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def create_possibilities(grid):
    """Create a dictionary of possible values for each cell."""
    possibilities = {}
    for row in range(9):
        for col in range(9):
            if grid[row][col] == 0:
                possibilities[(row, col)] = set(range(1, 10))  # All numbers are possible initially
            else:
                possibilities[(row, col)] = {grid[row][col]}  # Already filled cell
    return possibilities


def eliminate(possibilities, grid):
    """Eliminate impossible numbers from possibilities."""
    for row in range(9):
        for col in range(9):
            if len(possibilities[(row, col)]) == 1:  # If only one value, eliminate it from peers
                number = next(iter(possibilities[(row, col)]))
                # Eliminate from row, column, and 3x3 subgrid
                for i in range(9):
                    if (row, i) != (row, col):
                        possibilities[(row, i)].discard(number)  # Row
                    if (i, col) != (row, col):
                        possibilities[(i, col)].discard(number)  # Column
                r, c = (row // 3) * 3, (col // 3) * 3
                for i in range(3):
                    for j in range(3):
                        if (r + i, c + j) != (row, col):
                            possibilities[(r + i, c + j)].discard(number)  # Subgrid


def solve_with_constraints(grid):
    """Solve Sudoku using Constraint Propagation."""
    possibilities = create_possibilities(grid)
    while True:
        prev_state = {k: set(v) for k, v in possibilities.items()}  # Copy current state
        eliminate(possibilities, grid)
        # If no progress is made, break
        if all(prev_state[k] == possibilities[k] for k in possibilities):
            break

    # Fill the grid with determined values
    for row in range(9):
        for col in range(9):
            if len(possibilities[(row, col)]) == 1:
                grid[row][col] = next(iter(possibilities[(row, col)]))

    # If some cells still have multiple possibilities, return False
    if any(len(v) > 1 for v in possibilities.values()):
        return False
    return True