mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-11 05:40:15 +00:00
92 lines
2.5 KiB
Python
92 lines
2.5 KiB
Python
|
import queue
|
||
|
|
|
||
|
|
|
||
|
|
def swap(a, b):
|
||
|
|
a ^= b
|
||
|
|
b ^= a
|
||
|
|
a ^= b
|
||
|
|
return a, b
|
||
|
|
|
||
|
|
|
||
|
|
# creating sparse table which saves each nodes 2^ith parent
|
||
|
|
def creatSparse(max_node, parent):
|
||
|
|
j = 1
|
||
|
|
while (1 << j) < max_node:
|
||
|
|
for i in range(1, max_node + 1):
|
||
|
|
parent[j][i] = parent[j - 1][parent[j - 1][i]]
|
||
|
|
j += 1
|
||
|
|
return parent
|
||
|
|
|
||
|
|
|
||
|
|
# returns lca of node u,v
|
||
|
|
def LCA(u, v, level, parent):
|
||
|
|
# u must be deeper in the tree than v
|
||
|
|
if level[u] < level[v]:
|
||
|
|
u, v = swap(u, v)
|
||
|
|
# making depth of u same as depth of v
|
||
|
|
for i in range(18, -1, -1):
|
||
|
|
if level[u] - (1 << i) >= level[v]:
|
||
|
|
u = parent[i][u]
|
||
|
|
# at the same depth if u==v that mean lca is found
|
||
|
|
if u == v:
|
||
|
|
return u
|
||
|
|
# moving both nodes upwards till lca in found
|
||
|
|
for i in range(18, -1, -1):
|
||
|
|
if parent[i][u] != 0 and parent[i][u] != parent[i][v]:
|
||
|
|
u, v = parent[i][u], parent[i][v]
|
||
|
|
# returning longest common ancestor of u,v
|
||
|
|
return parent[0][u]
|
||
|
|
|
||
|
|
|
||
|
|
# runs a breadth first search from root node of the tree
|
||
|
|
# sets every nodes direct parent
|
||
|
|
# parent of root node is set to 0
|
||
|
|
# calculates depth of each node from root node
|
||
|
|
def bfs(level, parent, max_node, graph, root=1):
|
||
|
|
level[root] = 0
|
||
|
|
q = queue.Queue(maxsize=max_node)
|
||
|
|
q.put(root)
|
||
|
|
while q.qsize() != 0:
|
||
|
|
u = q.get()
|
||
|
|
for v in graph[u]:
|
||
|
|
if level[v] == -1:
|
||
|
|
level[v] = level[u] + 1
|
||
|
|
q.put(v)
|
||
|
|
parent[0][v] = u
|
||
|
|
return level, parent
|
||
|
|
|
||
|
|
|
||
|
|
def main():
|
||
|
|
max_node = 13
|
||
|
|
# initializing with 0
|
||
|
|
parent = [[0 for _ in range(max_node + 10)] for _ in range(20)]
|
||
|
|
# initializing with -1 which means every node is unvisited
|
||
|
|
level = [-1 for _ in range(max_node + 10)]
|
||
|
|
graph = {
|
||
|
|
1: [2, 3, 4],
|
||
|
|
2: [5],
|
||
|
|
3: [6, 7],
|
||
|
|
4: [8],
|
||
|
|
5: [9, 10],
|
||
|
|
6: [11],
|
||
|
|
7: [],
|
||
|
|
8: [12, 13],
|
||
|
|
9: [],
|
||
|
|
10: [],
|
||
|
|
11: [],
|
||
|
|
12: [],
|
||
|
|
13: []
|
||
|
|
}
|
||
|
|
level, parent = bfs(level, parent, max_node, graph, 1)
|
||
|
|
parent = creatSparse(max_node, parent)
|
||
|
|
print("LCA of node 1 and 3 is: ", LCA(1, 3, level, parent))
|
||
|
|
print("LCA of node 5 and 6 is: ", LCA(5, 6, level, parent))
|
||
|
|
print("LCA of node 7 and 11 is: ", LCA(7, 11, level, parent))
|
||
|
|
print("LCA of node 6 and 7 is: ", LCA(6, 7, level, parent))
|
||
|
|
print("LCA of node 4 and 12 is: ", LCA(4, 12, level, parent))
|
||
|
|
print("LCA of node 8 and 8 is: ", LCA(8, 8, level, parent))
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
main()
|