use the formula sqrt(abs(x1 - x2)**2 + abs(y1 - y2)**2) not abs(x1 - x2) + abs(y1 - y2)

Draw a polygon. the sum of its angles is pi*(n-2). The sum of pieces of circles is R*(n*pi-(n-2)*pi)=2*R*pi (you can see it easily if u draw)

Well, you have to know how to determine the distance between two points first.
It can be calculated by, dis = sqrt((x1-x2)^2+(y1-y2)^2).

You can say that, we can just calculate the distance in between the points but why the raidius of the nails are given. Its because the rope is wrapped around each and every nails. But the rope is not in fully contact with nails. The more nails we get, the less contact we have in between rope and nails.

The amount of which the rope is in contact with nail is : s = parameter of a nail/the number of nails.

So we are just required to print out : d(d is the sum of the distance between them) + number of nails * s(s is the amount which the rope is in contact with nails)

If you have problem understanding my word or for better understanding, give this a go : https://ideone.com/t1M3rK

Edited by author 21.02.2020 01:31

I can't understand what's wrong with my code
is my algorithm wrong? or what?
my code:

#include <stdio.h>
#include <math.h>
double x[102],y[102];

double dist(int i, int j){
    int d1=abs(x[i]-x[j]),d2=abs(y[i]-y[j]);
    if(d1==0)
        return (d2);
    else if(d2==0)
      return (d1);
    else
      return sqrt(d1*d1 + d2*d2);
}

int main(){
    int i;
    double n,s=0,r,pi=2*acos(0);
  scanf("%Lf %Lf",&n,&r);
  for(i=0;i<n;i++)
      scanf("%Lf %Lf",&x[i],&y[i]);
    for(i=1;i<n;i++)
        s+=dist(i,i-1);
    s+=dist(0,n-1);
    s+=2*pi*r;
    printf("%.2Lf\n",s);
  return 0;
}

if someone can help me I would appreciate very much
thanks!

public class Problem {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int r = sc.nextInt();
        double l = 0;
        if (n != 1) {
        double x1 = sc.nextDouble();
        double y1 = sc.nextDouble();
        double memoryX = x1, memoryY = y1;
        for (int i = 1; i <= n; i++) {
            if (i == n) {
                l += Math.sqrt((memoryX - x1) * (memoryX - x1) + (memoryY - y1) * (memoryY - y1));
                continue;
            }
            double x = sc.nextDouble();
            double y = sc.nextDouble();
            l += Math.sqrt((x - memoryX) * (x - memoryX) + (y - memoryY) * (y - memoryY));
            memoryX = x;
            memoryY = y;
        }
        }
        l += 2*Math.PI*r;
        System.out.printf("%.2f", l);
        sc.close();
    }

}

Radius and coords can be float
N can be 1

#include<stdio.h>
#include<math.h>
#define PI acos(-1)
int main()
{
    int N,i;
    double r;
    scanf("%d%lf",&N,&r);
    double xx,yy,cx,cy,fx,fy,sum=0,tsum=0,y,x,z;
    y=2*r;
    x=PI*r/2.0;
    z=N*(y-x);
    scanf("%lf%lf",&xx,&yy);
    fx=xx;
    fy=yy;
    for(i=2;i<=N;i++)
    {
        scanf("%lf%lf",&cx,&cy);
        sum=y+sum+sqrt((xx-cx)*(xx-cx)+(yy-cy)*(yy-cy));
        xx=cx;
        yy=cy;
        if(i==N)
        {
            sum=y+sum+sqrt((xx-fx)*(xx-fx)+(yy-fy)*(yy-fy));
            break;
        }
    }
    tsum=sum-z;
    printf("%.2lf\n",tsum);
    return 0;
}

I couldn't understand my mistake! On my tests it works correct.



program project1;
var
  n, i : longint;
  r, res, x, y, x1, y1, x0, y0 : extended;
begin
{$IFNDEF ONLINE_JUDGE}
   assign(input, 'input.txt');
   assign(output, 'output.txt');
   reset(input);
   rewrite(output);
{$ENDIF}
  readln(n, r);
  readln(x, y);
  x0:=x;
  y0:=y;
  res:=2*pi*r;
  for i:=1 to n-1 do begin
    readln(x1, y1);
    res:=res+sqrt(sqr(x1-x)+sqr(y1-y));
    y:=y1;
    x:=x1;
  end;
  res:=trunc(res*100)/100;
  write((res+sqrt(sqr(x1-x0)+sqr(y1-y0))):1:2);
{$IFNDEF ONLINE_JUDGE}
   close(input);
   close(output);
{$ENDIF}
end.

