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