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C Program To Implement N Queens Problem.

The N Queens puzzle is the problem of placing eight chess queens on an n×n chessboard so that no two queens threaten each other. Thus, a solution requires that no two queens share the same row, column, or diagonal. The number of rotationally and reflectively distinct solutions for the first few N are 1, 0, 0, 2, 10, 4, 40, 92,...

Example: The graphical demonstrations for the 8 queens problem: 

N Queen's Problem N Queen's Problem

Source code of N Queens Problem:
Method 1:
#include<stdio.h>
#include<math.h>

int board[20],count;

int main(){
int n,i,j;
void queen(int row,int n);

printf("**** N Queens Problem Solved Using Backtracking ****");

printf("\n\n\tEnter The Number Of Queens: ");
scanf("%d",&n);
queen(1,n);

printf("\n\n\nTotal Solutions = %d\n\n",count);
return 0;
}

//function for printing the solution
void print(int n) {

int i,j;
printf("\n\nSolution %d: ",++count);

for(i=1;i<=n;++i){
printf("\n\n");  

for(j=1;j<=n;++j) { //for nxn board

if(board[i]==j)
printf("\tQ"); //queen at i,j position

else
printf("\t."); //empty slot
}}}

/* funtion to check conflicts if no conflict for desired postion returns 1 otherwise returns 0 */

int place(int row,int column) {
int i;

for(i=1;i<=row-1;++i){
//checking column and digonal conflicts

if(board[i]==column)
return 0;

else
if(abs(board[i]-column)==abs(i-row))
return 0;
}

return 1; //no conflicts
}

//function to check for proper positioning of queen
void queen(int row,int n) {
int column;

for(column=1;column<=n;++column) {
if(place(row,column)) {
board[row]=column; //no conflicts so place queen

if(row==n) //dead end
print(n); //printing the board configuration

else //try queen with next position
queen(row+1,n);
}}}

Method 2:
#include<stdio.h>
#include<conio.h>
#include<math.h>

int a[30],count=0;
int place(int pos) {
int i;

for(i=1;i<pos;i++) {
if((a[i]==a[pos])||((abs(a[i]-a[pos])==abs(i-pos))))
return 0;
}

return 1;
}

void print_sol(int n) {
int i,j;

count++;
printf("\n\nSolution %d: ",count);

for(i=1;i<=n;i++) {
printf("\n\n");

for(j=1;j<=n;j++) {

if(a[i]==j)
printf("\tQ");

else
printf("\t.");
}}}

void queen(int n) {
int k=1;
a[k]=0;

while(k!=0){
a[k]=a[k]+1;

while((a[k]<=n)&&!place(k))
a[k]++;

if(a[k]<=n) {

if(k==n)
print_sol(n);

else {
k++;

a[k]=0;
}}
else
k--;
}}

void main() {
int i,n;

printf("***** N Queens Problem *****");

printf("\n\nEnter The Number Of Queens: ");
scanf("%d",&n);
queen(n);

printf("\n\nTotal Solutions = %d ",count);
getch();
}

Method 3:
#include <stdio.h>

int is_safe(int rows[5], int x, int y)  {
int i;

if (y == 0)
return 1;

for (i=0; i < y; ++i) {
if (rows[i] == x || rows[i] == x + y - i || rows[i] == x - y +i)
return 0;
}

return 1;
}

void putboard(int rows[5]){
static int s = 0;
int x, y;

printf("\nSolution #%d:\n-----------------------\n", ++s);

for (y=0; y < 5; ++y) {
for (x=0; x < 5; ++x)
printf(x == rows[y] ? "| Q " : "|   ");
printf("|\n-----------------------\n");
}}

void queens_helper(int rows[5], int y) {
int x;

for (x=0; x < 5; ++x) {
if (is_safe(rows, x, y)) {
rows[y] = x;

if (y == 4)
putboard(rows);

else
queens_helper(rows, y+1);
}}}

int main() {
printf("**** N Queens Problem Solved Using Backtracking Depth First Search (DFS) ****\n");

int rows[5];
queens_helper(rows, 0);
return 0;
}
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