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

  • Difficulty Level : Easy
  • Last Updated : 08 Jul, 2021

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. 

 

Approach: 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 <bits/stdc++.h>
using namespace std;
bool checkCheckMate(pair<int, int> a[], int n, int kx, int ky)
{
 
    // Pair of hash to mark the coordinates
    map<pair<int, int>, 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<int, int> a[] = { { 1, 0 }, { 0, 2 }, { 2, 5 },
                           { 4, 4 }, { 5, 0 }, { 6, 2 }};
 
    int n = sizeof(a) / sizeof(a[0]);
 
    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<pair,
            Integer> mpp = new HashMap<pair,
                                       Integer>();
 
    // 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][0]
        y = a[i][1]
 
        # 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

C#




// C# program for checking if a king
// can move a valid move or not when
// N nights are there in a modified chessboard
using System;
using System.Collections.Generic;
 
class GFG
{
class pair
{
    public int first, second;
    public pair(int first, int second)
    {
        this.first = first;
        this.second = second;
    }
}
 
static bool checkCheckMate(pair []a, int n,
                             int kx, int ky)
{
 
    // Pair of hash to mark the coordinates
    Dictionary<pair,
               int> mpp = new Dictionary<pair,
                                         int>();
 
    // 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.Add(new pair( x, y ), 1);
 
        // 1-st move
        mpp.Add(new pair( x - 2, y + 1 ), 1);
 
        // 2-nd move
        mpp.Add(new pair( x - 2, y - 1 ), 1);
 
        // 3-rd move
        mpp.Add(new pair( x + 1, y + 2 ), 1);
 
        // 4-th move
        mpp.Add(new pair( x + 1, y - 2 ), 1);
 
        // 5-th move
        mpp.Add(new pair( x - 1, y + 2 ), 1);
 
        // 6-th move
        mpp.Add(new pair( x + 2, y + 1 ), 1);
 
        // 7-th move
        mpp.Add(new pair( x + 2, y - 1 ), 1);
 
        // 8-th move
        mpp.Add(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.ContainsKey(p))
                {
                    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))
        Console.WriteLine("Not Checkmate!");
    else
        Console.WriteLine("Yes its checkmate!");
}
}
 
// This code is contributed by PrinciRaj1992

Javascript




<script>
 
// JavaScript program for checking if a king
// can move a valid move or not when
// N nights are there in a modified chessboard
 
class pair
{
    constructor(first, second)
    {
        this.first = first;
        this.second = second;
    }
}
 
function checkCheckMate(a, n, kx, ky)
{
 
    // Pair of hash to mark the coordinates
    var mpp = new Map();
 
    // iterate for Given N knights
    for (var i = 0; i < n; i++)
    {
        var x = a[i].first;
        var y = a[i].second;
 
        // mark all the "L" shaped coordinates
        // that can be reached by a Knight
 
        // initial position
        mpp.set(new pair( x, y ), 1);
 
        // 1-st move
        mpp.set(new pair( x - 2, y + 1 ), 1);
 
        // 2-nd move
        mpp.set(new pair( x - 2, y - 1 ), 1);
 
        // 3-rd move
        mpp.set(new pair( x + 1, y + 2 ), 1);
 
        // 4-th move
        mpp.set(new pair( x + 1, y - 2 ), 1);
 
        // 5-th move
        mpp.set(new pair( x - 1, y + 2 ), 1);
 
        // 6-th move
        mpp.set(new pair( x + 2, y + 1 ), 1);
 
        // 7-th move
        mpp.set(new pair( x + 2, y - 1 ), 1);
 
        // 8-th move
        mpp.set(new pair( x - 1, y - 2 ), 1);
    }
 
    // iterate for all possible 8 coordinates
    for (var i = -1; i < 2; i++)
    {
        for (var j = -1; j < 2; j++)
        {
            var nx = kx + i;
            var ny = ky + j;
            if (i != 0 && j != 0)
            {
 
                // check a move can be made or not
                var p = new pair(nx, ny);
                if (mpp.has(p))
                {
                    return true;
                }
            }
        }
    }
 
    // any moves
    return false;
}
 
// Driver Code
var 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 )];
var n = a.length;
var x = 3, y = 2;
if (checkCheckMate(a, n, x, y))
    document.write("Not Checkmate!");
else
    document.write("Yes its checkmate!");
 
</script>
Output: 
Yes its checkmate!

 




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