# 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.

**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 <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; ` `} ` |

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*filter_none*

## 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

**Output:**

Yes its checkmate!

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