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Program to detect cycles in 2D grid in Python
Suppose we have one 2D array of characters called grid of size m x n. We have to check whether we can detect a cycle inside it or not. Here a cycle is a path of length 4 or more in the grid that starts and ends at the same position. We can move in four directions (up, down, left, or right), if it has the same value of the current cell, and we cannot revisit some cell.
So, if the input is like
| m | m | m | p |
| m | k | m | m |
| m | m | s | m |
| f | t | m | m |
then the output will be True, because the green cells are forming cycle.
To solve this, we will follow these steps −
WHITE := 0, GRAY := 1, BLACK := 2
R := row count of grid
C := column count of grid
color := an empty map, whose default value is 0
Define a function dfs() . This will take r, c, pr:= -1,pc:= -1
color[r,c] := GRAY
for each pair (x,y) in di, do
(nr,nc) := (r+x,c+y)
if 0 <= nr < R and 0 <= nc < C and grid[r, c] is same as grid[nr, nc] and (nr, nc) is not same as (pr, pc), then
if color[nr,nc] is same as WHITE, then
if dfs(nr,nc,r,c) is true, then
return True
otherwise when color[nr,nc] is same as GRAY, then
return True
color[r,c] := BLACK
return False
From the main method, do the following
for r in range 0 to R - 1, do
for c in range 0 to C - 1, do
if color[r,c] is same as WHITE, then
if dfs(r,c) is true, then
return True
return False
Example
Let us see the following implementation to get better understanding
from collections import defaultdict di = [(0,1),(1,0),(0,-1),(-1,0)] def solve(grid): WHITE,GRAY,BLACK = 0 ,1 ,2 R,C = len(grid),len(grid[0]) color = defaultdict(int) def dfs(r,c,pr=-1,pc=-1): color[r,c] = GRAY for x,y in di: nr,nc = r+x,c+y if (0<=nr<R and 0<=nc<C and grid[r][c] == grid[nr][nc] and (nr,nc)!=(pr,pc)): if color[nr,nc]==WHITE: if dfs(nr,nc,r,c): return True elif color[nr,nc] == GRAY: return True color[r,c] = BLACK return False for r in range(R): for c in range(C): if color[r,c] == WHITE: if dfs(r,c): return True return False matrix = [["m","m","m","p"],["m","k","m","m"],["m","m","s","m"],["f","m","m","m"]] print(solve(matrix))
Input
7, [5,1,4,3]
Output
True
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