increment 1

data_structures/graph/bellman_ford.py

@@ -0,0 +1,54 @@
+from __future__ import print_function
+
+def printDist(dist, V):
+	print("\nVertex Distance")
+	for i in range(V):
+		if dist[i] != float('inf') :
+			print(i,"\t",int(dist[i]),end = "\t")
+		else:
+			print(i,"\t","INF",end="\t")
+		print()
+
+def BellmanFord(graph, V, E, src):
+	mdist=[float('inf') for i in range(V)]
+	mdist[src] = 0.0
+	
+	for i in range(V-1):
+		for j in range(V):
+			u = graph[j]["src"]
+			v = graph[j]["dst"]
+			w = graph[j]["weight"]
+
+			if mdist[u] != float('inf') and mdist[u] + w < mdist[v]:
+				mdist[v] = mdist[u] + w 
+	for j in range(V):
+			u = graph[j]["src"]
+			v = graph[j]["dst"]
+			w = graph[j]["weight"]
+
+			if mdist[u] != float('inf') and mdist[u] + w < mdist[v]:
+				print("Negative cycle found. Solution not possible.")
+				return
+	
+	printDist(mdist, V)	
+
+			
+
+#MAIN
+V = int(raw_input("Enter number of vertices: "))
+E = int(raw_input("Enter number of edges: "))
+
+graph = [dict() for j in range(E)]
+
+for i in range(V):
+	graph[i][i] = 0.0
+
+for i in range(E):
+	print("\nEdge ",i+1)
+	src = int(raw_input("Enter source:"))
+	dst = int(raw_input("Enter destination:"))
+	weight = float(raw_input("Enter weight:"))
+	graph[i] = {"src": src,"dst": dst, "weight": weight}
+	
+gsrc = int(raw_input("\nEnter shortest path source:"))
+BellmanFord(graph, V, E, gsrc)

data_structures/graph/breadth_first_search.py

@@ -0,0 +1,67 @@
+#!/usr/bin/python
+# encoding=utf8
+
+""" Author: OMKAR PATHAK """
+
+from __future__ import print_function
+
+
+class Graph():
+    def __init__(self):
+        self.vertex = {}
+
+    # for printing the Graph vertexes
+    def printGraph(self):
+        for i in self.vertex.keys():
+            print(i,' -> ', ' -> '.join([str(j) for j in self.vertex[i]]))
+
+    # for adding the edge beween two vertexes
+    def addEdge(self, fromVertex, toVertex):
+        # check if vertex is already present,
+        if fromVertex in self.vertex.keys():
+            self.vertex[fromVertex].append(toVertex)
+        else:
+            # else make a new vertex
+            self.vertex[fromVertex] = [toVertex]
+
+    def BFS(self, startVertex):
+        # Take a list for stoting already visited vertexes
+        visited = [False] * len(self.vertex)
+
+        # create a list to store all the vertexes for BFS
+        queue = []
+
+        # mark the source node as visited and enqueue it
+        visited[startVertex] = True
+        queue.append(startVertex)
+
+        while queue:
+            startVertex = queue.pop(0)
+            print(startVertex, end = ' ')
+
+            # mark all adjacent nodes as visited and print them
+            for i in self.vertex[startVertex]:
+                if visited[i] == False:
+                    queue.append(i)
+                    visited[i] = True
+
+if __name__ == '__main__':
+    g = Graph()
+    g.addEdge(0, 1)
+    g.addEdge(0, 2)
+    g.addEdge(1, 2)
+    g.addEdge(2, 0)
+    g.addEdge(2, 3)
+    g.addEdge(3, 3)
+
+    g.printGraph()
+    print('BFS:')
+    g.BFS(2)
+
+    # OUTPUT:
+    # 0  ->  1 -> 2
+    # 1  ->  2
+    # 2  ->  0 -> 3
+    # 3  ->  3
+    # BFS:
+    # 2 0 3 1