#include <stdio.h>
#include <math.h>
#define M_PI 3.14159

int main() {
  int N;
  float R, result = 0;
  scanf("%d", &N);
  scanf("%f", &R);
  if (N == 1) {
    result = 2 * R * M_PI;
  }
  else
  {
  float nails[N][2];

  for (int i =  0; i < N; i++) {
    for (int j = 0; j < 2; j++) {
      scanf("%f", &nails[i][j]);
    }
  }

  for (int i = 1; i <= N; i++) {
   result += sqrt((nails[i][0] - nails[i - 1][0]) * (nails[i][0] - nails[i - 1][0]) + (nails[i][1] - nails[i - 1][1]) * (nails[i][1] - nails[i - 1][1]));
}

  result += (M_PI * 2 * R);

  }
    printf("%.2f", result);
  return 0;
}

Edited by author 15.01.2018 06:34

#include <iostream>
#include <iomanip>
#include <cmath>
using std::cin;
using std::cout;
using std::endl;
using std::setprecision;
using std::fixed;
int main()
{
    int n;
    double r,s=0,x,y,x0,y0,xn,yn;
    cin >> n >> r;
    if (n==1) {
        cin >> x >> y;
    }
    if (n>1) {

            cin >> x >> y;
    for (int i=1;i<=n-1;i++) {
    cin >> x0 >> y0;
    s=s+sqrt((x0-x)*(x0-x)+(y0-y)*(y0-y));
    x=x0;y=y0;
    }
    s=s+sqrt((xn-x)*(xn-x)+(yn-y)*(yn-y));
            }
s=s+2*3.1415*r;
cout << fixed << setprecision(2) << s << endl;

    return 0;
}

DEV-C++ 5.11

Edited by author 04.06.2017 12:53

Edited by author 08.03.2017 14:32

import java.text.DecimalFormat;
import java.util.Scanner;

/**
 * Created by user on 06.02.2017.
 */
public class nytka {
    public static void main(String[] args) {
        double c = 0;
        Scanner sc = new Scanner(System.in);
        String a = sc.next();
        int b = Integer.valueOf(a);
        String q = sc.next();
        double r = Double.valueOf(q);
        double[] x = new double[b];
        double[] y = new double[b];
        if (100>b) {
            if (b > 0){
                for (int i = 0; i <= b - 1; i++) {
                    String x2 = sc.next();
                    double x1 = Double.valueOf(x2);
                    x[i] = x1;
                    String y2 = sc.next();
                    double y1 = Double.valueOf(y2);
                    y[i] = y1;

                }
                for (int i = b - 1; i > 0; i--) {
                    double rez = Math.sqrt(((x[i] - x[i - 1]) * (x[i] - x[i - 1])) + ((y[i] - y[i - 1]) * (y[i] - y[i - 1])));
                    c = c + rez;
                }
            }
        }
        double end = Math.sqrt(((x[b-1]-x[0])*(x[b-1]-x[0]))+((y[b-1]-y[0])*(y[b-1]-y[0])));
        c = c + end;
        double rad = (Math.PI*r*r)*(b/2);
        double endrez = c + rad;
        DecimalFormat f = new DecimalFormat("#,##0.00");
        System.out.print(f.format(endrez));
    }
}

using System;
using System.Threading;
using System.Globalization;

namespace TestOfCSharp
{
    class Program
    {
        static void Main(string[] args)
        {
            Thread.CurrentThread.CurrentCulture = CultureInfo.InvariantCulture;
            string[] input = Console.ReadLine().Split(' ');
            int N = int.Parse(input[0]);
            int R = int.Parse(input[1]);
            double sum = 0;
            for (int i = 0; i < N; i++)
            {
                input = Console.ReadLine().Split(' ');
                sum += double.Parse(input[0]) + double.Parse(input[1]);
            }
            sum += 2 * Math.PI * R;
            Console.WriteLine("{0:F2}", sum);
        }
    }
}

