In this HackerEarth Three rectangles problem solution, You are given a rectangle of height H and width W. You must divide this rectangle exactly into three pieces such that each piece is a rectangle of integral height and width. You are required to minimize Area(max) - Area(min) where Area(max) is the area of the largest rectangle and Area(min) is the area of the smallest rectangle, among all three rectangle pieces.


HackerEarth Three rectangles problem solution


HackerEarth Three rectangles problem solution.

#include<bits/stdc++.h>
using namespace std;

#define F first
#define S second
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define vi vector<int>
#define all(x) x.begin(),x.end()
#define fix fixed<<setprecision(10)
#define rep(i,a,b) for(int i=int(a);i<=int(b);i++)
#define repb(i,b,a) for(int i=int(b);i>=int(a);i--)
#define FastIO ios_base::sync_with_stdio(0),cin.tie(0)

typedef double db;
typedef long long ll;

const int N=2e5+5;
const int mod=1e9+7;

void solve(){
ll h,w;
cin>>h>>w;
ll ans=1e18;
rep(i,1,h-1){
ll nh=h-i,nw=w;
ll maxi=max({i*nw,nh/2*nw,(nh-nh/2)*nw});
ll mini=min({i*nw,nh/2*nw,(nh-nh/2)*nw});
ans=min(ans,maxi-mini);
maxi=max({i*nw,nw/2*nh,(nw-nw/2)*nh});
mini=min({i*nw,nw/2*nh,(nw-nw/2)*nh});
ans=min(ans,maxi-mini);
}
rep(i,1,w-1){
ll nw=w-i,nh=h;
ll maxi=max({i*nh,nw/2*nh,(nw-nw/2)*nh});
ll mini=min({i*nh,nw/2*nh,(nw-nw/2)*nh});
ans=min(ans,maxi-mini);
maxi=max({i*nh,nh/2*nw,(nh-nh/2)*nw});
mini=min({i*nh,nh/2*nw,(nh-nh/2)*nw});
ans=min(ans,maxi-mini);
}
cout<<ans<<'\n';
}

signed main(){
FastIO;
int t;
cin>>t;
while(t--) solve();
return 0;
}

Second solution

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

const int N = 1e5 + 14;

int solve(int h, int w) {
int ans = INT_MAX;
for (auto x : {(ll) w * h / (3 * h / 2), (ll) w * h / (3 * h / 2) + 1})
ans = min<ll>(ans, max({abs(x * ll(h / 2) - ll(w - x) * h), x * ll((h + 1) / 2) - ll(w - x) * h, h % 2 * x}));
return ans;
}

int main() {
ios::sync_with_stdio(0), cin.tie(0);
int t;
cin >> t;
while (t--) {
int h, w;
cin >> h >> w;
cout << min({h % 3 == 0 || w % 3 == 0 ? 0 : min(h, w), solve(h, w), solve(w, h)}) << '\n';
}
}