data_structures/graph/depth_first_search.py

@@ -0,0 +1,66 @@
+#!/usr/bin/python
+# encoding=utf8
+
+""" Author: OMKAR PATHAK """
+from __future__ import print_function
+
+
+class Graph():
+    def __init__(self):
+        self.vertex = {}
+
+    # for printing the Graph vertexes
+    def printGraph(self):
+        print(self.vertex)
+        for i in self.vertex.keys():
+            print(i,' -> ', ' -> '.join([str(j) for j in self.vertex[i]]))
+
+    # for adding the edge beween two vertexes
+    def addEdge(self, fromVertex, toVertex):
+        # check if vertex is already present,
+        if fromVertex in self.vertex.keys():
+            self.vertex[fromVertex].append(toVertex)
+        else:
+            # else make a new vertex
+            self.vertex[fromVertex] = [toVertex]
+
+    def DFS(self):
+        # visited array for storing already visited nodes
+        visited = [False] * len(self.vertex)
+
+        # call the recursive helper function
+        for i in range(len(self.vertex)):
+            if visited[i] == False:
+                self.DFSRec(i, visited)
+
+    def DFSRec(self, startVertex, visited):
+        # mark start vertex as visited
+        visited[startVertex] = True
+
+        print(startVertex, end = ' ')
+
+        # Recur for all the vertexes that are adjacent to this node
+        for i in self.vertex.keys():
+            if visited[i] == False:
+                self.DFSRec(i, visited)
+
+if __name__ == '__main__':
+    g = Graph()
+    g.addEdge(0, 1)
+    g.addEdge(0, 2)
+    g.addEdge(1, 2)
+    g.addEdge(2, 0)
+    g.addEdge(2, 3)
+    g.addEdge(3, 3)
+
+    g.printGraph()
+    print('DFS:')
+    g.DFS()
+
+    # OUTPUT:
+    # 0  ->  1 -> 2
+    # 1  ->  2
+    # 2  ->  0 -> 3
+    # 3  ->  3
+    # DFS:
+    # 0 1 2 3

data_structures/graph/dijkstra.py

@@ -0,0 +1,57 @@
+from __future__ import print_function
+
+def printDist(dist, V):
+	print("\nVertex Distance")
+	for i in range(V):
+		if dist[i] != float('inf') :
+			print(i,"\t",int(dist[i]),end = "\t")
+		else:
+			print(i,"\t","INF",end="\t")
+		print()
+
+def minDist(mdist, vset, V):
+	minVal = float('inf')
+	minInd = -1
+	for i in range(V):
+		if (not vset[i]) and mdist[i] < minVal :
+			minInd = i
+			minVal = mdist[i]
+	return minInd
+
+def Dijkstra(graph, V, src):
+	mdist=[float('inf') for i in range(V)]
+	vset = [False for i in range(V)]
+	mdist[src] = 0.0;
+	
+	for i in range(V-1):
+		u = minDist(mdist, vset, V)
+		vset[u] = True
+		
+		for v in range(V):
+			if (not vset[v]) and graph[u][v]!=float('inf') and mdist[u] + graph[u][v] < mdist[v]:
+				mdist[v] = mdist[u] + graph[u][v] 
+
+	
+
+	printDist(mdist, V)	
+
+			
+
+#MAIN
+V = int(raw_input("Enter number of vertices: "))
+E = int(raw_input("Enter number of edges: "))
+
+graph = [[float('inf') for i in range(V)] for j in range(V)]
+
+for i in range(V):
+	graph[i][i] = 0.0
+
+for i in range(E):
+	print("\nEdge ",i+1)
+	src = int(raw_input("Enter source:"))
+	dst = int(raw_input("Enter destination:"))
+	weight = float(raw_input("Enter weight:"))
+	graph[src][dst] = weight
+
+gsrc = int(raw_input("\nEnter shortest path source:"))
+Dijkstra(graph, V, gsrc)