Edited by author 20.12.2013 05:18

Edited by author 11.01.2017 16:19

Edited by author 11.01.2017 16:21

#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;

int main() {
    int i,j,N,p;
    std::cin>>N;

    float cd[N][2],R,dist = 0.0;
    std::cin>>R;

    for(p = 0;p < N;p++)
        std::cin>>cd[p][0]>>cd[p][1];

    i = 0;
    j = i + 1;

        dist = (2 * std::acos(-1.0) * R);

    while(i < N)
    {
        dist += std::sqrt( ( (cd[j][0] - cd[i][0]) * (cd[j][0] - cd[i][0]) ) +
( (cd[j][1] - cd[i][1]) * (cd[j][1] - cd[i][1]) ) );
        i++;
        j = (i + 1) % N;
    }

    std::cout <<std::setprecision(2) << std::fixed <<dist;
    return 0;
}

#include<stdio.h.>
#include<string.h>
#include<math.h>

int main()
{
    double len=0;
    int n,r,i,j;
    scanf("%d %d",&n,&r);
    double a[200][2];
    for(i=0;i<n;i++)
        for(j=0;j<2;j++)
            scanf("%lf",&a[i][j]);
    for(i=1;i<n;i++)
        len=len+sqrt((a[i][1]-a[i-1][1])*(a[i][1]-a[i-1][1])+(a[i][0]-a[i-1][0])*(a[i][0]-a[i-1][0]));
    len=len+sqrt((a[i-1][1]-a[0][1])*(a[i-1][1]-a[0][1])+(a[i-1][0]-a[0][0])*(a[i-1][0]-a[0][0]));
    len=len+3.141*2*r;
    printf("%.2lf",len);
    fflush(stdin);
    getchar();
    return 0;
}

Edited by author 01.06.2014 20:04

WA #3

#include <iostream>
#include <cmath>
#include <map>
#include <vector>
#include <cmath>
#include <stdio.h>
#include <iomanip>
#include <math.h>
using namespace std;

int main()
{
    const double PI = acos(-1.);
    int n;
    double r;
    cin >> n >> r;

    double x1, y1;
    cin >> x1 >> y1;

    if(n == 1)
    {
        cout << fixed << setprecision(2) << r << endl;
        return 0;
    }

    double vaultx, vaulty;
    vaultx = x1;
    vaulty = y1;

    double x2, y2;
    double d;
    double p = 0.0;
    for(int i = 0; i < n - 1; i++)
    {
        cin >> x2 >> y2;

        d = sqrt(pow(x2 - x1, 2) + pow(y2 - y1, 2));
        p += d;

        x1 = x2;
        y1 = y2;
    }

    p += sqrt(pow(x1 - vaultx, 2) + pow(y1 - vaulty, 2));

    p += 2 * PI * r;

    cout << fixed << setprecision(2) << p << endl;

    return 0;
}

import java.io.*;
import java.math.BigInteger;
import java.util.*;

import static java.lang.Math.*;

public class p2015_11_17_DZnaOlympSSAU_Timus1020_Thread implements Runnable {

    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        if (ONLINE_JUDGE) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        } else {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    public static void main(String[] args) {
        new Thread(null, new p2015_11_17_DZnaOlympSSAU_Timus1020_Thread(), "", 256 * (1L << 20)).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            init();
            solve();
            out.close();
            time();
        } catch (Exception e) {
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }

    void solve() throws IOException {
        int numberOfNails=readInt();

        double radiusOfNails=readDouble();
        if (numberOfNails==1){
            out.println(2*PI*radiusOfNails);
        } else {
            double xFirstNail = readDouble();
            double yFirstNail = readDouble();

            double xLastNail=xFirstNail;
            double yLastNail=yFirstNail;

            double xOfTheCurrentNail=xFirstNail;
            double yOfTheCurrentNail=yFirstNail;

             double lengthOfTheThread=0;

            for (int currentNail = 2; currentNail <= numberOfNails; currentNail++) {
                xLastNail=xOfTheCurrentNail;
                yLastNail=yOfTheCurrentNail;
                xOfTheCurrentNail=readDouble();
                yOfTheCurrentNail=readDouble();
                lengthOfTheThread+=(Math.sqrt((xOfTheCurrentNail-xLastNail)*(xOfTheCurrentNail-xLastNail)+(yOfTheCurrentNail-yLastNail)*(yOfTheCurrentNail-yLastNail)));
            }

            lengthOfTheThread+=(Math.sqrt((xFirstNail-xOfTheCurrentNail)*(xFirstNail-xOfTheCurrentNail)+(yFirstNail-yOfTheCurrentNail)*(yFirstNail-yOfTheCurrentNail)));
            lengthOfTheThread+=(2*PI*radiusOfNails);
            System.out.println( String.format("%.2f", lengthOfTheThread) );
        }
    }
}