Add follow up with matrix traversal

Author: yangshun

utilities/python/graph_dfs.py

@@ -17,6 +17,28 @@ def dfs(i, j):
         for j in range(cols):
             dfs(i, j)
 
+# Follow up:
+# 1) Diagonal cells are considered neighbors
+# 2) View the matrix like Earth, right boundary is adjacent to the left boundary, top adjacent to left, etc.
+def graph_dfs_diagonals(matrix):
+    rows, cols = len(matrix), len(matrix[0])
+    visited = set()
+    # Change 1: Add 4 more diagonal directions.
+    directions = ((0, 1), (0, -1), (1, 0), (-1, 0), (-1, -1), (1, 1), (1, -1), (-1, 1))
+    def dfs(i, j):
+        if (i, j) in visited:
+            return
+        print(matrix[i][j])
+        visited.add((i, j))
+        for direction in directions:
+            # Change 2: No more boundary, use modulo to allow traversal that exceed boundaries to wrap around.
+            next_i, next_j = (i + direction[0] + rows) % rows, (j + direction[1] + cols) % cols
+            dfs(next_i, next_j)
+
+    for i in range(rows):
+        for j in range(cols):
+            dfs(i, j)
+
 graph_dfs([
     [1, 2, 3, 4],
     [5, 6, 7, 8],