Merge pull request #209 from jerryderry/backtracking-python

backtracking 8 queens problem in python

python/39_backtracking/backtracking.py

@@ -0,0 +1,25 @@
+"""
+    Author: Wenru Dong
+"""
+
+from typing import List
+
+def eight_queens() -> None:
+    solutions = []
+
+    def backtracking(queens_at_column: List[int], index_sums: List[int], index_diffs: List[int]) -> None:
+        row = len(queens_at_column)
+        if row == 8:
+            solutions.append(queens_at_column)
+            return
+        for col in range(8):
+            if col in queens_at_column or row + col in index_sums or row - col in index_diffs: continue
+            backtracking(queens_at_column + [col], index_sums + [row + col], index_diffs + [row - col])
+    
+    backtracking([], [], [])
+    print(*(" " + " ".join("*" * i + "Q" + "*" * (8 - i - 1) + "\n" for i in solution) for solution in solutions), sep="\n")
+
+
+if __name__ == "__main__":
+
+    eight_queens()