HDU 4814 Golden Radio Base(2013 ACM/ICPC 长春赛区现场赛)

Golden Radio Base

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1219    Accepted Submission(s): 494

Problem Description

Golden ratio base (GRB) is a non-integer positional numeral system that uses the golden ratio (the irrational number (1+√5)/2 ≈ 1.61803399 symbolized by the Greek letter φ) as its base. It is sometimes referred to as base-φ, golden mean base, phi-base, or, phi-nary.

Any non-negative real number can be represented as a base-φ numeral using only the digits 0 and 1, and avoiding the digit sequence "11" – this is called a standard form. A base-φ numeral that includes the digit sequence "11" can always be rewritten in standard form, using the algebraic properties of the base φ — most notably that φ + 1 = φ ² . For instance, 11(φ) = 100(φ). Despite using an irrational number base, when using standard form, all on-negative integers have a unique representation as a terminating (finite) base-φ expansion. The set of numbers which possess a finite base-φ representation is the ring Z[1 + √5/2]; it plays the same role in this numeral systems as dyadic rationals play in binary numbers, providing a possibility to multiply.

Other numbers have standard representations in base-φ, with rational numbers having recurring representations. These representations are unique, except that numbers (mentioned above) with a terminating expansion also have a non-terminating expansion, as they do in base-10; for example, 1=0.99999….

Coach MMM, an Computer Science Professor who is also addicted to Mathematics, is extremely interested in GRB and now ask you for help to write a converter which, given an integer N in base-10, outputs its corresponding form in base-φ.

 

Input

There are multiple test cases. Each line of the input consists of one positive integer which is not larger than 10^9. The number of test cases is less than 10000. Input is terminated by end-of-file.

 

Output

For each test case, output the required answer in a single line. Note that trailing 0s after the decimal point should be wiped. Please see the samples for more details.

 

Sample Input

123610

 

Sample Output

110.01100.011010.000110100.0101
Hint
 

 

Source

2013 Asia Regional Changchun

 

Recommend

liuyiding

题意：

给你一个数字让你把他转化成无理数进制的形式并且只用01表示（同时不能出现相邻数字都是1）

思路：

这一题其他大佬的博客我第一眼直接看不懂，后来自己悟出来了，决定自己写清楚。

首先我的第一感觉就是这题的结果不是最终那个数，但是显然不是的。比如这题的10.01为什么是2很好懂的，按照进制转换的规则，是不是φ+φ^-2，这里这个数就是等于2。我们将数组的第50个元素首先设置为n，然后向两边扩散。

代码：

#include<cstdio>#include<cstring>#include<algorithm>#include<cmath>#include<iostream>#include<queue>using namespace std;const int MAXN = 205;int main(){    int a[MAXN],n,bas=100,flag;    while(scanf("%d",&n)!=EOF)    {        memset(a,0,sizeof(a));        a[50] = n,flag = 1;        while(flag)        {            flag = 0;            for(int i = 2; i < 100; i++)                if(a[i]>1)                {                    a[i-2]+=a[i]/2;                    a[i+1]+=a[i]/2;                    a[i]%=2;                    flag = 1;                }            for(int i = 0; i<100;i++)                if(a[i]&&a[i+1])                {                    int tmp = min(a[i],a[i+1]);                    a[i+2]+=tmp;                    a[i]-=tmp;                    a[i+1]-=tmp;                    flag = 1;                }        }        int st,ed;        for(int i = 100; i >= 0; i--)            if(a[i]){st = i;break;}        for(int i = 0; i < 100; i++)            if(a[i]){ed = i;break;}        for(int i = st; i >= ed; i--)        {            if(i==49) printf(".");            printf("%d",a[i]);        }        printf("\n");    }    return 0;}