rename Backtracking -> backtracking (#654)

backtracking/n_queens.cpp

@@ -0,0 +1,77 @@
+#include <iostream>
+#define N 4
+using namespace std;
+
+void printSolution(int board[N][N])
+{
+    cout << "\n";
+    for (int i = 0; i < N; i++)
+    {
+        for (int j = 0; j < N; j++)
+            cout << "" << board[i][j];
+        cout << "\n";
+    }
+}
+
+bool isSafe(int board[N][N], int row, int col)
+{
+    int i, j;
+
+    /* Check this row on left side */
+    for (i = 0; i < col; i++)
+        if (board[row][i])
+            return false;
+
+    /* Check upper diagonal on left side */
+    for (i = row, j = col; i >= 0 && j >= 0; i--, j--)
+        if (board[i][j])
+            return false;
+
+    /* Check lower diagonal on left side */
+    for (i = row, j = col; j >= 0 && i < N; i++, j--)
+        if (board[i][j])
+            return false;
+
+    return true;
+}
+
+void solveNQ(int board[N][N], int col)
+{
+
+    if (col >= N)
+    {
+        printSolution(board);
+        return;
+    }
+
+    /* Consider this column and try placing
+       this queen in all rows one by one */
+    for (int i = 0; i < N; i++)
+    {
+        /* Check if queen can be placed on
+          board[i][col] */
+        if (isSafe(board, i, col))
+        {
+            /* Place this queen in board[i][col] */
+            //            cout<<"\n"<<col<<"can place"<<i;
+            board[i][col] = 1;
+
+            /* recur to place rest of the queens */
+            solveNQ(board, col + 1);
+
+            board[i][col] = 0; // BACKTRACK
+        }
+    }
+}
+
+int main()
+{
+
+    int board[N][N] = {{0, 0, 0, 0},
+                       {0, 0, 0, 0},
+                       {0, 0, 0, 0},
+                       {0, 0, 0, 0}};
+
+    solveNQ(board, 0);
+    return 0;
+}