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

08 Jun, 2022
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++
Java
Python3
C#
Javascript
// 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 Codeint 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 program for checking if a king// can move a valid move or not when// N nights are there in a modified chessboardimport 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 Codepublic 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 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 Codeif __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# program for checking if a king// can move a valid move or not when// N nights are there in a modified chessboardusing 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 Codepublic 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
<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 Codevar 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>
Yes its checkmate!
Time Complexity: O(N).Auxiliary Space: O(N)
rituraj_jain
princiraj1992
Akanksha_Rai
rrrtnx
rohitsingh57
cpp-map
cpp-pair
Competitive Programming
Matrix
Matrix
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