给定二维笛卡尔坐标系中的N 个轴平行矩形和4N-1个顶点的坐标，任务是找到缺失的单个顶点。例子：
Input: N = 2, V[][] = {{1, 1}, {1, 2}, {4, 6}, {2, 1}, {9, 6}, {9, 3}, {4, 3}
Output: {2, 2}
Explanation:
The coordinates forming an axis parallel rectangle are {4, 6}, {9, 6}, {4, 3}, {9, 3}.
For the remaining coordinates to form a rectangle {1, 1}, {1, 2}, {2, 1}, the missing coordinate is {2, 2}
Input: N = 3, V[][] = {{3, 8}, {0, 0}, {4, 6}, {0, 2}, {9, 6}, {9, 3}, {4, 3}, {6, 4}, {1, 0}, {3, 4}, {6, 8}}
Output: {1, 2}
方法：
请按照以下步骤解决问题：
- 将频率x 坐标和y 坐标存储在 Map 中。
- 遍历 Map 以找到两个坐标具有奇数频率的元素。
- 最后，打印奇数频率的 x 和 y 坐标。
下面是上述方法的实现：
C++
// C++ Program to implement
// the above approach
#include
using namespace std;
void MissingPoint(vector > V,
int N)
{
map mp;
for (int i = 0; i < V.size(); i++) {
mp[V[i].first]++;
}
int x, y;
for (auto it : mp) {
if (it.second % 2 == 1) {
x = it.first;
break;
}
}
mp.clear();
for (int i = 0; i < V.size(); i++) {
mp[V[i].second]++;
}
for (auto it : mp) {
if (it.second % 2 == 1) {
y = it.first;
break;
}
}
cout << x << " " << y;
}
// Driver Code
int main()
{
// Number of rectangles
int N = 2;
// Stores the coordinates
vector > V;
// Insert the coordinates
V.push_back({ 1, 1 });
V.push_back({ 1, 2 });
V.push_back({ 4, 6 });
V.push_back({ 2, 1 });
V.push_back({ 9, 6 });
V.push_back({ 9, 3 });
V.push_back({ 4, 3 });
MissingPoint(V, N);
return 0;
} Java
// Java Program to implement
// the above approach
import java.util.*;
class GFG{
static class pair
{
int first, second;
public pair(int first, int second)
{
this.first = first;
this.second = second;
}
}
static void MissingPoint(Vector V, int N)
{
HashMap mp = new HashMap();
for (int i = 0; i < V.size(); i++)
{
if(mp.containsKey(V.get(i).first))
mp.put(V.get(i).first,
V.get(i).first + 1);
else
mp.put(V.get(i).first, 1);
}
int x = 0, y = 0;
for (Map.Entry it : mp.entrySet())
{
if (it.getValue() % 2 == 1)
{
x = it.getKey();
break;
}
}
mp.clear();
for (int i = 0; i < V.size(); i++)
{
if(mp.containsKey(V.get(i).second))
mp.put(V.get(i).second,
V.get(i).second + 1);
else
mp.put(V.get(i).second, 1);
}
for (Map.Entry it : mp.entrySet())
{
if (it.getValue() % 2 == 1)
{
y = it.getKey();
break;
}
}
System.out.print(x + " " + y);
}
// Driver Code
public static void main(String[] args)
{
// Number of rectangles
int N = 2;
// Stores the coordinates
Vector V = new Vector();
// Insert the coordinates
V.add(new pair(1, 1));
V.add(new pair(1, 2));
V.add(new pair(4, 6));
V.add(new pair(2, 1));
V.add(new pair(9, 6));
V.add(new pair(9, 3));
V.add(new pair(4, 3));
MissingPoint(V, N);
}
}
// This code is contributed by Rajput-Ji Python3
# Python3 program for the above approach
from collections import defaultdict
def MissingPoint(V, N):
mp = defaultdict(lambda : 0)
for i in range(len(V)):
mp[V[i][0]] += 1
for it in mp.keys():
if(mp[it] % 2 == 1):
x = it
break
del mp
mp = defaultdict(lambda : 0)
for i in range(len(V)):
mp[V[i][1]] += 1
for it in mp.keys():
if(mp[it] % 2 == 1):
y = it
break
print(x, y)
# Driver code
if __name__ == '__main__':
# Number of rectangles
N = 2
# Stores the coordinates
V = []
# Insert the coordinates
V.append([1, 1])
V.append([1, 2])
V.append([4, 6])
V.append([2, 1])
V.append([9, 6])
V.append([9, 3])
V.append([4, 3])
MissingPoint(V, N)
# This code is contributed by Shivam SinghC#
// C# Program to implement
// the above approach
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 void MissingPoint(List V,
int N)
{
Dictionary mp = new Dictionary();
for (int i = 0; i < V.Count; i++)
{
if(mp.ContainsKey(V[i].first))
mp[V[i].first] = mp[V[i].first] + 1;
else
mp.Add(V[i].first, 1);
}
int x = 0, y = 0;
foreach (KeyValuePair it in mp)
{
if (it.Value % 2 == 1)
{
x = it.Key;
break;
}
}
mp.Clear();
for (int i = 0; i < V.Count; i++)
{
if(mp.ContainsKey(V[i].second))
mp[V[i].second] = mp[V[i].second] + 1;
else
mp.Add(V[i].second, 1);
}
foreach (KeyValuePair it in mp)
{
if (it.Value % 2 == 1)
{
y = it.Key;
break;
}
}
Console.Write(x + " " + y);
}
// Driver Code
public static void Main(String[] args)
{
// Number of rectangles
int N = 2;
// Stores the coordinates
List V = new List();
// Insert the coordinates
V.Add(new pair(1, 1));
V.Add(new pair(1, 2));
V.Add(new pair(4, 6));
V.Add(new pair(2, 1));
V.Add(new pair(9, 6));
V.Add(new pair(9, 3));
V.Add(new pair(4, 3));
MissingPoint(V, N);
}
}
// This code is contributed by Rajput-Ji 输出：
2 2
时间复杂度： O(N)
辅助空间： O(N)