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Author: Manasi2001

Backtracking/Sudoku.py

@@ -0,0 +1,78 @@
+'''
+Aim: Given a 9*9 sudoku board, in which some entries are filled and others are 0 
+    (0 indicates that the cell is empty), you need to find out whether the Sudoku 
+    puzzle can be solved or not i.e. return true or false.
+    
+'''
+
+# checking if move could be made or not
+def isSafeToPut(i,j,option,board,n):
+    for k in range(n):
+        if board[k][j]==option or board[i][k]==option:
+            return False
+        
+    # finding the dimensions of the 3 X 3 box 
+    starti=(i//3)*3
+    startj=(j//3)*3
+
+    for p in range(starti,starti+3):
+        for q in range(startj,startj+3):
+            if board[p][q]==option:
+                return False
+    
+    return True
+
+# applying basic rules of the game to find the result
+def sudokuSolver(i,j,board,n):
+    if i==n:
+        return True
+    
+    if j==n:
+        return sudokuSolver(i+1,0,board,n)
+
+    if board[i][j]!=0:
+        return sudokuSolver(i,j+1,board,n)
+    
+    # checking if it's safe to put a number at a place
+    for option in range(1,10):
+        if isSafeToPut(i,j,option,board,n):
+            board[i][j]=option
+            canWeMoveFwd=sudokuSolver(i,j+1,board,n)
+            if canWeMoveFwd is True:
+                return True
+            board[i][j]=0
+
+    return False
+
+# getting the input
+board = [[ int(ele) for ele in input().split() ]for i in range(9)]
+ans = sudokuSolver(0,0,board,9)
+
+# printing out the results
+print(ans)
+
+'''
+
+Sample Input:   
+ 9 0 0 0 2 0 7 5 0 
+ 6 0 0 0 5 0 0 4 0 
+ 0 2 0 4 0 0 0 1 0 
+ 2 0 8 0 0 0 0 0 0 
+ 0 7 0 5 0 9 0 6 0 
+ 0 0 0 0 0 0 4 0 1 
+ 0 1 0 0 0 5 0 8 0 
+ 0 9 0 0 7 0 0 0 4 
+ 0 8 2 0 4 0 0 0 6
+ 
+Sample Output:  
+True
+
+Explanation:
+According to the rules of sudoku, this can be solved.
+
+COMPLEXITY:
+    
+     Time Complexity = O(9^(N*N))
+     Space complexity = O(N)
+     
+'''