UVA 575-Skew Binary

最新推荐文章于 2017-09-06 09:20:28 发布

原创最新推荐文章于 2017-09-06 09:20:28 发布 · 731 阅读

0 ·

CC 4.0 BY-SA版权

文章标签：

#Skew Binary #Uva

数论专栏收录该内容

29 篇文章

订阅专栏

本文介绍了如何将A-SkewBinary编码的数转换为十进制数，并提供了相应的C++代码实现。通过解析输入字符串并应用特定公式，可以轻松完成编码转换。

A - Skew Binary

Time Limit:3000MS Memory Limit:0KB 64bit IO Format:%lld & %llu

Description

When a number is expressed in decimal, the k-th digit represents a multiple of10^k. (Digits are numbered from right to left, where the least significant digit is number 0.) For example,

$\begin{displaymath}81307_{10} = 8 \times 10^4 + 1 \times 10^3 + 3 \times 10^2 + ......mes 10^1 +7 \times 10 0 = 80000 + 1000 + 300 + 0 + 7= 81307.\end{displaymath}$

When a number is expressed in binary, the k-th digit represents a multiple of2^k. For example,

$\begin{displaymath}10011_2 = 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 +1 \times 2^0 = 16 + 0 + 0 + 2 + 1 = 19.\end{displaymath}$

In skew binary, the k-th digit represents a multiple of2^k⁺¹ - 1. The only possible digits are 0 and 1, except that the least-significant nonzero digit can be a 2. For example,

$\begin{displaymath}10120_{skew} = 1 \times (2^5 - 1) + 0 \times (2^4-1) + 1 \tim......2 \times (2^2-1) + 0 \times (2^1-1)= 31 + 0 + 7 + 6 + 0 = 44.\end{displaymath}$

The first 10 numbers in skew binary are 0, 1, 2, 10, 11, 12, 20, 100, 101, and 102. (Skew binary is useful in some applications because it is possible to add 1 with at most one carry. However, this has nothing to do with the current problem.)

10120
200000000000000000000000000000
10
1000000000000000000000000000000
11
100
11111000001110000101101102000
0

Sample Output

题目大意：

给你一个斜二进制的数，叫你算出他的十进制。

题目解析：

这题很简单没什么难度，把字符串转化为数字。再按照题目所给的公式，计算输出就好了。

#include<iostream>
#include<string>
#include<math.h>

using namespace std;

int main() {
	string num;
	while(cin>>num) {
		if(num == "0")
			break;
		int len = num.size();
		long long sum = 0;
		int tmp;
		for(int i=0;i<len;i++) {
			tmp = num[i]-'0';
			sum += tmp * (pow(2,len-i) - 1);
		}
		cout<<sum<<endl;	
	}
	return 0;
}