faster sudoku solver

backtracking/sudoku_faster.py

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+import sys
+sys.setrecursionlimit(10**6) 
+
+
+grid, empty = [],[]
+row, col, table = [{x:set() for x in range(9)} for x in range(3)]
+
+def findemptycells():       # Finds all the empty cells and adds it for later
+    for x in range(9):
+        for y in range(9):
+            if grid[x][y] == 0:
+                empty.append((x,y))
+            else:
+                row[x].add(grid[x][y])
+                col[y].add(grid[x][y])
+                a,b = x//3,y//3
+                table[a*3+b].add(grid[x][y])
+
+
+def solver(i=0, j=0, n=0):
+    x,y = (-1,-1) if n>=len(empty) else empty[n]
+    if x == -1:return True
+
+    for z in range(1,10):
+        temp = (x//3)*3+y//3
+        if z not in row[x] and z not in col[y] and z not in table[temp]:
+            grid[x][y] = z
+            row[x].add(z)       # the new value is added to that specific row
+            col[y].add(z)       # the new value is added to that specific column
+            table[temp].add(z)       # the new value is added to that mini table
+
+            if solver(x,y,n+1):return True
+
+            grid[x][y] = 0
+            row[x].remove(z)       # the new value is removed from that specific row
+            col[y].remove(z)       # the new value is removed from that specific column
+            table[temp].remove(z)       # the new value is removed from that specific mini table
+
+    return False 
+
+
+
+#Testing
+
+values = ['800000000', '003600000', '070090200', '050007000', '000045700', '000100030', '001000068', '008500010', '090000400'] # World's hardest sudoku problem
+for i in values:
+    grid.append([int(x) for x in i])
+
+findemptycells()
+solver()        # recurses till a solution is found otherwise returns the same table
+
+
+[print(*x,sep="") for x in grid]
+
+
+# Output:
+#
+# 812753649
+# 943682175
+# 675491283
+# 154237896
+# 369845721
+# 287169534
+# 521974368
+# 438526917
+# 796318452
+#
+# Run time : 0.117s