Six Faces of a Box
National Olympiad — Regional round
Submission name: box.cpp
Problem summary
Six rectangular panels must be used as the six faces of a rectangular box. Panels may be rotated. Determine its volume if assembly is possible.
Input
Six pairs w h.
Output
The volume, or 0 if impossible.
Constraints
1 ≤ w,h ≤ 10000.
Worked example
An independently prepared example for this explanation.
Input
2 3 4 2 3 4 3 2 2 4 4 3
Output
24
Solution analysis
- Normalize each face so its shorter side comes first, then sort the six pairs.
- Opposite faces must form three equal pairs. For dimensions a≤b≤c, the sorted distinct face slots are (a,b),(a,c),(b,c).
- Check the shared dimensions and multiply a·b·c using 64 bits.
Why it works
Every rectangular box has exactly these paired faces. Conversely, matching these pairs constructs the required box.
Complexity: O(1) time and space (six faces).
Watch out. Cubes and repeated dimensions are valid; volume can exceed 32 bits.
Commented C++17 solution
An independently written complete program with standard headers.
// Key idea: Every rectangular box has exactly these paired faces. Conversely, matching these pairs
// constructs the required box.
#include<iostream>
#include<vector>
#include<algorithm>
#include<utility>
using namespace std;
int main(){
vector<pair<long long,long long>>f(6);
for(auto&[a,b]:f){
cin>>a>>b;
if(a>b){
swap(a,b);
}
}
sort(f.begin(),f.end());
bool ok=f[0]==f[1]&&f[2]==f[3]&&f[4]==f[5]&&f[0].first==f[2].first&&
f[0].second==f[4].first&&f[2].second==f[4].second;
cout<<(ok?f[0].first*f[0].second*f[2].second:0)<<'\n';
}