### dificilcoder's blog

By dificilcoder, history, 6 months ago, How to arrive at the correct solution which solves for large input values?

Problem : Hard Compare...

Question

Given 4 numbers A,B,C and D. If AB > CD, print "YES" otherwise, print "NO".

Input
Only one line containing 4 numbers A,B,C and D (1≤A,C≤107) , (1≤B,D≤1012)

Output
Print "YES" or "NO" according to the problem above.

My Program

    #include <iostream>
#define ll long long
using namespace std;

int main(){

ll res1, res2, a, b, c, d;
cin>>a>>b>>c>>d;
res1 = 1;
res2 = 1;
for(int i=1;i<=b; i++){
res1 = a % ((int)1e9+7) *  res1 % ((int)1e9+7);
}
for(int i=1;i<=d; i++){
res2 = c % ((int)1e9+7) *  res2 % ((int)1e9+7);
}

cout<<(res1>res2 ? "YES" : "NO");
return 0;
}


TestCases

Input : 2887969 614604076030 8478041 209676100616

Input : 8376260 70 8376259 70

Input : 2 1 1 1

Input : 1 7816997 1 1  Comments (8)
•  » » » Since $A, B, C, D > 1$We have $AB > CD \Leftrightarrow log_k(AB) > log_k(CD)$ for $k > 1$ You can also try $\frac{A}{C} > \frac{D}{B}$