data_structures/graph/dijkstra_algorithm.py

@@ -0,0 +1,212 @@
+# Title: Dijkstra's Algorithm for finding single source shortest path from scratch
+# Author: Shubham Malik
+# References: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm
+
+from __future__ import print_function
+import math
+import sys
+# For storing the vertex set to retreive node with the lowest distance
+
+
+class PriorityQueue:
+    # Based on Min Heap
+    def __init__(self):
+        self.cur_size = 0
+        self.array = []
+        self.pos = {}   # To store the pos of node in array
+
+    def isEmpty(self):
+        return self.cur_size == 0
+
+    def min_heapify(self, idx):
+        lc = self.left(idx)
+        rc = self.right(idx)
+        if lc < self.cur_size and self.array(lc)[0] < self.array(idx)[0]:
+            smallest = lc
+        else:
+            smallest = idx
+        if rc < self.cur_size and self.array(rc)[0] < self.array(smallest)[0]:
+            smallest = rc
+        if smallest != idx:
+            self.swap(idx, smallest)
+            self.min_heapify(smallest)
+
+    def insert(self, tup):
+        # Inserts a node into the Priority Queue
+        self.pos[tup[1]] = self.cur_size
+        self.cur_size += 1
+        self.array.append((sys.maxsize, tup[1]))
+        self.decrease_key((sys.maxsize, tup[1]), tup[0])
+
+    def extract_min(self):
+        # Removes and returns the min element at top of priority queue
+        min_node = self.array[0][1]
+        self.array[0] = self.array[self.cur_size - 1]
+        self.cur_size -= 1
+        self.min_heapify(1)
+        del self.pos[min_node]
+        return min_node
+
+    def left(self, i):
+        # returns the index of left child
+        return 2 * i + 1
+
+    def right(self, i):
+        # returns the index of right child
+        return 2 * i + 2
+
+    def par(self, i):
+        # returns the index of parent
+        return math.floor(i / 2)
+
+    def swap(self, i, j):
+        # swaps array elements at indices i and j
+        # update the pos{}
+        self.pos[self.array[i][1]] = j
+        self.pos[self.array[j][1]] = i
+        temp = self.array[i]
+        self.array[i] = self.array[j]
+        self.array[j] = temp
+
+    def decrease_key(self, tup, new_d):
+        idx = self.pos[tup[1]]
+        # assuming the new_d is atmost old_d
+        self.array[idx] = (new_d, tup[1])
+        while idx > 0 and self.array[self.par(idx)][0] > self.array[idx][0]:
+            self.swap(idx, self.par(idx))
+            idx = self.par(idx)
+
+
+class Graph:
+    def __init__(self, num):
+        self.adjList = {}   # To store graph: u -> (v,w)
+        self.num_nodes = num    # Number of nodes in graph
+        # To store the distance from source vertex
+        self.dist = [0] * self.num_nodes
+        self.par = [-1] * self.num_nodes  # To store the path
+
+    def add_edge(self, u, v, w):
+        #  Edge going from node u to v and v to u with weight w
+        # u (w)-> v, v (w) -> u
+        # Check if u already in graph
+        if u in self.adjList.keys():
+            self.adjList[u].append((v, w))
+        else:
+            self.adjList[u] = [(v, w)]
+
+        # Assuming undirected graph
+        if v in self.adjList.keys():
+            self.adjList[v].append((u, w))
+        else:
+            self.adjList[v] = [(u, w)]
+
+    def show_graph(self):
+        # u -> v(w)
+        for u in self.adjList:
+            print(u, '->', ' -> '.join(str("{}({})".format(v, w))
+                                       for v, w in self.adjList[u]))
+
+    def dijkstra(self, src):
+        # Flush old junk values in par[]
+        self.par = [-1] * self.num_nodes
+        # src is the source node
+        self.dist[src] = 0
+        Q = PriorityQueue()
+        Q.insert((0, src))  # (dist from src, node)
+        for u in self.adjList.keys():
+            if u != src:
+                self.dist[u] = sys.maxsize  # Infinity
+                self.par[u] = -1
+
+        while not Q.isEmpty():
+            u = Q.extract_min()  # Returns node with the min dist from source
+            # Update the distance of all the neighbours of u and
+            # if their prev dist was INFINITY then push them in Q
+            for v, w in self.adjList[u]:
+                new_dist = self.dist[u] + w
+                if self.dist[v] > new_dist:
+                    if self.dist[v] == sys.maxsize:
+                        Q.insert((new_dist, v))
+                    else:
+                        Q.decrease_key((self.dist[v], v), new_dist)
+                    self.dist[v] = new_dist
+                    self.par[v] = u
+
+        # Show the shortest distances from src
+        self.show_distances(src)
+
+    def show_distances(self, src):
+        print("Distance from node: {}".format(src))
+        for u in range(self.num_nodes):
+            print('Node {} has distance: {}'.format(u, self.dist[u]))
+
+    def show_path(self, src, dest):
+        # To show the shortest path from src to dest
+        # WARNING: Use it *after* calling dijkstra
+        path = []
+        cost = 0
+        temp = dest
+        # Backtracking from dest to src
+        while self.par[temp] != -1:
+            path.append(temp)
+            if temp != src:
+                for v, w in self.adjList[temp]:
+                    if v == self.par[temp]:
+                        cost += w
+                        break
+            temp = self.par[temp]
+        path.append(src)
+        path.reverse()
+
+        print('----Path to reach {} from {}----'.format(dest, src))
+        for u in path:
+            print('{}'.format(u), end=' ')
+            if u != dest:
+                print('-> ', end='')
+
+        print('\nTotal cost of path: ', cost)
+
+
+if __name__ == '__main__':
+    graph = Graph(9)
+    graph.add_edge(0, 1, 4)
+    graph.add_edge(0, 7, 8)
+    graph.add_edge(1, 2, 8)
+    graph.add_edge(1, 7, 11)
+    graph.add_edge(2, 3, 7)
+    graph.add_edge(2, 8, 2)
+    graph.add_edge(2, 5, 4)
+    graph.add_edge(3, 4, 9)
+    graph.add_edge(3, 5, 14)
+    graph.add_edge(4, 5, 10)
+    graph.add_edge(5, 6, 2)
+    graph.add_edge(6, 7, 1)
+    graph.add_edge(6, 8, 6)
+    graph.add_edge(7, 8, 7)
+    graph.show_graph()
+    graph.dijkstra(0)
+    graph.show_path(0, 4)
+
+# OUTPUT
+# 0 -> 1(4) -> 7(8)
+# 1 -> 0(4) -> 2(8) -> 7(11)
+# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)
+# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)
+# 3 -> 2(7) -> 4(9) -> 5(14)
+# 8 -> 2(2) -> 6(6) -> 7(7)
+# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)
+# 4 -> 3(9) -> 5(10)
+# 6 -> 5(2) -> 7(1) -> 8(6)
+# Distance from node: 0
+# Node 0 has distance: 0
+# Node 1 has distance: 4
+# Node 2 has distance: 12
+# Node 3 has distance: 19
+# Node 4 has distance: 21
+# Node 5 has distance: 11
+# Node 6 has distance: 9
+# Node 7 has distance: 8
+# Node 8 has distance: 14
+# ----Path to reach 4 from 0----
+# 0 -> 7 -> 6 -> 5 -> 4
+# Total cost of path:  21

