From a929a20f39ce736f51a74dd51d5f4e7668191fbc Mon Sep 17 00:00:00 2001 From: Dharaneedharan Date: Fri, 22 Oct 2021 12:09:08 +0530 Subject: [PATCH 1/7] Add Prim's algorithm for minimum spanning tree --- src/main/python/algorithms/graph/prim_mst.py | 60 ++++++++++++++++++++ 1 file changed, 60 insertions(+) create mode 100644 src/main/python/algorithms/graph/prim_mst.py diff --git a/src/main/python/algorithms/graph/prim_mst.py b/src/main/python/algorithms/graph/prim_mst.py new file mode 100644 index 0000000..b02e72b --- /dev/null +++ b/src/main/python/algorithms/graph/prim_mst.py @@ -0,0 +1,60 @@ +# A Python program for Prim's Minimum Spanning Tree (MST) algorithm. +# The program is for adjacency matrix representation of the graph + +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): + + # Initilaize min value + min = 1000000 + + 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 values used to pick minimum weight edge in cut + key = [1000000] * self.V + parent = [None] * self.V # Array to store constructed MST + key[0] = 0 # Make key 0 so that this vertex is picked as first vertex + mstSet = [False] * self.V + + parent[0] = -1 # First node is always the root of + + for cout in range(self.V): + + # Pick the minimum distance vertex from the set of vertices not + # yet processed. u is always equal to src in first iteration + u = self.minKey(key, mstSet) + + # Put the minimum distance vertex in the shortest path tree + mstSet[u] = True + + # Update dist value of the adjacent vertices of the picked vertex + # only if the current distance is greater than new distance and + # the vertex in not in the shotest path tree + for v in range(self.V): + # graph[u][v] is non zero only for adjacent vertices of m + # mstSet[v] is false for vertices not yet included in MST + # Update the key only if graph[u][v] is smaller than key[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) \ No newline at end of file From 4bf2f0ce8bbc42a3e43ba8f2f57fe199dc3ee0ff Mon Sep 17 00:00:00 2001 From: Dharaneedharan Date: Fri, 22 Oct 2021 12:22:50 +0530 Subject: [PATCH 2/7] Add driver code and test with input --- src/main/python/algorithms/graph/prim_mst.py | 14 +++++++++++++- 1 file changed, 13 insertions(+), 1 deletion(-) diff --git a/src/main/python/algorithms/graph/prim_mst.py b/src/main/python/algorithms/graph/prim_mst.py index b02e72b..1526990 100644 --- a/src/main/python/algorithms/graph/prim_mst.py +++ b/src/main/python/algorithms/graph/prim_mst.py @@ -57,4 +57,16 @@ def primMST(self): key[v] = self.graph[u][v] parent[v] = u - self.printMST(parent) \ No newline at end of file + self.printMST(parent) + +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() \ No newline at end of file From 101e1daaeb1b331ddbb126daceae6847b4fb22f5 Mon Sep 17 00:00:00 2001 From: Dharaneedharan Date: Fri, 22 Oct 2021 19:15:20 +0530 Subject: [PATCH 3/7] Add comments for functions --- src/main/python/algorithms/graph/prim_mst.py | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/src/main/python/algorithms/graph/prim_mst.py b/src/main/python/algorithms/graph/prim_mst.py index 1526990..0db31df 100644 --- a/src/main/python/algorithms/graph/prim_mst.py +++ b/src/main/python/algorithms/graph/prim_mst.py @@ -6,11 +6,14 @@ def __init__(self, vertices): self.V = vertices self.graph = [[0 for column in range(vertices)] for row in range(vertices)] - def printMST(self, parent): + # Function to print the constructed MST stored in parent[] + def printMST(self, parent): print("Edge \tWeight") for i in range(1, self.V): print(parent[i], "-", i, "\t", self.graph[i][parent[i]]) + # Function to find the vertex