Q587: There's treasure everywhere!

/*
  這題要注意誤差，因為double會有誤差
  Run time: 0.010
*/
#include <stdio.h>
#include <stdlib.h> // atoi(str) 要用
#include <string.h> // strlen(str), strcmp(str)要用
#include <ctype.h>  // isdigit(ch) 判斷是否為數字用的
#include <math.h>   // sqrt(2.0) 和 EPS 要用
#define EPS pow(10, -9)  // 誤差要用的, double容易有誤差
#define sqrt2 sqrt(2.0)
char str[201];
int main()
{
  int i;
  int len;
  double move;
  double x, y;
  int cnt = 0;

  while (gets(str))
  {
      if (!strcmp(str, "END"))    break;

      len = strlen(str);
      x = y = 0.0;

      for (i = 0; i < len; i++)
      {
          move = atoi(str+i); // 取出數字

          while (isdigit(str[i])) // 跳過數字到非數字
                i++;

          // N, E, S, W 四種方向其中之一
          if (str[i+1] == ',' || str[i+1] == '.')
          {
              switch (str[i])
              {
                  case 'N': y += move; break;
                  case 'E': x += move; break;
                  case 'S': y -= move; break;
                  case 'W': x -= move; break;
              }
              i++;
          }

          // NE, NW, SE, SW 四種方向其中之一
          else
          {
              // 座標要取cos(PI/4), sin(PI/4)

              move /= sqrt2;

              switch (str[i])
              {
                  case 'N':
                      x += (str[i+1] == 'E') ? move : -move;
                      y += move;
                      break;
                  case 'S':
                      x += (str[i+1] == 'E') ? move : -move;
                      y -= move;   break;
              }

              i+=2;
          }
      }
      printf("Map #%d\n", ++cnt);
      printf("The treasure is located at (%.3lf,%.3lf).\n", EPS+x, EPS+y);
      printf("The distance to the treasure is %.3lf.\n\n", EPS+sqrt(x*x+y*y));
  }

}