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Dijkstra算法以及各种海量数据排序算法
一、Dijkstra最短路径算法
是从一个顶点到其余各顶点的最短路径算法,解决的是有向图中最短路径问题。迪杰斯特拉算法主要特点是以起始点为中心向外层层扩展,直到扩展到终点为止。
实现一
//// Dijkstra// ACM// Find the number of minimal path//// Created by Rachel on 18-2-12.// Copyright (c) 2014年 ZJU. All rights reserved.//#include <iostream>#include <algorithm>#include <stdio.h>#include <functional>#include <utility>#include <memory.h>using namespace std;#define N 505#define INF 100000000#define min(a,b) a<b?a:b#define max(a,b) a>b?a:bint map[N][N];int minres[N]; //min distance from source to point_ibool visited[N];int weight[N];void init(int n){ int i,j; for (i=0; i<n; i++) { for (j=0; j<n; j++) { map[i][j] = INF; } minres[i] = INF; } memset(visited, false, sizeof(visited));}void dijkstra(int source, int dest, int n){ int i,j; for(i=0;i<n;i++) minres[i]=map[source][i]; visited[source]=true; // (n-1) times, each time select one point into the start point set for (j=0; j<n-1; j++) { //select a point to add into the start point set int minn = INF, point=-1; for(i=0;i<n;i++) if (!visited[i]&&minres[i]<minn) { minn = minres[i]; point = i; } visited[point] = true; //update the min distance of other points for (i=0; i<n; i++) { if (!visited[i]&&minres[i]>minres[point]+map[point][i]) { minres[i] = minres[point]+map[point][i]; } } }}void dfs(int source, int dest,int n, int curpoint, int curdis, int cursum, int* num, int* sum){ if (curpoint==dest && minres[dest]==curdis) { *num = *num+1; *sum = max(*sum, cursum); return; } if (curdis>minres[dest]) return; for (int i=0; i<n; i++) { if(!visited[i]&&map[curpoint][i]!=INF) { visited[i] = true; dfs(source, dest, n, i, curdis+map[curpoint][i], cursum+weight[i], num, sum); visited[i] = false; } }}int main(){ int i,m,n,a,b,t,source,dest; while (cin>>n>>m) { cin>>source>>dest; for (i=0; i<n; i++) { cin>>weight[i]; //#peoples @ each point } init(n); for(i=0;i<m;i++) { scanf("%d%d%d",&a,&b,&t); map[b][a] = map[a][b]= min(map[a][b],t); } dijkstra(source,dest,n); minres[source] = 0; int num = 0, sum = 0; memset(visited, false, sizeof(visited)); visited[source] = true; dfs(source, dest, n, source, 0, weight[source], &num, &sum); cout<<num<<" "<<sum<<endl; }}
实现二
/*Dijkstra求单源最短路径 2010.8.26*/ /*http://www.cnblogs.com/dolphin0520/archive/2011/08/26/2155202.html */#include <iostream>#include<stack>#define M 100#define N 100using namespace std;typedef struct node{ int matrix[N][M]; //邻接矩阵 int n; //顶点数 int e; //边数 }MGraph; void DijkstraPath(MGraph g,int *dist,int *path,int v0) //v0表示源顶点 { int i,j,k; bool *visited=(bool *)malloc(sizeof(bool)*g.n); for(i=0;i<g.n;i++) //初始化 { if(g.matrix[v0][i]>0&&i!=v0) { dist[i]=g.matrix[v0][i]; path[i]=v0; //path记录最短路径上从v0到i的前一个顶点 } else { dist[i]=INT_MAX; //若i不与v0直接相邻,则权值置为无穷大 path[i]=-1; } visited[i]=false; path[v0]=v0; dist[v0]=0; } visited[v0]=true; for(i=1;i<g.n;i++) //循环扩展n-1次 { int min=INT_MAX; int u; for(j=0;j<g.n;j++) //寻找未被扩展的权值最小的顶点 { if(visited[j]==false&&dist[j]<min) { min=dist[j]; u=j; } } visited[u]=true; for(k=0;k<g.n;k++) //更新dist数组的值和路径的值 { if(visited[k]==false&&g.matrix[u][k]>0&&min+g.matrix[u][k]<dist[k]) { dist[k]=min+g.matrix[u][k]; path[k]=u; } } } }void showPath(int *path,int v,int v0) //打印最短路径上的各个顶点 { stack<int> s; int u=v; while(v!