给定一个二维数组queues[][]由N个皇后在8*8棋盘中的坐标和一个表示国王坐标的数组king[]组成，任务是找到攻击国王的皇后
例子：
Input: queens[][] = {{0, 1}, {1, 0}, {4, 0}, {0, 4}, {3, 3}, {2, 4}}, king[] = {2, 3}
Output: {{0, 1}, {2, 4}, {3, 3}}
Explanation:The queens at coordinates {0, 1} and {3, 3} are diagonally attacking the king and the queen at {2, 4} is vertically below the king.
Input: queens[][]] = {{4, 1}, {1, 0}, {4, 0}}, king[] = {0, 0}
Output : {{1, 0}}
方法按照以下步骤解决问题：
- 迭代数组Queens[][] 。
- 对于遍历的每个坐标，检查所有攻击国王的可能性，即水平、垂直和对角线。如果发现正在攻击国王，请检查以下内容：
- 如果没有其他皇后从那个方向攻击国王，包括当前国王作为攻击者。
- 如果攻击者已经出现在那个方向，检查当前的女王是否是最近的攻击者。如果发现是真的，包括作为攻击者的分皇后。否则，继续下一个坐标。
- 最后，打印所有坐标。
下面是上述方法的实现：
C++
// C++ Program to implement
// the above approach
#include
using namespace std;
// Function to find the queen
// closest to king in an
// attacking position
int dis(vector ans,
vector attacker)
{
return abs(ans[0] - attacker[0])
+ abs(ans[1] - attacker[1]);
}
// Function to find all the queens
// attacking the king in the chessboard
vector > findQueens(
vector >& queens,
vector& king)
{
vector > sol;
vector > attackers(8);
// Iterating over the coordinates
// of the queens
for (int i = 0; i < queens.size(); i++) {
// If king is horizontally on
// the right of current queen
if (king[0] == queens[i][0]
&& king[1] > queens[i][1]) {
// If no attacker is present
// in that direction
if ((attackers[3].size() == 0)
// Or if the current queen is
// closest in that direction
|| (dis(attackers[3], king)
> dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[3] = queens[i];
}
// If king is horizontally on
// the left of current queen
if (king[0] == queens[i][0]
&& king[1] < queens[i][1]) {
// If no attacker is present
// in that direction
if ((attackers[4].size() == 0)
// Or if the current queen is
// closest in that direction
|| (dis(attackers[4], king)
> dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[4] = queens[i];
}
// If the king is attacked by a
// queen from the left by a queen
// diagonal above
if (king[0] - queens[i][0]
== king[1] - queens[i][1]
&& king[0] > queens[i][0]) {
// If no attacker is present in
// that direction
if ((attackers[0].size() == 0)
// Or the current queen is
// the closest attacker in
// that direction
|| (dis(attackers[0], king)
> dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[0] = queens[i];
}
// If the king is attacked by a
// queen from the left by a queen
// diagonally below
if (king[0] - queens[i][0]
== king[1] - queens[i][1]
&& king[0] < queens[i][0]) {
// If no attacker is present in
// that direction
if ((attackers[7].size() == 0)
// Or the current queen is
// the closest attacker in
// that direction
|| (dis(attackers[7], king)
> dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[7] = queens[i];
}
// If the king is attacked by a
// queen from the right by a queen
// diagonally above
if (king[1] - queens[i][1] == 0
&& king[0] > queens[i][0]) {
// If no attacker is present in
// that direction
if ((attackers[1].size() == 0)
// Or the current queen is
// the closest attacker in
// that direction
|| (dis(attackers[1], king)
> dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[1] = queens[i];
}
// If the king is attacked by a
// queen from the right by a queen
// diagonally below
if (king[1] - queens[i][1] == 0
&& king[0] < queens[i][0]) {
// If no attacker is present in
// that direction
if ((attackers[6].size() == 0)
// Or the current queen is
// the closest attacker in
// that direction
|| (dis(attackers[6], king)
> dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[6] = queens[i];
}
// If a king is vertically below
// the current queen
if (king[0] - queens[i][0]
== -(king[1] - queens[i][1])
&& king[0] > queens[i][0]) {
// If no attacker is present in
// that direction
if ((attackers[2].size() == 0)
// Or the current queen is
// the closest attacker in
// that direction
|| (dis(attackers[2], king)
> dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[2] = queens[i];
}
// If a king is vertically above
// the current queen
if (king[0] - queens[i][0]
== -(king[1] - queens[i][1])
&& king[0] < queens[i][0]) {
// If no attacker is present in
// that direction
if ((attackers[5].size() == 0)
// Or the current queen is
// the closest attacker in
// that direction
|| (dis(attackers[5], king)
> dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[5] = queens[i];
}
}
for (int i = 0; i < 8; i++)
if (attackers[i].size())
sol.push_back(attackers[i]);
// Return the coordinates
return sol;
}
// Print all the coordinates of the
// queens attacking the king
void print(vector > ans)
