Problem B #Round1C

b2.cc

#include <iostream>
#include <cstdio>
#include <cmath>
#include <string>
#include <vector>
using namespace std;

#define all(c)  (c).begin(),(c).end()
#define repN(var,n)  for(int var=1;var<=(n);var++)

inline int a(int x, int y) {
  return abs(x) + abs(y);
}
string solve(int X, int Y) {
  int axy = a(X,Y);
  int m_max = axy*2;
  int m_min = sqrt(axy*2) - 1;
  for (int m=m_min; m<=m_max; ++m) {
    vector<char> cs;
    int x = X, y = Y;
    for (int v=m; v>=1; --v) {
      if (a(v-abs(x),y) < a(x,v-abs(y))) {
        if (x > 0) {
          cs.push_back('E');
          x -= v;
        } else {
          cs.push_back('W');
          x += v;
        }
      } else {
        if (y > 0) {
          cs.push_back('N');
          y -= v;
        } else {
          cs.push_back('S');
          y += v;
        }
      }
    }
    if (a(x,y) == 0) {
      reverse(all(cs));
      return string(all(cs));
    }
  }
  return "?";
}

main(){
  int _T; cin>>_T;
  repN(_t,_T) {
    int X, Y; cin >> X >> Y;
    cout << "Case #" << _t << ": " << solve(X,Y) << endl;
  }
}