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

## Concept

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

Input

a1[] = { { 2, 1 }, { 1, 3 }, { 3, 6 },{ 5, 5 }, { 6, 1 }, { 7, 3 }} king -> {4, 3}

Output

Yes

The king is unable to make any move as it has been check mate.

Input

a1 [] = {{1, 1}} king -> {3, 4}

Output

No

The king can be able to make valid moves.

## Method

Here, the knight’s move is unusual among chess pieces. Its movement is towards a square that is two squares away horizontally and one square vertically, or two squares vertically and one square horizontally. So, the complete move looks like the letter “L” in every shape possible (8 possible moves). As a result of this, apply a hash map of pairs to mark all possible coordinates where the knight can move. If it has been seen that the King cannot move to any of its nearby 8 coordinates i.e., if the coordinate is hashed by a knight’s move, then it is declared as a “checkmate”.

## Example

Live Demo

// C++ program for verifying 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 checkCheckMate1(pair<int, int>a1[], int n1, int kx1, int ky1){
// Pair of hash to indicate or mark the coordinates
map<pair<int, int>, int> mpp1;
// iterate for Given N knights
for (int i = 0; i < n1; i++) {
int x = a1[i].first;
int y = a1[i].second;
// indicate or mark all the "L" shaped coordinates
// that can be reached by a Knight
// starting or initial position
mpp1[{ x, y }] = 1;
// 1-st move
mpp1[{ x - 2, y + 1 }] = 1;
// 2-nd move
mpp1[{ x - 2, y - 1 }] = 1;
// 3-rd move
mpp1[{ x + 1, y + 2 }] = 1;
// 4-th move
mpp1[{ x + 1, y - 2 }] = 1;
// 5-th move
mpp1[{ x - 1, y + 2 }] = 1;
// 6-th move
mpp1[{ x + 2, y + 1 }] = 1;
// 7-th move
mpp1[{ x + 2, y - 1 }] = 1;
// 8-th move
mpp1[{ 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 = kx1 + i;
int ny = ky1 + j;
if (i != 0 && j != 0) {
// verify or check a move can be made or not
if (!mpp1[{ nx, ny }]) {
return true;
}
}
}
}
// any moves
return false;
}
// Driver Code
int main(){
pair<int, int&lgt; a1[] = { { 2, 1 }, { 1, 3 }, { 3, 6 }, { 5, 5 }, { 6, 1 }, { 7, 3 }};
int n1 = sizeof(a1) / sizeof(a1[0]);
int x = 4, y = 3;
if (checkCheckMate1(a1, n1, x, y))
cout << "Not Checkmate!";
else
cout << "Yes its checkmate!";
return 0;
}

## Output

Yes its checkmate!

Updated on: 23-Jul-2020

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