November 2013 Bronze (Correction 2) Problem 1: Combination Lock

Result: 10/10 **********

This is more optimized than my previous correction though still in O(1) time.

combo2.cpp

#include <iostream>
#include <fstream>

#define loopi(x) loop_start(i,x,0)
#define loopj(x) loop_start(j,x,0)
#define loop_start(i, x,s) for(int i = (s); i < (x); ++i)
#define loop_rev(a,x,stop) for(int a = (x); a >= (stop); --a)

using namespace std;

int N;

// based on http://math.stackexchange.com/questions/494971/how-to-determine-the-number-of-degrees-overlap-between-two-circular-slices
int abswrap(int diff){
 // diff = wrap(diff)
 // diff if -N/2 <= diff <= N/2
 // diff + N if diff < -N/2
 if(diff < -N/2)
  diff += N;
 // diff - N if diff > N/2
 else if(diff > N/2)
  diff -= N;
 // return abs(wrap(diff))
 return abs(diff);
}
int overlap(int a, int b){
 // 2.5 + 2.5 - abswrap(a - b)
 // but 0 if negative
 return max(0, 5 - abswrap(a - b));
}

#define NUMCOMBO 3
int main() {
 ofstream fout ("combo.out");
 ifstream fin ("combo.in");
 // get input
 int combo1[NUMCOMBO];
 int combo2[NUMCOMBO];
 fin >> N;
 loopi(NUMCOMBO)
  fin >> combo1[i];
 loopi(NUMCOMBO)
  fin >> combo2[i];
 // calculate:
 // Special case: there is always N overlap if N <= 5
 if(N <= 5) // 2 * N ** 3 - N ** 3 = N ** 3
  // write output
  fout << (N * N * N);
 else{
  int overlap_a = overlap(combo1[0], combo2[0]);
  int overlap_b = overlap_a ? overlap(combo1[1], combo2[1]) : 0;
  int overlap_c = overlap_b ? overlap(combo1[2], combo2[2]) : 0;
  // 2 * 5 ** 3, but subtract the overlap
  // write output
  fout << (250 - overlap_a * overlap_b * overlap_c);
 }
 return 0;
}