mirror of
https://github.com/TheAlgorithms/Python.git
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92 lines
2.5 KiB
Python
92 lines
2.5 KiB
Python
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import queue
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def swap(a, b):
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a ^= b
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b ^= a
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a ^= b
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return a, b
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# creating sparse table which saves each nodes 2^ith parent
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def creatSparse(max_node, parent):
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j = 1
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while (1 << j) < max_node:
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for i in range(1, max_node + 1):
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parent[j][i] = parent[j - 1][parent[j - 1][i]]
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j += 1
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return parent
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# returns lca of node u,v
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def LCA(u, v, level, parent):
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# u must be deeper in the tree than v
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if level[u] < level[v]:
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u, v = swap(u, v)
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# making depth of u same as depth of v
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for i in range(18, -1, -1):
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if level[u] - (1 << i) >= level[v]:
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u = parent[i][u]
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# at the same depth if u==v that mean lca is found
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if u == v:
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return u
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# moving both nodes upwards till lca in found
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for i in range(18, -1, -1):
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if parent[i][u] != 0 and parent[i][u] != parent[i][v]:
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u, v = parent[i][u], parent[i][v]
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# returning longest common ancestor of u,v
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return parent[0][u]
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# runs a breadth first search from root node of the tree
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# sets every nodes direct parent
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# parent of root node is set to 0
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# calculates depth of each node from root node
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def bfs(level, parent, max_node, graph, root=1):
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level[root] = 0
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q = queue.Queue(maxsize=max_node)
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q.put(root)
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while q.qsize() != 0:
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u = q.get()
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for v in graph[u]:
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if level[v] == -1:
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level[v] = level[u] + 1
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q.put(v)
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parent[0][v] = u
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return level, parent
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def main():
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max_node = 13
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# initializing with 0
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parent = [[0 for _ in range(max_node + 10)] for _ in range(20)]
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# initializing with -1 which means every node is unvisited
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level = [-1 for _ in range(max_node + 10)]
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graph = {
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1: [2, 3, 4],
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2: [5],
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3: [6, 7],
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4: [8],
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5: [9, 10],
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6: [11],
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7: [],
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8: [12, 13],
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9: [],
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10: [],
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11: [],
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12: [],
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13: []
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}
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level, parent = bfs(level, parent, max_node, graph, 1)
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parent = creatSparse(max_node, parent)
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print("LCA of node 1 and 3 is: ", LCA(1, 3, level, parent))
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print("LCA of node 5 and 6 is: ", LCA(5, 6, level, parent))
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print("LCA of node 7 and 11 is: ", LCA(7, 11, level, parent))
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print("LCA of node 6 and 7 is: ", LCA(6, 7, level, parent))
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print("LCA of node 4 and 12 is: ", LCA(4, 12, level, parent))
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print("LCA of node 8 and 8 is: ", LCA(8, 8, level, parent))
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if __name__ == "__main__":
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main()
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