Add backtracking/nqueen_print_all_solutions.cpp (#622)

* Add files via upload

* Rename Backtracking/NQueen-PrintAllSolutions.cpp to backtracking/nqueen_print_all_solutions.cpp

* clang-format -i -style="{IndentWidth: 4}" *.cpp

* endl --> std::endl

Co-authored-by: Christian Clauss <cclauss@me.com>

backtracking/nqueen_print_all_solutions.cpp

@@ -0,0 +1,50 @@
+#include <iostream>
+#define n 4
+
+void PrintSol(int Board[n][n]) {
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < n; j++) {
+            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
+    for (int i = 0; i < col; i++) {
+        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;
+    }
+    for (int i = 0; i < n; i++) {
+        if (CanIMove(Board, i, col)) {
+            Board[i][col] = 1;
+            NQueenSol(Board, col + 1);
+            Board[i][col] = 0;
+        }
+    }
+}
+
+int main() {
+    int Board[n][n] = {0};
+    NQueenSol(Board, 0);
+}