1213. Massive Numbers

The number is called massive if it is represented in the form a^n, which means a raised in power n. You need to compare two massive numbers a^b and c^d, written in the form “<base>^<exponent>”.

Given two massive numbers, print the biggest one.

Input. Two massive numbers a and b in the form “<base>^<exponent>”. It is known that 1 ≤ <base>, <exponent> ≤ 1000.

Output. The biggest number among a and b.

Sample input	Sample output
3^100 2^150	3^100

SOLUTION

mathematics

Algorithm analysis

Take the logarithm on both sides of an inequality a^b < c^d and get b lg a < d lg c. The values of expressions b lg a and d lg c fit into the double type, so to compare them is not difficult.

Algorithm realization

Read the input data. Separate the base and exponent for each number.

scanf("%d^%d %d^%d",&a,&b,&c,&d);

Compare the logarithms of expressions b lg a and d lg c, then print the answer.

if (b * log(1.0 * a) < d * log(1.0 * c)) printf("%d^%d\n",c,d);

else printf("%d^%d\n",a,b);

Java realization

import java.util.*;

public class Main

{

public static void main(String[] args)

{

Scanner con = new Scanner(System.in);

String s = con.nextLine();

StringTokenizer st = new StringTokenizer(s," ^");

int a = Integer.valueOf(st.nextToken()),

b = Integer.valueOf(st.nextToken()),

c = Integer.valueOf(st.nextToken()),

d = Integer.valueOf(st.nextToken());

if(b * Math.log(a) > d * Math.log(c))

System.out.println(a + "^" + b);

else

System.out.println(c + "^" + d);

}

}

Java realization – Scanner, delimiter

import java.util.*;

public class Main

{

public static void main(String[] args)

{

Scanner con = new Scanner(System.in).useDelimiter("\\s|\\^");

//System.out.println(con.delimiter());

int a = con.nextInt();

int b = con.nextInt();

int c = con.nextInt();

int d = con.nextInt();

if(b * Math.log(a) > d * Math.log(c))

System.out.println(a + "^" + b);

else

System.out.println(c + "^" + d);

con.close();

}

}