{
for (int i = 0; i < ans.size();
i++) {
for (int j = 0; j < 2; j++)
cout << ans[i][j] << " ";
cout << "\n";
}
}
// Driver Code
int main()
{
vector king = { 2, 3 };
vector > queens
= { { 0, 1 }, { 1, 0 },
{ 4, 0 }, { 0, 4 },
{ 3, 3 }, { 2, 4 } };
vector > ans
= findQueens(queens, king);
print(ans);
} Java
// Java program to implement
// the above approach
import java.io.*;
import java.util.*;
import java.util.stream.Collectors;
class GFG{
// Method to find the queen closest
// to king in an attacking position
private static int dis(int[] ans, int[] attacker)
{
return Math.abs(ans[0] - attacker[0]) +
Math.abs(ans[1] - attacker[1]);
}
// Method to find all the queens
// attacking the king in the chessboard
private static List> findQueens(
int[][] queens, int[] king)
{
List> sol = new ArrayList>();
int[][] attackers = new int[8][2];
for(int i = 0; i < 8; i++)
{
Arrays.fill(attackers[i], -1);
}
for(int i = 0; i < queens.length; i++)
{
// If king is horizontally on
// the right of current queen
if (king[0] == queens[i][0] &&
king[1] > queens[i][1])
{
// If no attacker is present
// in that direction
if ((attackers[3][0] == -1) ||
// Or if the current queen is
// closest in that direction
(dis(attackers[3], king) >
dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[3] = queens[i];
}
// If king is horizontally on
// the left of current queen
if (king[0] == queens[i][0] &&
king[1] < queens[i][1])
{
// If no attacker is present
// in that direction
if ((attackers[4][0] == -1) ||
// Or if the current queen is
// closest in that direction
(dis(attackers[4], king) >
dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[4] = queens[i];
}
// If the king is attacked by a
// queen from the left by a queen
// diagonal above
if (king[0] - queens[i][0] ==
king[1] - queens[i][1] &&
king[0] > queens[i][0])
{
// If no attacker is present in
// that direction
if ((attackers[0][0] == -1) ||
// Or the current queen is
// the closest attacker in
// that direction
(dis(attackers[0], king) >
dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[0] = queens[i];
}
// If the king is attacked by a
// queen from the left by a queen
// diagonally below
if (king[0] - queens[i][0] ==
king[1] - queens[i][1] &&
king[0] < queens[i][0])
{
// If no attacker is present in
// that direction
if ((attackers[7][0] == -1) ||
// Or the current queen is
// the closest attacker in
// that direction
(dis(attackers[7], king) >
dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[7] = queens[i];
}
// If the king is attacked by a
// queen from the right by a queen
// diagonally above
if (king[1] - queens[i][1] == 0 &&
king[0] > queens[i][0])
{
// If no attacker is present in
// that direction
if ((attackers[1][0] == -1) ||
// Or the current queen is
// the closest attacker in
// that direction
(dis(attackers[1], king) >
dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[1] = queens[i];
}
// If the king is attacked by a
// queen from the right by a queen
// diagonally below
if (king[1] - queens[i][1] == 0 &&
king[0] < queens[i][0])
{
// If no attacker is present in
// that direction
if ((attackers[6][0] == -1) ||
// Or the current queen is
// the closest attacker in
// that direction
(dis(attackers[6], king) >
dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[6] = queens[i];
}
// If a king is vertically below
// the current queen
if (king[0] - queens[i][0] ==
-(king[1] - queens[i][1]) &&
king[0] > queens[i][0])
{
// If no attacker is present in
// that direction
if ((attackers[2][0] == -1) ||
// Or the current queen is
// the closest attacker in
// that direction
(dis(attackers[2], king) >
dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[2] = queens[i];
}
// If a king is vertically above
// the current queen
if (king[0] - queens[i][0] ==
-(king[1] - queens[i][1]) &&
king[0] < queens[i][0])
{
// If no attacker is present in
// that direction
if ((attackers[5][0] == -1) ||
// Or the current queen is
// the closest attacker in
// that direction
(dis(attackers[5], king) >
dis(queens[i], king)))
// Set current queen as
// the attacker
attackers[5] = queens[i];
}
}
for(int i = 0; i < 8; i++)
if (attackers[i][0] != -1)
sol.add(
Arrays.stream(
attackers[i]).boxed().collect(
Collectors.toList()));
// Return the coordinates
return sol;
}
// Print all the coordinates of the
// queens attacking the king
private static void print(List> ans)
{
for(int i = 0; i < ans.size(); i++)
{
for(int j = 0; j < 2; j++)
System.out.print(ans.get(i).get(j) + " ");
System.out.println();
}
}
// Driver Code
