ACM UVA (701)

/*
 *******************************************************************************
 *
 * Filename: 701.c
 *
 * Version: 0.1
 *
 * Author: Ye Xiaofeng , yexfeng # gmail.com
 *
 *******************************************************************************
 */

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

int length(unsigned in)
{
    int len = 0;
    
    if (in < 10) {
        return 1;
    } else {
        while (in > 0) {
            in /= 10;
            len++;
        }
    }

    return len;
}

void process(unsigned int in)
{
    int k;
    int e;
    double left, right;
    double log_2;
    double log_10;
    double d1;
    double d2;
    double d3;
    double d4;

    log_2 = log(2);
    log_10 = log(10);
    d1 = log(in) / log_2;
    d2 = log_10 / log_2;
    d3 = log(in+1) / log_2;
    d4 = log_10 / log_2;

    k = length(in) + 1;
    left = d1 + k * d2;
    right = d3 + k * d4;
    e = (int)ceil(left);
    while (e >= right) {
        k++;
        left = d1 + k * d2;
        right = d3 + k * d4;
        e = (int)ceil(left);
    }
    printf("%d\n", e);
}

int main(int argc, char *argv)
{
    unsigned int in;

    while (scanf("%u", &in) != EOF) {
        process(in);
    }

    return 0;
}