[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：

  1 #include <stdio.h>

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

  3 #include <time.h>   // for time()

  4 

  5 int which_sum_is_near_number( const int *array_number,

  6                               const int n_len,

  7                               const int equal_number )

  8 {

  9     int start_index = n_len - 1,

 10         *array_path = NULL,

 11         path_index  = 0,

 12         tmp_summary = 0,    // 计算临时和

 13         min_diff    = array_number[n_len - 1];    // 计算最小差值

 14 

 15     // 检查函数参数

 16     if ( NULL == array_number || n_len <= 0

 17         || equal_number <= 0 )

 18     {

 19         printf( "Error for argument.\n" );

 20         return -1;

 21     }

 22 

 23     // 分配计算路径存储空间

 24     array_path = (int *) calloc( n_len, sizeof(int) );

 25     if ( NULL == array_path )

 26     {

 27         printf( "Out of memory.\n" );

 28         return -1;

 29     }

 30 

 31     // 计算差值

 32     for ( ; start_index >= 0; --start_index )

 33     {

 34         tmp_summary += array_number[start_index];

 35 

 36         // 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，

 37         // 则排除本次计算值

 38         if ( tmp_summary > equal_number

 39             || ( equal_number - tmp_summary ) > min_diff )

 40         {

 41             tmp_summary -= array_number[start_index];

 42             continue;

 43         }

 44 

 45         // 添加路径元素

 46         array_path[path_index++] = array_number[start_index];

 47         // 更新最小差值

 48         min_diff = equal_number - tmp_summary;

 49         if ( tmp_summary == equal_number )

 50         {

 51             break;

 52         }

 53     }

 54 

 55     // 输出计算的路径值

 56     printf( "\nThe elements of path is \n" );

 57     while ( --path_index >= 0 )

 58     {

 59         printf( " %d", array_path[path_index] );

 60     }

 61     printf( "\n" );

 62     printf( "The difference is %d.\n", min_diff );

 63 

 64     // 释放空间

 65     free( array_path );

 66     array_path = NULL;

 67 

 68     return min_diff;

 69 }

 70 

 71 int compare_int( const void *lhs, const void *rhs )

 72 {

 73     return *(int *)lhs - *(int *)rhs;

 74 }

 75 

 76 void test_function()

 77 {

 78     const int array_size = 20;

 79     int array_number[array_size],

 80         start_index = 0,

 81         equal_number = 0;

 82 

 83     srand( (unsigned) time(0) );

 84     for ( ; start_index < array_size; ++start_index )

 85     {

 86         array_number[start_index] = rand() % 100;

 87     }

 88     equal_number = rand() % 200;

 89 

 90     // sorting

 91     qsort( array_number, array_size, sizeof(int), compare_int );

 92 

 93     printf( "\nThe elements in array is \n" );

 94     for ( start_index = 0; start_index < array_size; ++start_index )

 95         printf( " %d", array_number[start_index] );

 96     printf( "\nThe number is %d.\n", equal_number );

 97 

 98     which_sum_is_near_number( array_number, array_size, equal_number );

 99 }

100 

101 int main()

102 {

103     test_function();

104 

105     return 0;

106 }

View Code

　　

　　有问题欢迎大家知道！！