#### Question:

Hi! I am designing a game in C. The objective of the game is to arrange numbers in order

____7________8________4

____1________6________3

____2________5________0

by swapping them with 0

For any possible combination of these numbers…(i.e., arranging them in different possible combinations)..can we get answer…..(i.e., arrange them in order).

is it possible…..?

#### Answer:

It is definitely possible to solve such puzzles using the following logic:

Each number (let’s say x) would either be in it’s correct position or in a wrong position. If it is in it’s correct position, there is no problem. If not, some other number (let’s say y) should be in that position, and that would be the wrong position for that number. So, we can swap y with 0 ensuring that 0 comes to the right position for x. Then we can swap x with 0. If we repeat this in order (with x ranging from 1 to 8), the problem will be automatically solved!

The program for this is given below. Of course, I have used the brute force method, leaving ample scope for optimization. Any comments about how this may be optimized?

/* * number_swapper_game.c * * This program implements a simple game where the user enters a 3x3 grid * of numbers from 0 to 8, and the compute should arrange them from 1 to 9 * by swapping a number with 0 in each move. * * (c) 2008, Nagesh Rao, CyberPlus Infotech Pvt. Ltd. * */ #include <stdio.h> #include <stdlib.h> #include <string.h> int ok(int grid[3][3]); int solve(int grid[3][3]); int convert_to_position(int i, int j); int get_position(int number, int grid[3][3]); void swap(int position1, int position2, int grid[3][3]); void display_grid(int grid[3][3]); int main() { int grid[3][3]; int swaps; int i,j; do { printf("Enter the numbers (0-8) in the grid rowwise:"); for (i=0; i<3; i++) { for (j=0; j<3; j++) { scanf("%d",&grid[i][j]); } } if (!ok(grid)) printf("Invalid input!\n"); } while (!ok(grid)); swaps = solve(grid); printf("Solution obtained after %d swaps!\n",swaps); exit(0); } /* * This function checks whether the given grid contains all digits from 0-8 * and returns true if ok and false otherwise. * * The logic here is to put a "1" in a string at the slot belonging to a * digit and finally verifying that all the string contains 9 "1"s. * */ int ok(int grid[3][3]) { char pattern[10] = {0}; int i,j; for (i=0; i<3; i++) { for (j=0; j<3; j++) { if (grid[i][j]>=0 && grid[i][j]<=8) pattern[convert_to_position(i,j)] = '1'; } } return strncmp(pattern,"111111111",9) == 0; } /* * This function solves the problem and arranges the numbers in the right order * * The logic is as follows: * 1. For each number from 1 to 8, check whether it is in the right position * 2. If not, find out the number in the right place and swap that with 0 * This ensures that the number at the right place is now 0. * 3. Swap the current number with the 0. * This ensures that the current number has gone to its right place. * * The function displays the grid after every swap and returns the number * of swaps. */ int solve(int grid[3][3]) { int pos; int number; int swaps=0; for (pos=0; pos<8; pos++) { number = pos+1; /* This is the number we are analyzing */ if (get_position(number,grid) != pos) { /* Number is not in the correct position */ /* Swap number in correct position with 0 */ swap(pos, get_position(0,grid), grid); display_grid(grid); swaps++; /* Swap correct number with the 0 in the correct position */ swap(get_position(number,grid), pos, grid); display_grid(grid); swaps++; } } return swaps; } /* * This function accepts the row number (i) and column number (j) * and returns the corresponding position from 0 to 8. */ int convert_to_position(int i, int j) { return 3*i+j; } /* * This function returns a 0-based position of the given number within the * grid. * * Since validation has already taken place earlier, we do not have to * consider the case of the number not being present. */ int get_position(int number, int grid[3][3]) { int i,j; for (i=0; i<3; i++) { for (j=0; j<3; j++) { if (grid[i][j] == number) return convert_to_position(i,j); } } return 0; /* Will never happen, given here to eliminate warning! */ } /* * This function swaps two cells within the grid. * The inputs are the sequential positions of the cell. */ void swap(int position1, int position2, int grid[3][3]) { int row1, col1, row2, col2; int temp; row1 = position1/3; col1 = position1%3; row2 = position2/3; col2 = position2%3; temp = grid[row1][col1]; grid[row1][col1] = grid[row2][col2]; grid[row2][col2] = temp; } /* * This function displays the grid contents */ void display_grid(int grid[3][3]) { int i,j; for (i=0; i<3; i++) { for (j=0; j<3; j++) { printf("%3d",grid[i][j]); } printf("\n"); } printf("\n"); }

This is the output obtained on my system:

Enter the numbers (0-8) in the grid rowwise:7 8 4 1 6 3 2 5 0 0 8 4 1 6 3 2 5 7 1 8 4 0 6 3 2 5 7 1 0 4 8 6 3 2 5 7 1 2 4 8 6 3 0 5 7 1 2 0 8 6 3 4 5 7 1 2 3 8 6 0 4 5 7 1 2 3 0 6 8 4 5 7 1 2 3 4 6 8 0 5 7 1 2 3 4 0 8 6 5 7 1 2 3 4 5 8 6 0 7 1 2 3 4 5 0 6 8 7 1 2 3 4 5 6 0 8 7 1 2 3 4 5 6 0 8 7 1 2 3 4 5 6 7 8 0 Solution obtained after 14 swaps!