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* from __future__ import annotations
* fixup! from __future__ import annotations
* fixup! from __future__ import annotations
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
118 lines
3.2 KiB
Python
118 lines
3.2 KiB
Python
# https://en.wikipedia.org/wiki/Lowest_common_ancestor
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# https://en.wikipedia.org/wiki/Breadth-first_search
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from __future__ import annotations
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import queue
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def swap(a: int, b: int) -> tuple[int, int]:
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"""
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Return a tuple (b, a) when given two integers a and b
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>>> swap(2,3)
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(3, 2)
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>>> swap(3,4)
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(4, 3)
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>>> swap(67, 12)
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(12, 67)
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"""
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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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def create_sparse(max_node: int, parent: list[list[int]]) -> list[list[int]]:
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"""
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creating sparse table which saves each nodes 2^i-th parent
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"""
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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 lowest_common_ancestor(
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u: int, v: int, level: list[int], parent: list[list[int]]
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) -> list[list[int]]:
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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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def breadth_first_search(
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level: list[int],
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parent: list[list[int]],
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max_node: int,
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graph: dict[int, int],
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root=1,
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) -> tuple[list[int], list[list[int]]]:
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"""
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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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"""
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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() -> None:
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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 = breadth_first_search(level, parent, max_node, graph, 1)
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parent = create_sparse(max_node, parent)
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print("LCA of node 1 and 3 is: ", lowest_common_ancestor(1, 3, level, parent))
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print("LCA of node 5 and 6 is: ", lowest_common_ancestor(5, 6, level, parent))
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print("LCA of node 7 and 11 is: ", lowest_common_ancestor(7, 11, level, parent))
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print("LCA of node 6 and 7 is: ", lowest_common_ancestor(6, 7, level, parent))
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print("LCA of node 4 and 12 is: ", lowest_common_ancestor(4, 12, level, parent))
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print("LCA of node 8 and 8 is: ", lowest_common_ancestor(8, 8, level, parent))
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if __name__ == "__main__":
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main()
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