data_structures/graph/even_tree.py

@@ -0,0 +1,70 @@
+"""
+You are given a tree(a simple connected graph with no cycles). The tree has N
+nodes numbered from 1 to N and is rooted at node 1.
+
+Find the maximum number of edges you can remove from the tree to get a forest
+such that each connected component of the forest contains an even number of
+nodes.
+
+Constraints
+2 <= 2 <= 100
+
+Note: The tree input will be such that it can always be decomposed into
+components containing an even number of nodes.
+"""
+from __future__ import print_function
+# pylint: disable=invalid-name
+from collections import defaultdict
+
+
+def dfs(start):
+    """DFS traversal"""
+    # pylint: disable=redefined-outer-name
+    ret = 1
+    visited[start] = True
+    for v in tree.get(start):
+        if v not in visited:
+            ret += dfs(v)
+    if ret % 2 == 0:
+        cuts.append(start)
+    return ret
+
+
+def even_tree():
+    """
+    2 1
+    3 1
+    4 3
+    5 2
+    6 1
+    7 2
+    8 6
+    9 8
+    10 8
+    On removing edges (1,3) and (1,6), we can get the desired result 2.
+    """
+    dfs(1)
+
+
+if __name__ == '__main__':
+    n, m = 10, 9
+    tree = defaultdict(list)
+    visited = {}
+    cuts = []
+    count = 0
+    edges = [
+        (2, 1),
+        (3, 1),
+        (4, 3),
+        (5, 2),
+        (6, 1),
+        (7, 2),
+        (8, 6),
+        (9, 8),
+        (10, 8),
+    ]
+    for u, v in edges:
+        tree[u].append(v)
+        tree[v].append(u)
+    even_tree()
+    print(len(cuts) - 1)

