hihocoder1696 折线中点（几何）

https://hihocoder.com/problemset/problem/1696

求折线中点，一开始想成先求横坐标中点了，肯定是错的。

一定要从线段长度求中点，然后中点公式推了好久。。

#include<iostream>
#include<cstdio>
#include<queue>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<map>
#define lson l, m, rt<<1
#define rson m+1, r, rt<<1|1
#define IO ios::sync_with_stdio(false);cin.tie(0);
#define INF 0x3f3f3f3f
typedef long long ll;
using namespace std;
int n;
typedef struct{
    int x, y;
}Node;
Node node[110];
double a[110];
double dist(int a, int b)
{
    return sqrt(a*a+b*b);
}
int main()
{
    double sum = 0;
    cin >> n;
    for(int i = 0; i < n; i++){
        cin >> node[i].x >> node[i].y;
    }
    for(int i = 0; i < n-1; i++){
        sum += dist(node[i+1].x-node[i].x, node[i+1].y-node[i].y);
        a[i] = sum;//存放到点i+1为止的折线长度 
    }
    sum /= 2;
    int i;
    for(i = 0; i < n-1; i++){
        if(sum < a[i]||sum-a[i]<1e-6){//小于或等于 
            break;
        }
    }
    sum -= a[i-1];
    double tx = node[i+1].x-node[i].x;
    double ty = node[i+1].y-node[i].y;
    double midx = sum/dist(node[i+1].x-node[i].x, node[i+1].y-node[i].y)*tx+node[i].x;
    double midy = sum/dist(node[i+1].x-node[i].x, node[i+1].y-node[i].y)*ty+node[i].y;
    printf("%.1lf %.1lf
", midx, midy);
    return 0;
}