=v0) { s.push(v); v=path[v]; } s.push(v); while(!s.empty()) { cout<<s.top()<<" "; s.pop(); }} int main(int argc, char *argv[]){ int n,e; //表示输入的顶点数和边数 while(cin>>n>>e&&e!=0) { int i,j; int s,t,w; //表示存在一条边s->t,权值为w MGraph g; int v0; int *dist=(int *)malloc(sizeof(int)*n); int *path=(int *)malloc(sizeof(int)*n); for(i=0;i<N;i++) for(j=0;j<M;j++) g.matrix[i][j]=0; g.n=n; g.e=e; for(i=0;i<e;i++) { cin>>s>>t>>w; g.matrix[s][t]=w; } cin>>v0; //输入源顶点 DijkstraPath(g,dist,path,v0); for(i=0;i<n;i++) { if(i!=v0) { showPath(path,i,v0); cout<<dist[i]<<endl; } } } return 0;}
二、基于bitset排序
各种排序算法,生成随机文件程序。
//purpose: 生成随机的不重复的测试数据 //copyright@ 2011.04.19 yansha //1000w数据量,要保证生成不重复的数据量,一般的程序没有做到。 //但,本程序做到了。 //July、2010.05.30。 #include <iostream> #include <time.h> #include <assert.h> using namespace std; const int size = 10000000; int num[size]; int main() { int n; FILE *fp = fopen("data.txt", "w"); assert(fp); for (n = 1; n <= size; n++) //之前此处写成了n=0;n<size。导致下面有一段小程序的测试数据出现了0,特此订正。 num[n] = n; srand((unsigned)time(NULL)); int i, j; for (n = 0; n < size; n++) { i = (rand() * RAND_MAX + rand()) % 10000000; j = (rand() * RAND_MAX + rand()) % 10000000; swap(num[i], num[j]); } for (n = 0; n < size; n++) fprintf(fp, "%d ", num[n]); fclose(fp); return 0; }
基于bitset实现方法
#include<iostream>#include<bitset>#include<assert.h>#include<time.h>using namespace std;const int max_each_scan=5000000;int main(){ clock_t begin=clock(); bitset<max_each_scan> bitmap; bitmap.reset(); FILE* fp_unsort_file=fopen("data.txt","r"); assert(fp_unsort_file); int num; while(fscanf(fp_unsort_file,"%d",&num)!=EOF){ if(num<max_each_scan) bitmap.set(num,1); } FILE* fp_sort_file=fopen("sort.txt","w"); assert(fp_sort_file); int i ; for(i=0;i<max_each_scan;i++){ if(bitmap[i]==1) fprintf(fp_sort_file, "%d\n", i); } int result=fseek(fp_unsort_file,0,SEEK_SET); if(result) cout<<"failed" else{ bitmap.reset(); while(fscanf(fp_unsort_file,"%d",$num)!=EOF){ if(num>max_each_scan&&num<10000000){ num=num-max_ean_scan; bitmap.set(num,1); } } for(i=0;i<max_each_scan;i++){ if(bitmap[i]==1){ fprintf(fp_sort_file, "%d\n", max_each_scan+i); } } } clock_t end=clock(); cout<<"排序用时:"<<endl; cout << (end - begin) / CLK_TCK << "s" << endl; fclose(fp_sort_file); fclose(fp_unsort_file); return 0; }
三、海量数据排序实例
//copyright@ yansha //July、updated,2011.05.28。 #include <iostream> #include <string> #include <algorithm> #include <time.h> using namespace std; int sort_num = 10000000; int memory_size = 250000; //每次只对250k个小数据量进行排序 int read_data(FILE *fp, int *space) { int index = 0; while (index < memory_size && fscanf(fp, "%d ", &space[index]) != EOF) index++; return index; } void write_data(FILE *fp, int *space, int num) { int index = 0; while (index < num) { fprintf(fp, "%d ", space[index]); index++; } } // check the file pointer whether valid or not. void check_fp(FILE *fp) { if (fp == NULL) { cout << "The file pointer is invalid!" << endl; exit(1); } } int compare(const void *first_num, const void *second_num) { return *(int *)first_num - *(int *)second_num; } string new_file_name(int n) { char file_name[20]; sprintf(file_name, "data%d.txt", n); return file_name; } int memory_sort() { // open the target file. FILE *fp_in_file = fopen("data.txt", "r"); check_fp(fp_in_file); int counter = 0; while (true) { // allocate space to store data read from file. int *space = new int[memory_size]; int num = read_data(fp_in_file, space); // the memory sort have finished if not numbers any more. if (num == 0) break; // quick sort. qsort(space, num, sizeof(int), compare); // create a new auxiliary file name. string file_name = new_file_name(++counter); FILE *fp_aux_file = fopen(file_name.c_str(), "w"); check_fp(fp_aux_file); // write the orderly numbers into auxiliary file. write_data(fp_aux_file, space, num); fclose(fp_aux_file); delete []space; } fclose(fp_in_file); // return the number of auxiliary files. return counter; } void merge_sort(int file_num) { if (file_num <= 0) return; // create a new file to store result. FILE *fp_out_file = fopen("result.txt", "w"); check_fp(fp_out_file); // allocate a array to store the file pointer. FILE **fp_array = new FILE *[file_num]; int i; for (i = 0; i < file_num; i++) { string file_name = new_file_name(i + 1); fp_array[i] = fopen(file_name.c_str(), "r"); check_fp(fp_array[i]); } int *first_data = http://www.mamicode.com/new int[file_num]; "%d ", &first_data[i]); while (true) { int index = 0; while (index < file_num && finish[index]) index++; // the finish condition of the merge sort. if (index >= file_num) break; //主要的修改在上面两行代码,就是merge sort结束条件。 //要保证所有文件都读完,必须使得finish[0]...finish[40]都为真 //July、yansha,555,2011.05.29。 int min_data = http://www.mamicode.com/first_data[index]; "%d ", min_data); if (fscanf(fp_array[index], "%d ", &first_data[index]) == EOF) finish[index] = true; } fclose(fp_out_file); delete []finish; delete []first_data; for (i = 0; i < file_num; i++) fclose(fp_array[i]); delete [] fp_array; } int main() { clock_t start_memory_sort = clock(); int aux_file_num = memory_sort(); clock_t end_memory_sort = clock(); cout << "The time needs in memory sort: " << end_memory_sort - start_memory_sort << endl; clock_t start_merge_sort = clock(); merge_sort(aux_file_num); clock_t end_merge_sort = clock(); cout << "The time needs in merge sort: " << end_merge_sort - start_merge_sort << endl; system("pause"); return 0; }
四、多路归并排序
//copyright@ 纯净的天空 && yansha //5、July,updated,2010.05.28。 //harryshayne,update again。2011.6.30 #include <iostream> #include <ctime> #include <fstream> //#include "ExternSort.h" using namespace std; //使用多路归并进行外排序的类 //ExternSort.h /* * 大数据量的排序 * 多路归并排序 * 以千万级整数从小到大排序为例 * 一个比较简单的例子,没有建立内存缓冲区 */ #ifndef EXTERN_SORT_H #define EXTERN_SORT_H #include <cassert> //#define k 5 #define MIN -1//这里开始的时候出现了一个BUG,如果定义的MIN大于等于待排序的数,则会是算法出现错误#define MAX 10000000//最大值,附加在归并文件结尾typedef int* LoserTree;typedef int* External;class ExternSort { public: void sort() { time_t