data_structures/graph/floyd_warshall.py

@@ -0,0 +1,48 @@
+from __future__ import print_function
+
+def printDist(dist, V):
+	print("\nThe shortest path matrix using Floyd Warshall algorithm\n")
+	for i in range(V):
+		for j in range(V):
+			if dist[i][j] != float('inf') :
+				print(int(dist[i][j]),end = "\t")
+			else:
+				print("INF",end="\t")
+		print()
+
+
+
+def FloydWarshall(graph, V):
+	dist=[[float('inf') for i in range(V)] for j in range(V)]
+	
+	for i in range(V):
+		for j in range(V):
+			dist[i][j] = graph[i][j]
+
+	for k in range(V):
+		for i in range(V):
+			for j in range(V):
+				if dist[i][k]!=float('inf') and dist[k][j]!=float('inf') and dist[i][k]+dist[k][j] < dist[i][j]:
+					dist[i][j] = dist[i][k] + dist[k][j]
+
+	printDist(dist, V)	
+
+			
+
+#MAIN
+V = int(raw_input("Enter number of vertices: "))
+E = int(raw_input("Enter number of edges: "))
+
+graph = [[float('inf') for i in range(V)] for j in range(V)]
+
+for i in range(V):
+	graph[i][i] = 0.0
+
+for i in range(E):
+	print("\nEdge ",i+1)
+	src = int(raw_input("Enter source:"))
+	dst = int(raw_input("Enter destination:"))
+	weight = float(raw_input("Enter weight:"))
+	graph[src][dst] = weight
+
+FloydWarshall(graph, V)

data_structures/graph/graph.py

@@ -0,0 +1,44 @@
+#!/usr/bin/python
+# encoding=utf8
+
+from __future__ import print_function
+# Author: OMKAR PATHAK
+
+# We can use Python's dictionary for constructing the graph
+
+class AdjacencyList(object):
+    def __init__(self):
+        self.List = {}
+
+    def addEdge(self, fromVertex, toVertex):
+        # check if vertex is already present
+        if fromVertex in self.List.keys():
+            self.List[fromVertex].append(toVertex)
+        else:
+            self.List[fromVertex] = [toVertex]
+
+    def printList(self):
+        for i  in self.List:
+            print((i,'->',' -> '.join([str(j) for j in self.List[i]])))
+
+if __name__ == '__main__':
+    al = AdjacencyList()
+    al.addEdge(0, 1)
+    al.addEdge(0, 4)
+    al.addEdge(4, 1)
+    al.addEdge(4, 3)
+    al.addEdge(1, 0)
+    al.addEdge(1, 4)
+    al.addEdge(1, 3)
+    al.addEdge(1, 2)
+    al.addEdge(2, 3)
+    al.addEdge(3, 4)
+
+    al.printList()
+
+    # OUTPUT:
+    # 0 -> 1 -> 4
+    # 1 -> 0 -> 4 -> 3 -> 2
+    # 2 -> 3
+    # 3 -> 4
+    # 4 -> 1 -> 3

data_structures/graph/graph_list.py

@@ -0,0 +1,31 @@
+from __future__ import print_function
+
+
+class Graph:
+    def __init__(self, vertex):
+        self.vertex = vertex
+        self.graph = [[0] for i in range(vertex)]
+
+    def add_edge(self, u, v):
+        self.graph[u - 1].append(v - 1)
+
+    def show(self):
+        for i in range(self.vertex):
+            print('%d: '% (i + 1), end=' ')
+            for j in self.graph[i]:
+                print('%d-> '% (j + 1), end=' ')
+            print(' ')
+
+
+
+g = Graph(100)
+
+g.add_edge(1,3)
+g.add_edge(2,3)
+g.add_edge(3,4)
+g.add_edge(3,5)
+g.add_edge(4,5)
+
+
+g.show()
+

data_structures/graph/graph_matrix.py

@@ -0,0 +1,32 @@
+from __future__ import print_function
+
+
+class Graph:
+
+    def __init__(self, vertex):
+        self.vertex = vertex
+        self.graph = [[0] * vertex for i in range(vertex) ]
+
+    def add_edge(self, u, v):
+        self.graph[u - 1][v - 1] = 1
+        self.graph[v - 1][u - 1] = 1
+
+    def show(self):
+
+        for i in self.graph:
+            for j in i:
+                print(j, end=' ')
+            print(' ')
+
+
+
+
+g = Graph(100)
+
+g.add_edge(1,4)
+g.add_edge(4,2)
+g.add_edge(4,5)
+g.add_edge(2,5)
+g.add_edge(5,3)
+g.show()
+