must be the root of a strongly connected component and so we save it and it's equireachable vertices as a strongly
+    connected component.
+
+    Complexity: strong_connect() is called at most once for each node and has a complexity of O(|E|) as it is DFS.
+    Therefore this has complexity O(|V| + |E|) for a graph G = (V, E)
+
+    """
+
+    n = len(g)
+    stack = deque()
+    on_stack = [False for _ in range(n)]
+    index_of = [-1 for _ in range(n)]
+    lowlink_of = index_of[:]
+
+    def strong_connect(v, index, components):
+        index_of[v] = index  # the number when this node is seen
+        lowlink_of[v] = index  # lowest rank node reachable from here
+        index += 1
+        stack.append(v)
+        on_stack[v] = True
+
+        for w in g[v]:
+            if index_of[w] == -1:
+                index = strong_connect(w, index, components)
+                lowlink_of[v] = lowlink_of[w] if lowlink_of[w] < lowlink_of[v] else lowlink_of[v]
+            elif on_stack[w]:
+                lowlink_of[v] = lowlink_of[w] if lowlink_of[w] < lowlink_of[v] else lowlink_of[v]
+
+        if lowlink_of[v] == index_of[v]:
+            component = []
+            w = stack.pop()
+            on_stack[w] = False
+            component.append(w)
+            while w != v:
+                w = stack.pop()
+                on_stack[w] = False
+                component.append(w)
+            components.append(component)
+        return index
+
+    components = []
+    for v in range(n):
+        if index_of[v] == -1:
+            strong_connect(v, 0, components)
+
+    return components
+
+
+def create_graph(n, edges):
+    g = [[] for _ in range(n)]
+    for u, v in edges:
+        g[u].append(v)
+    return g
+
+
+if __name__ == '__main__':
+    # Test
+    n_vertices = 7
+    source = [0, 0, 1, 2, 3, 3, 4, 4, 6]
+    target = [1, 3, 2, 0, 1, 4, 5, 6, 5]
+    edges = [(u, v) for u, v in zip(source, target)]
+    g = create_graph(n_vertices, edges)
+
+    assert [[5], [6], [4], [3, 2, 1, 0]] == tarjan(g)