Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

49愛的鼓勵 6訂閱站台

Elias code can be used to efficiently encode positive integers when there is no prior information about the cardinality of the integers to be encoded and it is known that the probability of getting a large integer is smaller than or equal to the probability of getting a small integer. For practical reasons, however, in this contest we do pose a limit on the size of the input integers. For the same reason we restrict the input integer to be greater than 1.

Elias developed three variants of the code: the Elias gamma, Elias delta, and Elias omega coding methods. This problem presents the Elias gamma and Elias omega methods and calls for implementing the Elias omega code. The following is a background, definition, and illustration of the problem.

Background

Suppose that Alice wants to transmit a positive integer n to Bob through a binary channel and let (n) stand for the binary representation of n. If Bob knows |(n)| (the number of bits required for the binary representation of n) in advance, then Alice should use (n) for the transmission. On the other hand, if Bob does not have this information, then Alice can first send |(n)|, using efficient and distinguishable encoding, then she can send the actual beta code F₁ = (n). The end result is a two field code < F₁, F₂ >.

Elias code and its variants differ in the way they encode these two pieces of information (F₁ and F₂). The main difference between variants lies in the representation of F₁. This may imply modifications in the representation of F₁. In addition, some of the variants apply repetition or recursion to the representation of F₁. We use a specific variant specified below.

Definition

Formally, in Elias gamma coding, a positive integer n is encoded using two concatenated bit fields. The first field, the prefix, contains log₂n bits of 0 ( x is the floor of x). The second field, the postfix, is the actual binary representation of n using log₂n + 1 bits. For example, the binary representation of the decimal number 9 is 1001. Under Elias coding 9 is encoded as 0001001. The first three leading zeros denote that four bits are required for the binary representation of 9. The next four bits contain the binary representation of 9. Elias delta code applies the gamma code to the prefix( log₂n) of the gamma code and Elias omega code applies a recursion over the prefix Elias gamma representation of log₂n.

Illustration (detailed example)

To further illustrate the Elias omega code, consider the integer 536870907. The binary representation of this integer is 1 1111 1111 1111 1111 1111 1111 1011 which is required 29 bits. Hence, in the first step it is encoded as follows:

where blanks, dots, commas, and brackets, are inserted for readability.

To emphasize, for this contest the recursion stops when the first field of a recursive stage contains one 0.

Looking at all the bits generated by all the steps and using (n) to denote the binary representation of n, we have:

a.

<28 0's, (536870907) > =

<0000 0000 0000 0000 0000 0000 0000, 1 1111 1111 1111 1111 1111 1111 1011>

b.

< <4 0's, (28) > ,(536870907) > =

< <0000, 1 1100>, 1 1111 1111 1111 1111 1111 1111 1011>

c.

< < <2 0's, (4) >, (28) > ,(536870907) > =

< < <00, 100>, 1 1100>, 1 1111 1111 1111 1111 1111 1111 1011>

d.

< < < <one 0, (2) >, (4) >, (28) >, (536870907) > =

< < < <0, 10>, 100>, 1 1100>, 1 1111 1111 1111 1111 1111 1111 1011>

Taking away all the blanks, dots, commas, and brackets we get that the Elias omega code of 536870907 is: 0101001110011111111111111111111111111011. This code is distinguishable (uniquely decodable). It can be decoded in a unique way and yield back the number 536870907.

Problem statement

Given some positive integers in the range of 2...2 x 10⁹, you are to write a program to produce the Elias omega codes for these integers.

Input 

The input contains positive integers each in a separate line. Each integer is in between 2 and ­ 2,000,000,000, inclusive. The end of input is indicated by a zero. The input can contain up to one hundred lines.

Output 

The output consists of lines each corresponding to an input integer except the last zero. Each line contains the Elias omega code of each input integer. The output should not contain any blanks or blank lines.

Sample Input 

2 
510 
7 
120000 
536870905 
49 
5
0

Sample Output 

010 
0111000111111110 
010111 
0101001000011101010011000000 
0101001110011111111111111111111111111001 
010101110001
010101

---

看懂就好做了，沒有什麼難度。

#include <stdio.h>
#include <math.h>
void bNum(int n) {
    if(n) {
        bNum(n/2);
        printf("%d", n%2);
    }
}
void transform(int n) {
    if(n == 1) {
        printf("0");
        return;
    }
    transform((int)log2(n));
    bNum(n);
}
int main() {
    int n;
    while(scanf("%d", &n) == 1 && n) {
        transform(n);
        puts("");
    }
    return 0;
}