[算法 笔记] 求近似和

　　问题出自blog：http://blog.csdn.net/v_july_v/article/details/6803368

　　问题描述：有n个正实数（按照大小升序排列），另一个实数m。需要算出若干个x，使这个几个x的和与m最接近。请描述实现算法啊，并指出算法复杂度。

　　利用贪婪算法，从后向前仅考虑当前计算结果最接近实数m的值，时间复杂度O（n）

　　源代码：

#include <stdio.h>
#include <stdlib.h> // for srand(), rand()
#include <time.h>   // for time()

int which_sum_is_near_number( const int *array_number,
                              const int n_len,
                              const int equal_number )
{
    int start_index = n_len - 1,
        *array_path = NULL,
        path_index  = 0,
        tmp_summary = 0,    // 计算临时和
        min_diff    = array_number[n_len - 1];    // 计算最小差值

    // 检查函数参数
    if ( NULL == array_number || n_len <= 0
        || equal_number <= 0 )
    {
        printf( "Error for argument.
" );
        return -1;
    }

    // 分配计算路径存储空间
    array_path = (int *) calloc( n_len, sizeof(int) );
    if ( NULL == array_path )
    {
        printf( "Out of memory.
" );
        return -1;
    }

    // 计算差值
    for ( ; start_index >= 0; --start_index )
    {
        tmp_summary += array_number[start_index];

        // 若计算的临时和大于要求值或计算差值大于当前最小差值，
        // 则排除本次计算值
        if ( tmp_summary > equal_number
            || ( equal_number - tmp_summary ) > min_diff )
        {
            tmp_summary -= array_number[start_index];
            continue;
        }

        // 添加路径元素
        array_path[path_index++] = array_number[start_index];
        // 更新最小差值
        min_diff = equal_number - tmp_summary;
        if ( tmp_summary == equal_number )
        {
            break;
        }
    }

    // 输出计算的路径值
    printf( "
The elements of path is 
" );
    while ( --path_index >= 0 )
    {
        printf( " %d", array_path[path_index] );
    }
    printf( "
" );
    printf( "The difference is %d.
", min_diff );

    // 释放空间
    free( array_path );
    array_path = NULL;

    return min_diff;
}

int compare_int( const void *lhs, const void *rhs )
{
    return *(int *)lhs - *(int *)rhs;
}

void test_function()
{
    const int array_size = 20;
    int array_number[array_size],
        start_index = 0,
        equal_number = 0;

    srand( (unsigned) time(0) );
    for ( ; start_index < array_size; ++start_index )
    {
        array_number[start_index] = rand() % 100;
    }
    equal_number = rand() % 200;

    // sorting
    qsort( array_number, array_size, sizeof(int), compare_int );

    printf( "
The elements in array is 
" );
    for ( start_index = 0; start_index < array_size; ++start_index )
        printf( " %d", array_number[start_index] );
    printf( "
The number is %d.
", equal_number );

    which_sum_is_near_number( array_number, array_size, equal_number );
}

int main()
{
    test_function();

    return 0;
}

　　

　　有问题欢迎大家知道！！