## Solución al problema número 10263 de UVA - 10263.

Cualquier duda no dudes en contactar.

``````#include <bits/stdc++.h>
#define INF 0x3f3f3f3f
#define EPS 1e-10
#define PI acos(-1.0)
using namespace std;

struct point{
double x,y;
point(){x=y=0;}
point(double _x,double _y){x=_x,y=_y;}
};

double dist(point p1, point p2) {                // Euclidean distance
// hypot(dx, dy) returns sqrt(dx * dx + dy * dy)
return hypot(p1.x - p2.x, p1.y - p2.y); }           // return double

struct vec { double x, y;  // name: `vec' is different from STL vector
vec(double _x, double _y) : x(_x), y(_y) {} };

vec toVec(point a, point b) {       // convert 2 points to vector a->b
return vec(b.x - a.x, b.y - a.y); }

double dot(vec a, vec b) { return (a.x * b.x + a.y * b.y); }

double norm_sq(vec v) { return v.x * v.x + v.y * v.y; }

vec scale(vec v, double s) {        // nonnegative s = [<1 .. 1 .. >1]
return vec(v.x * s, v.y * s); }               // shorter.same.longer

point translate(point p, vec v) {        // translate p according to v
return point(p.x + v.x , p.y + v.y); }

double distToLine(point p, point a, point b, point &c) {
// formula: c = a + u * ab
vec ap = toVec(a, p), ab = toVec(a, b);
double u = dot(ap, ab) / norm_sq(ab);
c = translate(a, scale(ab, u));                  // translate a to c
return dist(p, c); }           // Euclidean distance between p and c

double distToLineSegment(point p, point a, point b, point &c) {
vec ap = toVec(a, p), ab = toVec(a, b);
double u = dot(ap, ab) / norm_sq(ab);
if (u < 0.0) { c = point(a.x, a.y);                   // closer to a
return dist(p, a); }         // Euclidean distance between p and a
if (u > 1.0) { c = point(b.x, b.y);                   // closer to b
return dist(p, b); }         // Euclidean distance between p and b
return distToLine(p, a, b, c); }          // run distToLine as above
int main()
{
double x,y,x_,y_;
while(scanf("%lf\n%lf",&x,&y)==2)
{
point pn = point(x,y);
point resP;
int n; scanf("%d",&n);
double res = INF;
vector<point> V;
for(int i=0; i<n+1;i++)
{
scanf("%lf\n%lf",&x_,&y_);
V.push_back(point(x_,y_));
}
for(int i=0; i<n;i++)
{
point p3;
double resl = distToLineSegment(pn,V[i],V[i+1],p3);
if(res>resl){ res=resl; resP = p3;}
}

printf("%.4lf\n%.4lf\n",resP.x,resP.y);
}
return 0;
}
``````