with minimum distance value, from + # the set of vertices not yet included in shortest path tree def minKey(self, key, mstSet): # Initilaize min value @@ -23,6 +26,8 @@ def minKey(self, key, mstSet): return min_index + # Function to construct and print MST for a graph represented using + # adjacency matrix representation def primMST(self): # Key values used to pick minimum weight edge in cut @@ -31,7 +36,7 @@ def primMST(self): key[0] = 0 # Make key 0 so that this vertex is picked as first vertex mstSet = [False] * self.V - parent[0] = -1 # First node is always the root of + parent[0] = -1 # First node is always the root for cout in range(self.V): From 6412df499c6c3ff585c990917cc09c329099f8a2 Mon Sep 17 00:00:00 2001 From: Dharaneedharan Date: Sat, 23 Oct 2021 06:41:59 +0530 Subject: [PATCH 4/7] Add Kruskal Algorithm --- .../python/algorithms/graph/kruskal_mst.py | 71 +++++++++++++++++++ 1 file changed, 71 insertions(+) create mode 100644 src/main/python/algorithms/graph/kruskal_mst.py diff --git a/src/main/python/algorithms/graph/kruskal_mst.py b/src/main/python/algorithms/graph/kruskal_mst.py new file mode 100644 index 0000000..952be11 --- /dev/null +++ b/src/main/python/algorithms/graph/kruskal_mst.py @@ -0,0 +1,71 @@ +# Python program for Kruskal's algorithm to find +# Minimum Spanning Tree of a given connected, +# undirected and weighted graph + +from collections import defaultdict + +# Class to represent a graph +class Graph: + + def __init__(self, vertices): + self.V = vertices + self.graph = [] + + def addEdge(self, u, v, w): + self.graph.append([u, v, w]) + + + def find(self, parent, i): + if parent[i] == i: + return i + return self.find(parent, parent[i]) + + + def union(self, parent, rank, x, y): + xroot = self.find(parent, x) + yroot = self.find(parent, y) + + if rank[xroot] < rank[yroot]: + parent[xroot] = yroot + elif rank[xroot] > rank[yroot]: + parent[yroot] = xroot + + else: + parent[yroot] = xroot + rank[xroot] += 1 + + def KruskalMST(self): + + result = [] + i = 0 + e = 0 + + self.graph = sorted(self.graph, + key=lambda item: item[2]) + + parent = [] + rank = [] + + for node in range(self.V): + parent.append(node) + rank.append(0) + + while e < self.V - 1: + + u, v, w = self.graph[i] + i = i + 1 + x = self.find(parent, u) + y = self.find(parent, v) + + + if x != y: + e = e + 1 + result.append([u, v, w]) + self.union(parent, rank, x, y) + + minimumCost = 0 + print ("Edges in the construvted MST") + for u, v, weight in result: + minimumCost += weight + print("%d -- %d = %d" % (u, v, weight)) + print("Minimum Spanning Tree" , minimumCost) From 0e1bdc4864666e00208845cdc130f2ed5608def1 Mon Sep 17 00:00:00 2001 From: Dharaneedharan Date: Sat, 23 Oct 2021 06:44:01 +0530 Subject: [PATCH 5/7] Add driver code with graph input --- src/main/python/algorithms/graph/kruskal_mst.py | 10 ++++++++++ 1 file changed, 10 insertions(+) diff --git a/src/main/python/algorithms/graph/kruskal_mst.py b/src/main/python/algorithms/graph/kruskal_mst.py index 952be11..ad7a21f 100644 --- a/src/main/python/algorithms/graph/kruskal_mst.py +++ b/src/main/python/algorithms/graph/kruskal_mst.py @@ -69,3 +69,13 @@ def KruskalMST(self): minimumCost += weight print("%d -- %d = %d" % (u, v, weight)) print("Minimum Spanning Tree" , minimumCost) + +# Driver code +g = Graph(4) +g.addEdge(0, 1, 10) +g.addEdge(0, 2, 6) +g.addEdge(0, 3, 5) +g.addEdge(1, 3, 15) +g.addEdge(2, 3, 4) + +g.KruskalMST() \ No newline at end of file From b5d93534bb40f98965cbd4ea85aabf9078bf6e7e Mon Sep 17 00:00:00 2001 From: Dharaneedharan Date: Sat, 23 Oct 2021 06:53:26 +0530 Subject: [PATCH 6/7] Add informative