![PROGRAM
#include<stdio.h>
#include<math.h>
int board[20],count;
int main()
{
int n,i,j;
void queen(int row,int n);
print f(" - N Queens Problem Using Backtracking -");
print f("nn Enter number of Queens:");
scan f("%d",&n);
queen(1,n);
return 0;
}](https://image.slidesharecdn.com/puzzle-190304175019/85/Puzzle-in-c-program-5-320.jpg)
![void print(int n)
{
int i,j;
printf("nnSolution %d:nn",++count);
for(i=1;i<=n;++i)
printf("t%d",i);
for(i=1;i<=n;++i)
{
printf("nn%d",i);
for(j=1;j<=n;++j) //for nxn board
{
if(board[i]==j)
printf("tQ"); //queen at i,j position
else](https://image.slidesharecdn.com/puzzle-190304175019/85/Puzzle-in-c-program-6-320.jpg)
![printf("t-"); //empty slot
}
}
}
int place(int row,int column)
{
int i;
for(i=1;i<=row-1;++i)
{
if(board[i]==column)
return 0;
else
if(abs(board[i]-column)==abs(i-row))](https://image.slidesharecdn.com/puzzle-190304175019/85/Puzzle-in-c-program-7-320.jpg)
![return 1; //no conflicts
}
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);
}
}}](https://image.slidesharecdn.com/puzzle-190304175019/85/Puzzle-in-c-program-8-320.jpg)
Puzzle in c program
- 3. N QUEENS PROBLEM IN C USING BACKTRACKING • N Queens Problem is a famous puzzle in which n- queens are to be placed on a N x N chess board • No two queens are in the same row, same column or same diagonal. • Sharing the C program to find solution for N number of Queens problem using backtracking. Below animations show the solution for 8 queens problem using the backtracking.
- 5. PROGRAM #include<stdio.h> #include<math.h> int board[20],count; int main() { int n,i,j; void queen(int row,int n); print f(" - N Queens Problem Using Backtracking -"); print f("nn Enter number of Queens:"); scan f("%d",&n); queen(1,n); return 0; }
- 6. void print(int n) { int i,j; printf("nnSolution %d:nn",++count); for(i=1;i<=n;++i) printf("t%d",i); for(i=1;i<=n;++i) { printf("nn%d",i); for(j=1;j<=n;++j) //for nxn board { if(board[i]==j) printf("tQ"); //queen at i,j position else
- 7. printf("t-"); //empty slot } } } int place(int row,int column) { int i; for(i=1;i<=row-1;++i) { if(board[i]==column) return 0; else if(abs(board[i]-column)==abs(i-row))
- 8. return 1; //no conflicts } 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); } }}
- 9. OUTPUT