# Source code for tryalgo.dfs

```
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""\
Depth-first search - DFS
jill-jênn vie et christoph durr - 2015-2019
"""
# snip{ dfs-recursive
[docs]def dfs_recursive(graph, node, seen):
"""DFS, detect connected component, recursive implementation
:param graph: directed graph in listlist or listdict format
:param int node: to start graph exploration
:param boolean-table seen: will be set true for the connected component
containing node.
:complexity: `O(|V|+|E|)`
"""
seen[node] = True
for neighbor in graph[node]:
if not seen[neighbor]:
dfs_recursive(graph, neighbor, seen)
# snip}
# snip{ dfs-iterative
[docs]def dfs_iterative(graph, start, seen):
"""DFS, detect connected component, iterative implementation
:param graph: directed graph in listlist or listdict format
:param int node: to start graph exploration
:param boolean-table seen: will be set true for the connected component
containing node.
:complexity: `O(|V|+|E|)`
"""
seen[start] = True
to_visit = [start]
while to_visit:
node = to_visit.pop()
for neighbor in graph[node]:
if not seen[neighbor]:
seen[neighbor] = True
to_visit.append(neighbor)
# snip}
# snip{ dfs-tree
[docs]def dfs_tree(graph, start=0):
"""DFS, build DFS tree in unweighted graph
:param graph: directed graph in listlist or listdict format
:param int start: source vertex
:returns: precedence table
:complexity: `O(|V|+|E|)`
"""
to_visit = [start]
prec = [None] * len(graph)
while to_visit: # an empty queue equals False
node = to_visit.pop()
for neighbor in graph[node]:
if prec[neighbor] is None:
prec[neighbor] = node
to_visit.append(neighbor)
return prec
# snip}
[docs]def dfs_grid_recursive(grid, i, j, mark='X', free='.'):
"""DFS on a grid, mark connected component, iterative version
:param grid: matrix, 4-neighborhood
:param i,j: cell in this matrix, start of DFS exploration
:param free: symbol for walkable cells
:param mark: symbol to overwrite visited vertices
:complexity: linear
"""
height = len(grid)
width = len(grid[0])
grid[i][j] = mark # mark path
for ni, nj in [(i + 1, j), (i, j + 1),
(i - 1, j), (i, j - 1)]:
if 0 <= ni < height and 0 <= nj < width:
if grid[ni][nj] == free:
dfs_grid(grid, ni, nj)
# snip{ dfs-grid
[docs]def dfs_grid(grid, i, j, mark='X', free='.'):
"""DFS on a grid, mark connected component, iterative version
:param grid: matrix, 4-neighborhood
:param i,j: cell in this matrix, start of DFS exploration
:param free: symbol for walkable cells
:param mark: symbol to overwrite visited vertices
:complexity: linear
"""
height = len(grid)
width = len(grid[0])
to_visit = [(i, j)]
grid[i][j] = mark
while to_visit:
i1, j1 = to_visit.pop()
for i2, j2 in [(i1 + 1, j1), (i1, j1 + 1),
(i1 - 1, j1), (i1, j1 - 1)]:
if (0 <= i2 < height and 0 <= j2 < width and
grid[i2][j2] == free):
grid[i2][j2] = mark # mark path
to_visit.append((i2, j2))
# snip}
# pylint: disable=too-many-nested-blocks, no-else-return
[docs]def find_cycle(graph):
"""find a cycle in an undirected graph
:param graph: undirected graph in listlist or listdict format
:returns: list of vertices in a cycle or None
:complexity: `O(|V|+|E|)`
"""
n = len(graph)
prec = [None] * n # ancestor marks for visited vertices
for u in range(n):
if prec[u] is None: # unvisited vertex
S = [u] # start new DFS
prec[u] = u # mark root (not necessary for this algorithm)
while S:
u = S.pop()
for v in graph[u]: # for all neighbors
if v != prec[u]: # except arcs to father in DFS tree
if prec[v] is not None:
cycle = [v, u] # cycle found, (u,v) back edge
while u not in (prec[v], prec[u]): # directed
u = prec[u] # climb up the tree
cycle.append(u)
return cycle
else:
prec[v] = u # v is new vertex in tree
S.append(v)
return None
```