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。
1 #include <stdio.h> 2 #include <stdlib.h> 3 #include "chain.c" //include the chain.c to create chain and list 4 #define NUMBER_SCOPE 69000 5 #define ARRAY_SIZE 100000000 6 #define PLUS_RESULT 5 7 8 int *createArray(long length){ 9 int i; 10 int *array=(int*)malloc(length*sizeof(int)); 11 srand((int)time(0)); 12 printf("Array:"); 13 for(i = 0;i<length;i++){ 14 array[i]=rand()%NUMBER_SCOPE - (NUMBER_SCOPE)/2; 15 //printf("%d,",array[i]); 16 } 17 return array; 18 } 19 20 /* 21 find the max number from a array 22 */ 23 int maxNum(int *array,int length){ 24 int i,max; 25 max = array[0]; 26 for(i = 1;i<length;i++){ 27 if(array[i] > max){ 28 max = array[i]; 29 } 30 } 31 return max; 32 } 33 /* 34 find the min number from a array 35 */ 36 int minNum(int *array,int length){ 37 int i,min; 38 min = array[0]; 39 for(i = 1;i<length;i++){ 40 if(array[i] < min){ 41 min = array[i]; 42 } 43 } 44 return min; 45 } 46 /* 47 this function to fill barrel ,first parameter is the barrel,second is array 48 */ 49 int *fillBarrel(int *barrel,int *array){ 50 int i,site; 51 for(i = 0;i < ARRAY_SIZE;i++){ 52 site = array[i] - barrel[1] + 3; 53 barrel[site] = 1; 54 } 55 return barrel; 56 } 57 /* 58 this function get a barrel array ,return a result chain, 59 it create by Quick Sort 60 */ 61 struct chain *createResult(int *barrel){ 62 int l_site,r_site,l_index,r_index; 63 struct chain *result; 64 struct list lst; 65 l_index = 3; 66 r_index = barrel[0] - 1; 67 while(l_index < r_index && 1){ 68 if((barrel[l_index] == 1) && (barrel[r_index] == 1)){ 69 l_site = l_index - 3 + barrel[1]; 70 r_site = r_index - 3 + barrel[1]; 71 // printf("\nl_site = %d\tr_site = %d",l_site,r_site); 72 // printf("\nbarrel[%d] = %d \nbarrel[%d] = %d",l_index,barrel[l_index],r_index,barrel[r_index]); 73 if((l_site + r_site) == PLUS_RESULT){ 74 lst.firstNum = l_site; 75 lst.secondNum = r_site; 76 /*add in chain*/ 77 result = addlink(result,lst); 78 l_index ++; 79 r_index --; 80 } 81 else if((l_site + r_site) > PLUS_RESULT){ 82 r_index--; 83 } 84 else{ 85 l_index++; 86 } 87 }else if(barrel[l_index] != 1){ 88 l_index ++; 89 } 90 else{ 91 r_index --; 92 } 93 } 94 return result; 95 } 96 /* 97 this function well create a barrel array by the array in the parameters 98 */ 99 int *createBarrel(int *array,int length){ 100 int min,max,capacity,*barrel,i; 101 min = minNum(array,length); 102 max = maxNum(array,length); 103 capacity = max - min + 4; //+4,because save capacity,min and max. 104 barrel = (int*)malloc(capacity*sizeof(int)); 105 for(i = 0;i<capacity;i++){ 106 barrel[i] = 0; 107 } 108 barrel[0] = capacity; //save barrel capacity in barrel[0] 109 barrel[1] = min; //save min number in barrel[1] 110 barrel[2] = max; //save max number in barrel[2] 111 return barrel; 112 } 113 114 /* 115 this function could display the information about the barrel and the content 116 */ 117 void showBarrel(int *barrel){ 118 int i; 119 // for(i = 3;i < barrel[0];i++){ 120 // printf("%d\t",barrel[i]); 121 // } 122 printf("\narray_length = %d\ncapacity = %d\nmin = %d\nmax = %d\n",ARRAY_SIZE,barrel[0],barrel[1],barrel[2]); 123 } 124 125 main(){ 126 int *array,*barrel; 127 long length; 128 struct chain *result; 129 //int a[] = {1,2,3,4,5,7,7,7,7,0}; 130 printf("======main() begin=======\n"); 131 length = ARRAY_SIZE; 132 array = createArray(length); 133 //array = a; 134 //printf("\n====create array over======="); 135 barrel = createBarrel(array,length); 136 //printf("\n====create barrel over======="); 137 barrel = fillBarrel(barrel,array); 138 //printf("\n====fill barrel over=======\n"); 139 showBarrel(barrel); 140 //printf("\n====show barrel over=======\n"); 141 result = create(); 142 //printf("\n====create result over=======\n"); 143 result = createResult(barrel); 144 printf("\n====computer result over=======\n"); 145 /* the function to display the result chain*/ 146 showChain(result); 147 }