Merge pull request BeeBombshell#118 from glacias07/new_branch

Added backtracking solutions for knights_tour and n_queens

Author: BeeBombshell

Backtracking/Knights_tour.py

@@ -0,0 +1,23 @@
+def knights_tour(n, row, col):
+    visited = [[False]*n for i in range(n)]
+    res = []
+    def path_gen(path,r,c,visited,step):
+        if r < 0 or c < 0 or r >= n or c >= n or visited[r][c]:
+            return
+        if step == n*n:
+            res.append(path + f'({r},{c})')
+            return   
+        visited[r][c] = True
+        path_gen(path + f'({r},{c}) ', r - 2, c + 1, visited, step+1)
+        path_gen(path + f'({r},{c}) ', r - 2, c - 1, visited, step+1)
+        path_gen(path + f'({r},{c}) ', r - 1, c + 2, visited, step+1)
+        path_gen(path + f'({r},{c}) ', r - 1, c - 2, visited, step+1)
+        path_gen(path + f'({r},{c}) ', r + 2, c + 1, visited, step+1)
+        path_gen(path + f'({r},{c}) ', r + 2, c - 1, visited, step+1)
+        path_gen(path + f'({r},{c}) ', r + 1, c + 2, visited, step+1)
+        path_gen(path + f'({r},{c}) ', r + 1, c - 2, visited, step+1)
+        visited[r][c] = False
+    path_gen('', row, col,visited,1)
+    return res
+
+print(knights_tour(5, 2, 2))

Backtracking/N_queens.py

@@ -0,0 +1,26 @@
+def n_queens(n):
+    res = []
+    board = [['.']*n for i in range(n)]
+    cols = set()
+    pdiags = set()
+    ndiags = set()
+    def gen(r):
+        if r == n:
+            res.append([''.join(row) for row in board])
+            return
+        for c in range(n):
+            if c in cols or r+c in pdiags or r-c in ndiags:
+                continue
+            board[r][c] = 'Q'
+            cols.add(c)
+            pdiags.add(r+c)
+            ndiags.add(r-c)
+            gen(r + 1)
+            board[r][c] = '.'
+            cols.remove(c)
+            pdiags.remove(r+c)
+            ndiags.remove(r-c)
+    gen(0)
+    return res
+
+print(n_queens(8))