Check if a king can move a valid move or not when N nights are there in a modified chessboard

Given an infinite chessboard with the same rules as that of chess. Also given are N knights coordinates on the infinite chessboard(-10^9 <= x, y <= 10^9) and the king’s coordinate, the task is to check if the King is checkmate or not.

Examples:

Input: a[] = { {1, 0}, {0, 2}, {2, 5}, {4, 4}, {5, 0}, {6, 2} } king -> {3, 2}
Output: Yes
The king cannot make any move as it has been check mate.

Input: a[] = { {1, 1} } king -> {3, 4}
Output: No
The king can make valid moves.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approah: The knight’s move is unusual among chess pieces. It moves to a square that is two squares away horizontally and one square vertically, or two squares vertically and one square horizontally. The complete move, therefore, looks like the letter “L” in every shape possible(8 possible moves). Hence, use a hash map of pairs to mark all possible coordinates where the knight can move. If the King cannot move to any of its nearby 8 coordinates i.e., if the coordinate is hashed by a knight’s move, then its a “checkmate”.

Below is the implementation of the above approach.

C++

 // C++ program for checking if a king // can move a valid move or not when // N nights are there in a modified chessboard #include using namespace std; bool checkCheckMate(pair a[], int n, int kx, int ky) {        // Pair of hash to mark the coordinates     map, int> mpp;        // iterate for Given N knights     for (int i = 0; i < n; i++) {         int x = a[i].first;         int y = a[i].second;            // mark all the "L" shaped coordinates         // that can be reached by a Knight            // initial position         mpp[{ x, y }] = 1;            // 1-st move         mpp[{ x - 2, y + 1 }] = 1;            // 2-nd move         mpp[{ x - 2, y - 1 }] = 1;            // 3-rd move         mpp[{ x + 1, y + 2 }] = 1;            // 4-th move         mpp[{ x + 1, y - 2 }] = 1;            // 5-th move         mpp[{ x - 1, y + 2 }] = 1;            // 6-th move         mpp[{ x + 2, y + 1 }] = 1;            // 7-th move         mpp[{ x + 2, y - 1 }] = 1;            // 8-th move         mpp[{ x - 1, y - 2 }] = 1;     }        // iterate for all possible 8 coordinates     for (int i = -1; i < 2; i++) {         for (int j = -1; j < 2; j++) {             int nx = kx + i;             int ny = ky + j;             if (i != 0 && j != 0) {                    // check a move can be made or not                 if (!mpp[{ nx, ny }]) {                     return true;                 }             }         }     }        // any moves     return false; }    // Driver Code int main() {     pair a[] = { { 1, 0 }, { 0, 2 }, { 2, 5 },                             { 4, 4 }, { 5, 0 }, { 6, 2 }};        int n = sizeof(a) / sizeof(a);        int x = 3, y = 2;     if (checkCheckMate(a, n, x, y))         cout << "Not Checkmate!";     else         cout << "Yes its checkmate!";        return 0; }

Java

 // Java program for checking if a king // can move a valid move or not when // N nights are there in a modified chessboard import java.util.*;    class GFG  { static class pair {      int first, second;      public pair(int first, int second)      {          this.first = first;          this.second = second;      }  }     static boolean checkCheckMate(pair a[], int n,                               int kx, int ky) {        // Pair of hash to mark the coordinates     HashMap mpp = new HashMap();        // iterate for Given N knights     for (int i = 0; i < n; i++)      {         int x = a[i].first;         int y = a[i].second;            // mark all the "L" shaped coordinates         // that can be reached by a Knight            // initial position         mpp.put(new pair( x, y ), 1);            // 1-st move         mpp.put(new pair( x - 2, y + 1 ), 1);            // 2-nd move         mpp.put(new pair( x - 2, y - 1 ), 1);            // 3-rd move         mpp.put(new pair( x + 1, y + 2 ), 1);            // 4-th move         mpp.put(new pair( x + 1, y - 2 ), 1);            // 5-th move         mpp.put(new pair( x - 1, y + 2 ), 1);            // 6-th move         mpp.put(new pair( x + 2, y + 1 ), 1);            // 7-th move         mpp.put(new pair( x + 2, y - 1 ), 1);            // 8-th move         mpp.put(new pair( x - 1, y - 2 ), 1);     }        // iterate for all possible 8 coordinates     for (int i = -1; i < 2; i++)      {         for (int j = -1; j < 2; j++)          {             int nx = kx + i;             int ny = ky + j;             if (i != 0 && j != 0)             {                    // check a move can be made or not                 pair p =new pair(nx, ny );                 if (mpp.get(p) != null)                 {                     return true;                 }             }         }     }        // any moves     return false; }    // Driver Code public static void main(String[] args)  {     pair a[] = {new pair( 1, 0 ), new pair( 0, 2 ),                  new pair( 2, 5 ), new pair( 4, 4 ),                  new pair( 5, 0 ), new pair( 6, 2 )};        int n = a.length;        int x = 3, y = 2;     if (checkCheckMate(a, n, x, y))         System.out.println("Not Checkmate!");     else         System.out.println("Yes its checkmate!");     } }    // This code is contributed by PrinciRaj1992

Python3

 # Python3 program for checking if a king  # can move a valid move or not when  # N nights are there in a modified chessboard     def checkCheckMate(a, n, kx, ky):         # Pair of hash to mark the coordinates      mpp = {}         # iterate for Given N knights      for i in range(0, n):          x = a[i]          y = a[i]             # mark all the "L" shaped coordinates          # that can be reached by a Knight             # initial position          mpp[(x, y)] = 1            # 1-st move          mpp[(x - 2, y + 1)] = 1            # 2-nd move          mpp[(x - 2, y - 1)] = 1            # 3-rd move          mpp[(x + 1, y + 2)] = 1            # 4-th move          mpp[(x + 1, y - 2)] = 1            # 5-th move          mpp[(x - 1, y + 2)] = 1            # 6-th move          mpp[(x + 2, y + 1)] = 1            # 7-th move          mpp[(x + 2, y - 1)] = 1            # 8-th move          mpp[(x - 1, y - 2)] = 1            # iterate for all possible 8 coordinates      for i in range(-1, 2):          for j in range(-1, 2):              nx = kx + i              ny = ky + j                             if i != 0 and j != 0:                                     # check a move can be made or not                  if not mpp[(nx, ny)]:                      return True            # any moves      return False    # Driver Code  if __name__ == "__main__":         a = [[1, 0], [0, 2], [2, 5],           [4, 4], [5, 0], [6, 2]]         n = len(a)      x, y = 3, 2            if checkCheckMate(a, n, x, y):          print("Not Checkmate!")      else:         print("Yes its checkmate!")    # This code is contributed by Rituraj Jain

Output:

Yes its checkmate!

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