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