Merge pull request #741 from deadshotsb/master

Create n_queens_all_solution_optimised.cpp

backtracking/n_queens_all_solution_optimised.cpp

@@ -0,0 +1,75 @@
+#include <iostream>
+#define n 4
+#define inc_loop(var, start, stop) for (int var=start; var <= stop; var++)
+#define dec_loop(var, start, stop) for (int var=start; var >= stop; var--)
+void PrintSol(int Board[n][n]) {
+    inc_loop(i, 0, n-1) {
+        inc_loop(j, 0, n-1)
+            std::cout << Board[i][j] << " ";
+        std::cout << std::endl;
+    }
+    std::cout << std::endl;
+    if (n%2 == 0 || (n%2 == 1 && Board[n/2+1][0] != 1)) {
+        inc_loop(i, 0, n-1) {
+            dec_loop(j, n-1, 0)
+                std::cout << Board[i][j] << " ";
+            std::cout << std::endl;
+        }
+        std::cout << std::endl;
+    }
+}
+
+bool CanIMove(int Board[n][n], int row, int col) {
+    /// check in the row
+    inc_loop(i, 0, col-1) {
+        if (Board[row][i] == 1)
+            return false;
+    }
+    /// check the first diagonal
+    for (int i = row, j = col; i >= 0 && j >= 0; i--, j--) {
+        if (Board[i][j] == 1)
+            return false;
+    }
+    /// check the second diagonal
+    for (int i = row, j = col; i <= n - 1 && j >= 0; i++, j--) {
+        if (Board[i][j] == 1)
+            return false;
+    }
+    return true;
+}
+
+void NQueenSol(int Board[n][n], int col) {
+    if (col >= n) {
+        PrintSol(Board);
+        return;
+    }
+    inc_loop(i, 0, n-1) {
+        if (CanIMove(Board, i, col)) {
+            Board[i][col] = 1;
+            NQueenSol(Board, col + 1);
+            Board[i][col] = 0;
+        }
+    }
+}
+
+int main() {
+    int Board[n][n] = {0};
+    if (n%2 == 0) {
+        inc_loop(i, 0, n/2-1) {
+            if (CanIMove(Board, i, 0)) {
+                Board[i][0] = 1;
+                NQueenSol(Board, 1);
+                Board[i][0] = 0;
+            }
+        }
+    } else {
+        inc_loop(i, 0, n/2) {
+            if (CanIMove(Board, i, 0)) {
+                Board[i][0] = 1;
+                NQueenSol(Board, 1);
+                Board[i][0] = 0;
+            }
+        }
+    }
+    return 0;
+}