2014
01-05

Verdis Quo

The Romans used letters from their Latin alphabet to represent each of the seven numerals in their number system. The list below shows which
letters they used and what numeric value each of those letters represents:

I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000

Using these seven numerals, any desired number can be formed by following the two basic additive and subtractive rules. To form a number using
the additive rule the Roman numerals are simply written from left to right in descending order, and the value of each roman numeral is added
together. For example, the number MMCLVII has the value 1000 + 1000 + 100 + 50 + 5 + 1 + 1 = 2157. Using the addition rule alone could lead to
very long strings of letters, so the subtraction rule was invented as a result. Using this rule, a smaller Roman numeral to the left of a larger one is
subtracted from the total. In other words, the number MCMXIV is interpreted as 1000 – 100 + 1000 + 10 – 1 + 5 = 1914.

Over time the Roman number writing system became more standardized and several additional rules were developed. The additional rules used today
are:

1. The I, X, or C Roman numerals may only be repeated up to three times in succession. In other words, the number 4 must be represented as IV
and not as IIII.
2. The V, L, or D numerals may never be repeated in succession, and the M numeral may be repeated as many 2. times as necessary.
3. Only one smaller numeral can be placed to the left of another. For example, the number 18 is represented as XVIII but not as XIIX.
4. Only the I, X, or C can be used as subtractive numerals.
5. A subtractive I can only be used to the left of a V or X. Likewise a X can only appear to the left of a L or C, and a C can only be used to the
left of a D or M. For example, 49 must be written as XLIX and not as IL.

Your goal is to write a program which converts Roman numbers to base 10 integers.

The input to this problem will consist of the following:

A line with a single integer "N" (1 ≤ N ≤ 1000), where N indicates how many Roman numbers are to be converted.
A series of N lines of input with each line containing one Roman number. Each Roman number will be in the range of 1 to 10,000 (inclusive)
and will obey all of the rules laid out in the problem’s introduction.

The input to this problem will consist of the following:

A line with a single integer "N" (1 ≤ N ≤ 1000), where N indicates how many Roman numbers are to be converted.
A series of N lines of input with each line containing one Roman number. Each Roman number will be in the range of 1 to 10,000 (inclusive)
and will obey all of the rules laid out in the problem’s introduction.

3
IX
MMDCII
DXII

9
2602
512

#include"stdio.h"
#include"string.h"
#define N 33000
int a[N];
int bit(int x)
{
return x&(-x);
}
int sum(int x)
{
int i;
int ans=0;
for(i=x;i>0;i-=bit(i))
ans+=a[i];
return ans;
}
{
int i;
for(i=x;i<N;i+=bit(i))
a[i]++;
}
int main()
{
int i;
int n;
int A[N/2];
while(scanf("%d",&n)!=-1)
{
memset(a,0,sizeof(a));
memset(A,0,sizeof(A));
int x,y;
for(i=0;i<n;i++)
{
scanf("%d%d",&x,&y);
x++;
A[sum(x)]++;
}
for(i=0;i<n;i++)
printf("%d\n",A[i]);
}
return 0;
}


1. 约瑟夫也用说这么长……很成熟的一个问题了，分治的方法解起来o(n)就可以了，有兴趣可以看看具体数学的第一章，关于约瑟夫问题推导出了一系列的结论，很漂亮

2. 很高兴你会喜欢这个网站。目前还没有一个开发团队，网站是我一个人在维护，都是用的开源系统，也没有太多需要开发的部分，主要是内容整理。非常感谢你的关注。