Added K-Knights and Count-N-queens

algorithms/CPlusPlus/Backtracking/count-n-queens.cpp

@@ -0,0 +1,69 @@
+// Time Complexity: O(N!)
+#include <iostream>
+#include <vector>
+using namespace std;
+
+bool Check(vector<vector<int>> &arr, int row, int col)
+{
+    // Check column
+    int i{0}, j{0};
+    for (i = 0; i < row; i++)
+    {
+        if (arr[i][col] == 1)
+        {
+            return false;
+        }
+    }
+    // Diagonals
+    for (i = row, j = col; i >= 0 && j >= 0; i--, j--)
+    {
+        if (arr[i][j] == 1)
+        {
+            return false;
+        }
+    }
+    for (i = row, j = col; i >= 0 && j < arr.size(); i--, j++)
+    {
+        if (arr[i][j] == 1)
+        {
+            return false;
+        }
+    }
+    return true;
+}
+int countQueens(vector<vector<int>> &arr, int row)
+{
+    if (row >= arr.size())
+    {
+        return 1;
+    }
+
+    int count = 0;
+    for (int i = 0; i < arr.size(); i++)
+    {
+        if (Check(arr, row, i) == 1)
+        {
+            arr[row][i] = 1;
+            count += countQueens(arr, row + 1);
+            arr[row][i] = 0;
+        }
+      
+    }
+    return count;
+}
+
+void totalNQueens(int n)
+{
+    vector<vector<int>> arr(n, vector<int>(n, 0));
+    cout << countQueens(arr, 0);
+}
+
+int main(int argc, char const *argv[])
+{
+    totalNQueens(5); // Checks how many queens can be placed in a 5 x 5 board
+
+    return 0;
+}
+
+
+// Output: 10

algorithms/CPlusPlus/Backtracking/k-knights.cpp

@@ -0,0 +1,113 @@
+// Time Complexity : O(8^(n^2))
+// There are N2 Cells and for each, we have a maximum of 8 possible moves to choose from
+#include <iostream>
+#include <vector>
+#include <algorithm>
+using namespace std;
+
+void Display(vector<vector<int>> &arr)
+{
+    for (auto row : arr)
+    {
+        for (auto num : row)
+        {
+            if (num)
+                cout << "K ";
+            else
+                cout << "x ";
+        }
+        cout << endl;
+    }
+    cout << endl;
+}
+bool IsValid(vector<vector<int>> &arr, int row, int col)
+{
+    if (row >= 0 && row < arr.size() && col >= 0 && col < arr.size())
+    {
+        return true;
+    }
+    return false;
+}
+bool IsSafe(vector<vector<int>> &arr, int row, int col)
+{
+    if (IsValid(arr, row - 2, col - 1) == 1)
+    {
+        if (arr[row - 2][col - 1] == 1)
+            return false;
+    }
+    if (IsValid(arr, row - 2, col + 1) == 1)
+    {
+        if (arr[row - 2][col + 1] == 1)
+            return false;
+    }
+    if (IsValid(arr, row + 1, col + 2) == 1)
+    {
+        if (arr[row + 1][col + 2] == 1)
+            return false;
+    }
+    if (IsValid(arr, row - 1, col + 2) == 1)
+    {
+        if (arr[row - 1][col + 2] == 1)
+            return false;
+    }
+    if (IsValid(arr, row + 2, col - 1) == 1)
+    {
+        if (arr[row + 2][col - 1] == 1)
+            return false;
+    }
+    if (IsValid(arr, row + 2, col + 1) == 1)
+    {
+        if (arr[row + 2][col + 1] == 1)
+            return false;
+    }
+    if (IsValid(arr, row + 1, col - 2) == 1)
+    {
+        if (arr[row + 1][col - 2] == 1)
+            return false;
+    }
+    if (IsValid(arr, row - 1, col - 2) == 1)
+    {
+        if (arr[row - 1][col - 2] == 1)
+            return false;
+    }
+    return true;
+}
+
+void Knight(vector<vector<int>> &board, int row, int col, int knights)
+{
+    if (knights == 0) // If all knights are places than show the board
+    {
+        Display(board);
+        return;
+    }
+    if (row == board.size() - 1 && col == board.size())
+    {
+        return; // out of bounds
+    }
+    if (col == board.size())
+    {
+        Knight(board, row + 1, 0, knights); // switching rows
+        return;
+    }
+    if (IsSafe(board, row, col))
+    {
+        board[row][col] = true; // Placing the knight
+        Knight(board, row, col + 1, knights - 1);
+        board[row][col] = false; // Backtraking
+    }
+    Knight(board, row, col + 1, knights);
+}
+
+int main(int argc, char const *argv[])
+{
+    vector<vector<int>> arr =
+        {
+            {0, 0, 0, 0},
+            {0, 0, 0, 0},
+            {0, 0, 0, 0},
+            {0, 0, 0, 0}};
+    // Display(arr);
+    Knight(arr, 0, 0, 5);
+
+    return 0;
+}

algorithms/CPlusPlus/README.md

@@ -206,3 +206,5 @@
 ## Backtracking
 
 - [N-Queens Problem](Backtracking/n-queens.cpp)
+- [Count N-Queens](Backtracking/count-n-queens.cpp)
+- [K-Knights Problem](Backtracking/k-knights.cpp)