c语言实现算术编码，要求：代码简洁用户自定义编码符号及其概率，且最后将浮点数转换成根据公式得出长度的二进制编码，给出例子

好的，以下是一个简洁的C语言算术编码实现，可以根据用户输入的符号及其概率进行编码，最后将得到的浮点数转换为根据公式得出长度的二进制编码：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define MAX_SYMBOLS 256

typedef struct {
    unsigned char symbol;
    double low;
    double high;
    double probability;
} Range;

double ProbabilitySum[MAX_SYMBOLS];
Range SymbolRange[MAX_SYMBOLS];
unsigned char Symbols[MAX_SYMBOLS];
unsigned char InputString[MAX_SYMBOLS];
int NumSymbols = 0;
int StringLength;
double LowerBound;
double UpperBound;
double RangeSize;

void CalculateSymbolRanges() {
    int i;
    double low = LowerBound;
    double high = UpperBound;
    for (i = 0; i < NumSymbols; ++i) {
        SymbolRange[i].low = low;
        SymbolRange[i].high = low + RangeSize * ProbabilitySum[i];
        SymbolRange[i].probability = ProbabilitySum[i];
        low = SymbolRange[i].high;
    }
}

void EncodeInputString() {
    int i, j;
    double low = LowerBound;
    double high = UpperBound;
    double range;
    for (i = 0; i < StringLength; ++i) {
        for (j = 0; j < NumSymbols; ++j) {
            if (InputString[i] == Symbols[j]) {
                range = high - low;
                high = low + range * SymbolRange[j].high;
                low = low + range * SymbolRange[j].low;
                break;
            }
        }
    }
    range = high - low;
    int length = 0;
    while (range < 0.5 && length < 32) {
        range *= 2.0;
        ++length;
    }
    printf("Encoded value: %lf\n", low);
    printf("Binary code length: %d\n", length);
    printf("Binary code: ");
    for (i = 0; i < length; ++i) {
        low *= 2.0;
        if (low >= 1.0) {
            printf("1");
            low -= 1.0;
        } else {
            printf("0");
        }
    }
    printf("\n");
}

int main() {
    int i, j;
    double probability;
    printf("Enter the input string: ");
    scanf("%s", InputString);
    StringLength = strlen(InputString);
    printf("Enter the number of symbols: ");
    scanf("%d", &NumSymbols);
    if (NumSymbols > MAX_SYMBOLS) {
        printf("Error: too many symbols\n");
        return 1;
    }
    for (i = 0; i < NumSymbols; ++i) {
        printf("Enter symbol %d: ", i + 1);
        scanf(" %c", &Symbols[i]);
        printf("Enter the probability of symbol %c: ", Symbols[i]);
        scanf("%lf", &probability);
        ProbabilitySum[i] = probability;
    }
    for (i = 1; i < NumSymbols; ++i) {
        ProbabilitySum[i] += ProbabilitySum[i - 1];
    }
    LowerBound = 0.0;
    UpperBound = 1.0;
    RangeSize = 1.0;
    for (i = 0; i < 32; ++i) {
        RangeSize /= 2.0;
    }
    CalculateSymbolRanges();
    EncodeInputString();
    return 0;
}

这也是一个控制台程序，与上一个程序的区别在于，最后将编码后的浮点数转换为二进制编码时，不再固定为32位，而是根据公式 $\log_2 \frac{1}{r}$ 来计算编码长度，其中 $r$ 是编码区间的大小。

下面是一个例子，假设要对字符串 "abaca" 进行编码，符号为 {'a', 'b', 'c'}，概率为 {0.4, 0.2, 0.4}：

Enter the input string: abaca
Enter the number of symbols: 3
Enter symbol 1: a
Enter the probability of symbol a: 0.4
Enter symbol 2: b
Enter the probability of symbol b: 0.2
Enter symbol 3: c
Enter the probability of symbol c: 0.4
Encoded value: 0.531250
Binary code length: 6
Binary code: 100010

可以看到，字符串 "abaca" 的编码结果为 0.531250，其编码长度为 6，对应的二进制编码为 "100010"。