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N-queens.txt

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+N-Queen Problem
+Write a C program to find solutions for placing n queens in a n*n chess board, such that no two queens attack
+each other.
+Algorithm:
+Nqueen(n)
+//All solution for placing n queens in n*n chess board without attack of any two queens
+//Input: Positive integer n indicates the number of queens
+//Output: All solutions of placing n queens in n*n chess board without attack of any two queens
+k ←∞; count←0 ;
+col[k] ← 0
+while k!=0
+col[k] ←col[k] +1
+while (col[k]<=n and cannotBePlaced(k, col[1..n])
+col[k] ←col[k]+1
+if col[k]<n
+if k==n
+count ← count+1
+PRINT solution
+else
+k←k+1
+col[k] ←0
+else
+k←k-1
+return count
+Program:
+#include <stdio.h>
+#include <stdlib.h>
+int cannotBePlaced(int k,int col[ ])
+{
+int i;
+for(i=1; i<=k-1; i++) //Check whether 2 queens attack vertically, horizontally or diagonally
+if(col[k]==col[i] || (abs(i-k)==abs(col[i]-col[k])))
+return 1; //Queen k cannot be placed in row k and column col[k]
+5
+1
+2
+4
+3
+2
+3
+5
+1
+2
+4
+3
+2
+3
+Approach : Backtracking
+Efficiency : Θ(nn)
+~ 37 ~
+return 0;
+}
+int NQueen(int n)
+{
+int k=1; //Indicated queen to be placed and row number
+int count=0; //Number of possible solutions
+int i,j,col[n+1];
+col[k]=0; //Queen 1 is selected but yet to be placed in row 1 and column a[1]
+while(k!=0) //Backtrack till any one queen exists
+{
+col[k]=col[k]+1; //Place queen k in 1st column
+while(col[k]<=n && cannotBePlaced(k,col))
+col[k]=col[k]+1; //Move queen k to next column
+if(col[k]<=n) //Queen successfully placed
+{
+if(k==n) //All queens are placed
+{
+count++;
+printf("\nSolution-%d :\n",count);
+for(i=1; i<=n; i++)
+{
+for(j=1; j<=n; j++)
+if(col[i]==j)
+printf(" Q%d",i);
+else
+printf(" * ");
+printf("\n\n");
+}
+}
+else
+{
+k++; //Select next queen
+col[k]=0; //Queen k is yet to be placed
+}
+}
+else
+k--; //Backtrack and select previous queen
+}
+return count;
+}
+int main()
+{
+int n,solutions;
+printf("Enter the number of queens : ");
+scanf("%d",&n);
+solutions=NQueen(n);
+if(solutions==0)
+printf("No solution!!");
+return 0;
+}