Extra Algorithms added

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(input("Enter number of vertices: "))
+e = int(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))