关于数据结构，关于算法，关于hash桶算法

       在之前，我都从来不看重数据结构和算法的执行效率，什么时间复杂度和空间复杂度搞得我头晕，但是前几天逄洪江给我出了一道题，在我用两种算法实际比较后发现算法真的很重要。题目大意如下：从一个随机数组中，找出两数相加之和等于5的所有结果。

        当时我想也没想就用嵌套for循环做了出来，但是他让我用一亿个数据和20万范围去测试，结果我的算法直接死机……用十万条数据去计算，也用了十多秒的时间才算完。后来逄洪江给我介绍了hash桶算法，大意是生成20万大小的数组作为桶 ，如果数组中存在某数据，就在桶中同一下标数据变为1，不存在则为0。然后把桶中数据用快速排序轮一遍，相加等于5的数据存入链表中即可。此算法时间复杂度可以达到O(n)的水平。我实现算法后，才测试了一下，同样是一亿数据，20万范围，最快3.7秒全部处理完！这就是算法的力量！

       桶算法主要代码如下：//忽略了与之配套的chain.c文件，该文件是链表生成，链表添加，结构设计部分。             

#include <stdio.h>
#include <stdlib.h>
#include "chain.c" //include the chain.c to create chain and list
#define NUMBER_SCOPE 69000
#define ARRAY_SIZE 100000000
#define PLUS_RESULT 5
    
int *createArray(long length){
    int i;
    int *array=(int*)malloc(length*sizeof(int));
    srand((int)time(0));
    printf("Array:");
    for(i = 0;i<length;i++){
        array[i]=rand()%NUMBER_SCOPE - (NUMBER_SCOPE)/2;
        //printf("%d,",array[i]);
    }
    return array;
}
    
/*
find the max number from a array 
*/
int maxNum(int *array,int length){
    int i,max;
    max = array[0];
    for(i = 1;i<length;i++){
        if(array[i] > max){
            max = array[i];
        }
    }
    return max;
}
/*
find the min number from a array 
*/
int minNum(int *array,int length){
    int i,min;
    min = array[0];
    for(i = 1;i<length;i++){
        if(array[i] < min){
            min = array[i];
        }
    }
    return min;
}
/*
this function to fill barrel ,first parameter is the barrel,second is array
*/
int *fillBarrel(int *barrel,int *array){
    int i,site;
    for(i = 0;i < ARRAY_SIZE;i++){
        site = array[i] - barrel[1] + 3;
        barrel[site] = 1;
    }
    return barrel;
}
/*
this function get a barrel array ,return a result chain,
it create by Quick Sort
*/
struct chain *createResult(int *barrel){
    int l_site,r_site,l_index,r_index;
    struct chain *result;
    struct list lst;
    l_index = 3;
    r_index = barrel[0] - 1;
    while(l_index < r_index && 1){
        if((barrel[l_index] == 1) && (barrel[r_index] == 1)){
            l_site = l_index - 3 + barrel[1];
            r_site = r_index - 3 + barrel[1];
            // printf("\nl_site = %d\tr_site = %d",l_site,r_site);
            // printf("\nbarrel[%d] = %d \nbarrel[%d] = %d",l_index,barrel[l_index],r_index,barrel[r_index]);
            if((l_site + r_site) == PLUS_RESULT){
                lst.firstNum  = l_site;
                lst.secondNum = r_site;
                /*add in chain*/
                result = addlink(result,lst);
                l_index ++;
                r_index --;
            }
            else if((l_site + r_site) > PLUS_RESULT){
                r_index--;
            }
            else{
                l_index++;
            }
        }else if(barrel[l_index] != 1){
            l_index ++;
        }
        else{
            r_index --;
        }
    }
    return result;
}
/*
this function well create a barrel array by the array in the parameters
*/
int *createBarrel(int *array,int length){
    int min,max,capacity,*barrel,i;
    min = minNum(array,length);
    max = maxNum(array,length);
    capacity = max - min + 4;   //+4,because save capacity,min and max.
    barrel = (int*)malloc(capacity*sizeof(int));
    for(i = 0;i<capacity;i++){
        barrel[i] = 0;
    }
    barrel[0] = capacity;   //save barrel capacity in barrel[0]
    barrel[1] = min;        //save min number in barrel[1]
    barrel[2] = max;        //save max number in barrel[2]
    return barrel;
}
    
/*
this function could display the information about the barrel and the content
*/
void showBarrel(int *barrel){
    int i;
    // for(i = 3;i < barrel[0];i++){
    //  printf("%d\t",barrel[i]);
    // }
    printf("\narray_length = %d\ncapacity = %d\nmin = %d\nmax = %d\n",ARRAY_SIZE,barrel[0],barrel[1],barrel[2]);
}
    
main(){
    int *array,*barrel;
    long length;
    struct chain *result;
    //int a[] = {1,2,3,4,5,7,7,7,7,0};
    printf("======main() begin=======\n");
    length = ARRAY_SIZE;
    array = createArray(length);
    //array = a;
    //printf("\n====create array over=======");
    barrel = createBarrel(array,length);
    //printf("\n====create barrel over=======");
    barrel = fillBarrel(barrel,array);
    //printf("\n====fill barrel over=======\n");
    showBarrel(barrel);
    //printf("\n====show barrel over=======\n");
    result = create();
    //printf("\n====create result over=======\n");
    result = createResult(barrel);
    printf("\n====computer result over=======\n");
    /* the function to display the result chain*/
    showChain(result);
}