A - Seismic magnitude scales

Time Limit: \(2\; sec\) / Memory Limit: \(1024\; MB\)

Score : \(100\; points\)

Problem Statement|題目描述

• The magnitude of an earthquake is a logarithmic scale of the energy released by the earthquake. It is known that each time the magnitude increases by \(1\), the amount of energy gets multiplied by approximately \(32\)

  .

• 地震的震級是地震釋放能量的對數尺度。已知震級每增加 \(1\) ，能量就會變為原來的大約 \(32\) 倍。

• Here, we assume that the amount of energy gets multiplied by exactly \(32\) each time the magnitude increases by \(1\). In this case, how many times is the amount of energy of a magnitude \(A\) earthquake as much as that of a magnitude \(B\)

  earthquake?

• 在本題中，我們假設每次震級增加 \(1\) 時，能量正好乘以 \(32\) 。在這種情況下， \(A\) 地震的能量是 \(B\) 級地震能量的多少倍？

Constraints|資料範圍

• \(3\leq B\leq A\leq 9\)
• \(A\) and \(B\) are integers.
• \(3\leq B\leq A\leq 9\)
• \(A\) 和 \(B\) 均為整數。

Input|輸入

• Input is given from Standard Input in the following format:
  A B

• 輸入為以下格式的標準輸入：
  A B

Output|輸出

• Print the answer as an integer.

• 輸出一個整數答案。

Sample Input 1 |樣例輸入 1

6 4

Sample Output 1 |樣例輸出 1

1024

• \(6\) is \(2\) greater than \(4\), so a magnitude \(6\) earthquake has \(32\times 32=1024\) times as much energy as a magnitude \(4\) earthquake has.
• \(6\) 級地震的能量是 \(4\)級地震的 \(32\times 32=1024\) 倍。

Sample Input 2 |樣例輸入 2

5 5

Sample Output 2 |樣例輸出 2

1

• Earthquakes with the same magnitude have the same amount of energy.
• 相同震級的地震具有相同的能量。

分析

作為一個謹慎的人，我終究還是開了\(long\;long\)，又用了快速冪。

AC程式碼奉上

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
inline ll power(ll a,ll b){
	if(!b)return 1;
	ll ans=1;
	while(b){
		if(b&1)ans=ans*a;
		b>>=1;
		a*=a;
	}
	return ans;
}
int main(){
	freopen("magnitude.in","r",stdin);
	freopen("magnitude.out","w",stdout);
	int a,b;
	cin>>a>>b;
	cout<<power(32,a-b);
	return 0;
}