N-Queens

NeetCode/n-queens/step1.py

@@ -0,0 +1,66 @@
+"""
+ダメだったやつ
+"""
+
+class Solution:
+    def solveNQueens(self, n: int) -> List[List[str]]:
+        board = [[None] * n for _ in range(n)]
+
+        def mark_vertical(w, mark):
+            for i in range(n):
+                if not board[i][w]:
+                    board[i][w] = mark
+
+        def mark_horizontal(r, mark):
+            for i in range(n):
+                if not board[r][i]:
+                    board[r][i] = mark
+
+        def mark_diagonal(r, w, mark):
+            for i in range(-n, n):
+                cur_r = r + i
+                cur_w = w + i
+                if (cur_r not in range(n) or
+                    cur_w not in range(n) or
+                    board[cur_r][cur_w]
+                ): continue
+                board[cur_r][cur_w] = mark
+            for i in range(-n, n):
+                cur_r = r + i
+                cur_w = w - i
+                if (cur_r not in range(n) or
+                    cur_w not in range(n) or
+                    board[cur_r][cur_w]
+                ): continue
+                board[cur_r][cur_w] = mark
+
+        def mark_attack_tiles(r, w, mark):
+            mark_vertical(w, mark)
+            mark_horizontal(r, mark)
+            mark_diagonal(r, w, mark)
+
+        def fill_none():
+            for i in range(n):
+                for j in range(n):
+                    if not board[i][j]:
+                        board[i][j] = "."
+
+        res = []
+
+        def append_queen_paterns():
+            for i in range(n):
+                for j in range(n):
+                    if not board[i][j]:
+                        board[i][j] = "Q"
+                        mark_attack_tiles(i, j, ".")
+                        append_queen_paterns()
+                        board[i][j] = None
+                        mark_attack_tiles(i, j, None)
+            fill_none()
+            formatted_board = []
+            for row in board:
+                formatted_board.append("".join(row))
+            res.append(formatted_board)
+
+        append_queen_paterns()
+        return res

NeetCode/n-queens/step2.py

@@ -0,0 +1,39 @@
+"""
+左上から右下への斜めは和が一定
+    colが増えたらrowが減るから
+左下から右上への斜めは差が一定
+    colが増えたらrowも増えるから
+"""
+
+# time: < n^n
+# space: n^2
+class Solution:
+    def solveNQueens(self, n: int) -> List[List[str]]:
+        board = [["."] * n for _ in range(n)]
+        res = []
+        ng_col = set()
+        ng_pros_diag = set()
+        ng_minus_diag = set()
+
+        def backtrack(row):
+            if row == n:
+                res.append(["".join(row) for row in board])
+                return
+
+            for col in range(n):
+                if col in ng_col or row + col in ng_pros_diag or row - col in ng_minus_diag:
+                    continue
+                board[row][col] = "Q"
+                ng_col.add(col)
+                ng_pros_diag.add(row + col)
+                ng_minus_diag.add(row - col)
+
+                backtrack(row + 1)
+
+                board[row][col] = "."
+                ng_col.remove(col)
+                ng_pros_diag.remove(row + col)
+                ng_minus_diag.remove(row - col)
+
+        backtrack(0)
+        return res