def solve_recursively(sudoku_possible_values):
# Check if we ran into a contradiction:
if contradiction(sudoku_possible_values):
return None;
else:
# Propagate
propagate(sudoku_possible_values, k);
# Check for contradictions
if contradiction(sudoku_possible_values):
return None;
# Find a cell that is still uncertain
uncertain_cell = find_uncertain_cell(sudoku_possible_values);
if uncertain_cell == None:
return sudoku_possible_values;
else:
i,j = uncertain_cell;
# Recurse on the different values for cell i,j
possibilities = sudoku_possible_values[i][j];
for poss in possibilities:
sudoku_possible_values_copy = deep_copy(sudoku_possible_values);
sudoku_possible_values_copy[i][j] = [poss];
answer = solve_recursively(sudoku_possible_values_copy);
if answer != None:
return answer;
# If no solution was found in the recursion, conclude there is no solution
return None;
def solve_recursively(sudoku_possible_values):
"""
This function first checks whether the sudoku_possible_values includes a contradiction,
using the function contradiction()
"""
# Check if we ran into a contradiction:
"""
This function just checks if stuff is valid
"""
if contradiction(sudoku_possible_values):
return None
else:
# Propagate
sudoku_possible_values = propagate(sudoku_possible_values, k)
# Check for contradictions *again*
if contradiction(sudoku_possible_values):
return None
# Find a cell that is still uncertain (?)
"""
this function determines whether the possible values matrix still has entries with len > 1
if this is not the case, and given that the matrix has no contradictions, we return the sudoku_possible_values
otherwise, we recurse on the different values for cell i,j in the matrix
"""
uncertain_cell = find_uncertain_cell(sudoku_possible_values)
if uncertain_cell == None:
return sudoku_possible_values
else:
i, j = uncertain_cell
# Recurse on the different values for cell i,j
possibilities = sudoku_possible_values[i][j]
for poss in possibilities:
sudoku_possible_values_copy = deep_copy(
sudoku_possible_values)
sudoku_possible_values_copy[i][j] = [poss]
answer = solve_recursively(sudoku_possible_values_copy)
if answer != None:
return answer
# If no solution was found in the recursion, conclude there is no solution
return None