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* ci(pre-commit): Add pep8-naming to `pre-commit` hooks (#7038) * refactor: Fix naming conventions (#7038) * Update arithmetic_analysis/lu_decomposition.py Co-authored-by: Christian Clauss <cclauss@me.com> * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * refactor(lu_decomposition): Replace `NDArray` with `ArrayLike` (#7038) * chore: Fix naming conventions in doctests (#7038) * fix: Temporarily disable project euler problem 104 (#7069) * chore: Fix naming conventions in doctests (#7038) Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
72 lines
2.0 KiB
Python
72 lines
2.0 KiB
Python
# Eulerian Path is a path in graph that visits every edge exactly once.
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# Eulerian Circuit is an Eulerian Path which starts and ends on the same
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# vertex.
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# time complexity is O(V+E)
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# space complexity is O(VE)
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# using dfs for finding eulerian path traversal
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def dfs(u, graph, visited_edge, path=None):
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path = (path or []) + [u]
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for v in graph[u]:
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if visited_edge[u][v] is False:
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visited_edge[u][v], visited_edge[v][u] = True, True
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path = dfs(v, graph, visited_edge, path)
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return path
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# for checking in graph has euler path or circuit
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def check_circuit_or_path(graph, max_node):
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odd_degree_nodes = 0
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odd_node = -1
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for i in range(max_node):
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if i not in graph.keys():
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continue
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if len(graph[i]) % 2 == 1:
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odd_degree_nodes += 1
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odd_node = i
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if odd_degree_nodes == 0:
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return 1, odd_node
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if odd_degree_nodes == 2:
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return 2, odd_node
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return 3, odd_node
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def check_euler(graph, max_node):
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visited_edge = [[False for _ in range(max_node + 1)] for _ in range(max_node + 1)]
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check, odd_node = check_circuit_or_path(graph, max_node)
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if check == 3:
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print("graph is not Eulerian")
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print("no path")
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return
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start_node = 1
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if check == 2:
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start_node = odd_node
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print("graph has a Euler path")
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if check == 1:
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print("graph has a Euler cycle")
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path = dfs(start_node, graph, visited_edge)
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print(path)
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def main():
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g1 = {1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
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g2 = {1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
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g3 = {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
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g4 = {1: [2, 3], 2: [1, 3], 3: [1, 2]}
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g5 = {
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1: [],
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2: []
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# all degree is zero
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}
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max_node = 10
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check_euler(g1, max_node)
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check_euler(g2, max_node)
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check_euler(g3, max_node)
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check_euler(g4, max_node)
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check_euler(g5, max_node)
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if __name__ == "__main__":
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main()
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