---
tags: [Zerojudge,解題,解題心得,TOI,202205,新手練習賽,C++]
---
# i378: 垂直對稱 (Symmetry) C++解法
### 題目
https://zerojudge.tw/ShowProblem?problemid=i378

### 解題思路
1. 照y的大小排序
2. 如果y的大小一樣，檢查y是比對稱軸大還是小。如果大，則x大的放後面；如果小，則x大的放前面
3. 如果n%2 (奇數) ， 則中間點必在對稱軸上，而其他點必兩兩對稱，或在對稱軸上；如果n為偶數，點必兩兩對稱，或在對稱軸上

### 程式碼

#include <bits/stdc++.h>
using namespace std;

struct points{
  int x, y;
} point[501];

int main() {
  int n, line;
  cin>>n;
  bool check;
  for(int i=0;i<n;i++){
    cin>>point[i].x>>point[i].y;
  }
  struct points tmp;
  //照y排  
  for(int i=n;i>0;i--){
    for(int j=0;j<i-1;j++){
      if(point[j].y > point[j+1].y){
        tmp = point[j];
        point[j] = point[j+1];
        point[j+1] = tmp;
      }
    }
  }
  //sort完長這樣
  // cout<<"sort= ";
  // for(int i=0;i<n-1;i++){
  //     cout<<point[i].x<<" "<<point[i].y<<", ";
  // }
  // cout<<point[n-1].x<<" "<<point[n-1].y<<endl;
  //

  line = (point[0].y + point[n-1].y)/2;
  for(int i=n;i>0;i--){
    for(int j=0;j<i-1;j++){
      if(point[j].y == point[j+1].y){//跟隔壁的同y
        if(point[j].y < line){//比對稱軸的y大
          if(point[j].x > point[j+1].x){
            tmp = point[j];
            point[j] = point[j+1];
            point[j+1] = tmp;
          }
        }
        else if(point[j].y > line){
          if(point[j].x < point[j+1].x){
            tmp = point[j];
            point[j] = point[j+1];
            point[j+1] = tmp;
          }
        }
      }
    }
  }      
  
  if(n%2 == 1){ //odd
    if(line != point[n/2].y) 
      check = false;
    else{
      for(int i=0;i<n;i++){
        if((point[i].x == point[n-i-1].x) && ((point[i].y + point[n-i-1].y)/2) == line){
          check = true;
        }
        else if(point[i].y == line) check = true;
        else{
          check = false;
          break;
        }
      }
    }
  }
  else{//even
    for(int i=0;i<n;i++){
        if((point[i].x == point[n-i-1].x) && ((point[i].y + point[n-i-1].y)/2) == line){
          check = true;
        }
        else if(point[i].y == line) check = true;//如果在線上
        else{
          check = false;
          break;//繼續跑可能會洗掉
        }
      }
  }
  if(check) cout<<"success"<<endl;
  else cout<<"failure"<<endl;
  return 0;
}

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