comments --- .../python/algorithms/graph/kruskal_mst.py | 45 +++++++++++++++---- 1 file changed, 37 insertions(+), 8 deletions(-) diff --git a/src/main/python/algorithms/graph/kruskal_mst.py b/src/main/python/algorithms/graph/kruskal_mst.py index ad7a21f..76f8b23 100644 --- a/src/main/python/algorithms/graph/kruskal_mst.py +++ b/src/main/python/algorithms/graph/kruskal_mst.py @@ -5,63 +5,91 @@ from collections import defaultdict # Class to represent a graph + + class Graph: def __init__(self, vertices): - self.V = vertices - self.graph = [] + self.V = vertices # No. of vertices + self.graph = [] # default dictionary + # to store graph + # function to add an edge to graph def addEdge(self, u, v, w): self.graph.append([u, v, w]) - + # A utility function to find set of an element i + # (uses path compression technique) def find(self, parent, i): if parent[i] == i: return i return self.find(parent, parent[i]) - + # A function that does union of two sets of x and y + # (uses union by rank) def union(self, parent, rank, x, y): xroot = self.find(parent, x) yroot = self.find(parent, y) - + + # Attach smaller rank tree under root of + # high rank tree (Union by Rank) if rank[xroot] < rank[yroot]: parent[xroot] = yroot elif rank[xroot] > rank[yroot]: parent[yroot] = xroot + # If ranks are same, then make one as root + # and increment its rank by one else: parent[yroot] = xroot rank[xroot] += 1 + # The main function to construct MST using Kruskal's + # algorithm def KruskalMST(self): - result = [] + result = [] # This will store the resultant MST + + # An index variable, used for sorted edges i = 0 + + # An index variable, used for result[] e = 0 + # Step 1: Sort all the edges in + # non-decreasing order of their + # weight. If we are not allowed to change the + # given graph, we can create a copy of graph self.graph = sorted(self.graph, key=lambda item: item[2]) parent = [] rank = [] + # Create V subsets with single elements for node in range(self.V): parent.append(node) rank.append(0) + # Number of edges to be taken is equal to V-1 while e < self.V - 1: + # Step 2: Pick the smallest edge and increment + # the index for next iteration u, v, w = self.graph[i] i = i + 1 x = self.find(parent, u) y = self.find(parent, v) - + # If including this edge does't + # cause cycle, include it in result + # and increment the indexof result + # for next edge if x != y: e = e + 1 result.append([u, v, w]) self.union(parent, rank, x, y) + # Else discard the edge minimumCost = 0 print ("Edges in the construvted MST") @@ -69,7 +97,7 @@ def KruskalMST(self): minimumCost += weight print("%d -- %d = %d" % (u, v, weight)) print("Minimum Spanning Tree" , minimumCost) - + # Driver code g = Graph(4) g.addEdge(0, 1, 10) @@ -78,4 +106,5 @@ def KruskalMST(self): g.addEdge(1, 3, 15) g.addEdge(2, 3, 4) +# Function call g.KruskalMST() \ No newline at end of file From eafcacd10ca5bdac17816bd48e693b3a5260b88a Mon Sep 17 00:00:00 2001 From: Dharaneedharan Date: Sat, 23 Oct 2021 08:21:31 +0530 Subject: [PATCH 7/7] Fix typo error --- src/main/python/algorithms/graph/kruskal_mst.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/main/python/algorithms/graph/kruskal_mst.py b/src/main/python/algorithms/graph/kruskal_mst.py index 76f8b23..1f1904d 100644 --- a/src/main/python/algorithms/graph/kruskal_mst.py +++ b/src/main/python/algorithms/graph/kruskal_mst.py @@ -92,7 +92,7 @@ def KruskalMST(self): # Else discard the edge minimumCost = 0 - print ("Edges in the construvted MST") + print ("Edges in the constructed MST") for u, v, weight in result: minimumCost += weight print("%d -- %d = %d" % (u, v, weight))