public static void main(String[] args)
{
int[] king = { 2, 3 };
int[][] queens = { { 0, 1 }, { 1, 0 },
{ 4, 0 }, { 0, 4 },
{ 3, 3 }, { 2, 4 } };
List> ans = findQueens(queens, king);
print(ans);
}
}
// This code is contributed by jithin Python3
# Python3 program to implement
# the above approach
# Function to find the queen
# closest to king in an
# attacking position
def dis(ans, attacker):
return (abs(ans[0] - attacker[0]) +
abs(ans[1] - attacker[1]))
# Function to find all the
# queens attacking the king
# in the chessboard
def findQueens(queens, king):
sol = []
attackers = [[0 for x in range(8)]
for y in range(8)]
# Iterating over the coordinates
# of the queens
for i in range(len(queens)):
# If king is horizontally on
# the right of current queen
if (king[0] == queens[i][0] and
king[1] > queens[i][1]):
# If no attacker is present
# in that direction
if ((len(attackers[3]) == 0)
# Or if the current queen is
# closest in that direction
or ((dis(attackers[3], king) >
dis(queens[i], king)))):
# Set current queen as
# the attacker
attackers[3] = queens[i];
# If king is horizontally on
# the left of current queen
if (king[0] == queens[i][0] and
king[1] < queens[i][1]):
# If no attacker is present
# in that direction
if ((len(attackers[4]) == 0)
# Or if the current queen is
# closest in that direction
or (dis(attackers[4], king) >
dis(queens[i], king))):
# Set current queen as
# the attacker
attackers[4] = queens[i];
# If the king is attacked by a
# queen from the left by a queen
# diagonal above
if (king[0] - queens[i][0] ==
king[1] - queens[i][1] and
king[0] > queens[i][0]):
# If no attacker is present in
# that direction
if ((len(attackers[0]) == 0)
# Or the current queen is
# the closest attacker in
# that direction
or (dis(attackers[0], king) >
dis(queens[i], king))):
# Set current queen as
# the attacker
attackers[0] = queens[i]
# If the king is attacked by a
# queen from the left by a queen
# diagonally below
if (king[0] - queens[i][0] ==
king[1] - queens[i][1] and
king[0] < queens[i][0]):
# If no attacker is present in
# that direction
if ((len(attackers[7]) == 0)
# Or the current queen is
# the closest attacker in
# that direction
or (dis(attackers[7], king) >
dis(queens[i], king))):
# Set current queen as
# the attacker
attackers[7] = queens[i]
# If the king is attacked by a
# queen from the right by a queen
# diagonally above
if (king[1] - queens[i][1] == 0 and
king[0] > queens[i][0]):
# If no attacker is present in
# that direction
if ((len(attackers[1]) == 0)
# Or the current queen is
# the closest attacker in
# that direction
or (dis(attackers[1], king) >
dis(queens[i], king))):
# Set current queen as
# the attacker
attackers[1] = queens[i]
# If the king is attacked by a
# queen from the right by a queen
# diagonally below
if (king[1] - queens[i][1] == 0 and
king[0] < queens[i][0]):
# If no attacker is present in
# that direction
if ((len(attackers[6]) == 0)
# Or the current queen is
# the closest attacker in
# that direction
or (dis(attackers[6], king) >
dis(queens[i], king))):
# Set current queen as
# the attacker
attackers[6] = queens[i];
# If a king is vertically below
# the current queen
if (king[0] - queens[i][0] ==
-(king[1] - queens[i][1]) and
king[0] > queens[i][0]):
# If no attacker is present in
# that direction
if ((len(attackers[2]) == 0)
# Or the current queen is
# the closest attacker in
# that direction
or (dis(attackers[2], king) >
dis(queens[i], king))):
# Set current queen as
# the attacker
attackers[2] = queens[i]
# If a king is vertically above
# the current queen
if (king[0] - queens[i][0] ==
-(king[1] - queens[i][1]) and
king[0] < queens[i][0]):
# If no attacker is present in
# that direction
if ((len(attackers[5]) == 0)
# Or the current queen is
# the closest attacker in
# that direction
or (dis(attackers[5], king) >
dis(queens[i], king))):
# Set current queen as
# the attacker
attackers[5] = queens[i]
for i in range(8):
f = 1
for x in attackers[i]:
if x != 0:
f = 0
break
if f == 0:
sol.append(attackers[i])
# Return the coordinates
return sol
# Print all the coordinates of the
# queens attacking the king
def print_board(ans):
for i in range(len(ans)):
for j in range(2):
print(ans[i][j],
end = " ")
print()
# Driver Code
if __name__ == "__main__":
king = [2, 3]
queens = [[0, 1], [1, 0],
[4, 0], [0, 4],
[3, 3], [2, 4]]
ans = findQueens(queens, king);
print_board(ans);
# This code is contributed by Chitranayal输出：
0 1
2 4
3 3
时间复杂度： O(N)，其中 N 是皇后的数量
辅助空间： O(N)
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