start = time(NULL); //将文件内容分块在内存中排序,并分别写入临时文件 k = memory_sort(); // //归并临时文件内容到输出文件 //merge_sort(file_count); ls=new int[k]; b=new int[k+1]; K_Merge(); delete []ls; delete []b; time_t end = time(NULL); printf("total time:%f\n", (end - start) * 1000.0/ CLOCKS_PER_SEC); } //input_file:输入文件名 //out_file:输出文件名 //count: 每次在内存中排序的整数个数 ExternSort(const char *input_file, const char * out_file, int count) { m_count = count; m_in_file = new char[strlen(input_file) + 1]; strcpy(m_in_file, input_file); m_out_file = new char[strlen(out_file) + 1]; strcpy(m_out_file, out_file); } virtual ~ExternSort() { delete [] m_in_file; delete [] m_out_file; } private: int m_count; //数组长度 char *m_in_file; //输入文件的路径 char *m_out_file; //输出文件的路径 int k;//归并数,此数必须要内排序之后才能得到,所以下面的ls和b都只能定义为指针(注意和书上区别) LoserTree ls;//定义成为指针,之后动态生成数组 External b;//定义成为指针,在成员函数中可以把它当成数组使用 //int External[k];protected: int read_data(FILE* f, int a[], int n) { int i = 0; while(i < n && (fscanf(f, "%d", &a[i]) != EOF)) i++; printf("read:%d integer\n", i); return i; } void write_data(FILE* f, int a[], int n) { for(int i = 0; i < n; ++i) fprintf(f, "%d ", a[i]); fprintf(f,"%d",MAX);//在最后写上一个最大值 } char* temp_filename(int index) { char *tempfile = new char[100]; sprintf(tempfile, "temp%d.txt", index); return tempfile; } static int cmp_int(const void *a, const void *b) { return *(int*)a - *(int*)b; } int memory_sort() { FILE* fin = fopen(m_in_file, "rt"); int n = 0, file_count = 0; int *array = new int[m_count]; //每读入m_count个整数就在内存中做一次排序,并写入临时文件 while(( n = read_data(fin, array, m_count)) > 0) { qsort(array, n, sizeof(int), cmp_int); //这里,调用了库函数阿,在第四节的c实现里,不再调用qsort。 char *fileName = temp_filename(file_count++); FILE *tempFile = fopen(fileName, "w"); free(fileName); write_data(tempFile, array, n); fclose(tempFile); } delete [] array; fclose(fin); return file_count; } void Adjust(int s) {//沿从叶子节点b[s]到根节点ls[0]的路径调整败者树 int t=(s+k)/2;//ls[t]是b[s]的双亲节点 while(t>0) { if(b[s]>b[ls[t]])//如果失败,则失败者位置s留下,s指向新的胜利者 { int tmp=s; s=ls[t]; ls[t]=tmp; } t=t/2; } ls[0]=s;//ls[0]存放调整后的最大值的位置 } void CreateLoserTree() { b[k]=MIN;//额外的存储一个最小值 for(int i=0;i<k;i++)ls[i]=k;//先初始化为指向最小值,这样后面的调整才是正确的 //这样能保证非叶子节点都是子树中的“二把手” for(i=k-1;i>=0;i--) Adjust(i);//依次从b[k-1],b[k-2]...b[0]出发调整败者树 } void K_Merge() {//利用败者数把k个输入归并段归并到输出段中 //b中前k个变量存放k个输入段中当前记录的元素 //归并临时文件 FILE *fout = fopen(m_out_file, "wt"); FILE* *farray = new FILE*[k]; int i; for(i = 0; i < k; ++i) //打开所有k路输入文件 { char* fileName = temp_filename(i); farray[i] = fopen(fileName, "rt"); free(fileName); } for(i = 0; i < k; ++i) //初始读取 { if(fscanf(farray[i], "%d", &b[i]) == EOF)//读每个文件的第一个数到data数组 { printf("there is no %d file to merge!",k); return; } } // for(int i=0;i<k;i++)input(b[i]); CreateLoserTree(); int q; while(b[ls[0]]!=MAX)// { q=ls[0];//q用来存储b中最小值的位置,同时也对应一路文件 //output(q); fprintf(fout,"%d ",b[q]); //input(b[q],q); fscanf(farray[q],"%d",&b[q]); Adjust(q); } //output(ls[0]); fprintf(fout,"%d ",b[ls[0]]); //delete [] hasNext; //delete [] data; for(i = 0; i < k; ++i) //清理工作 { fclose(farray[i]); } delete [] farray; fclose(fout); } /* void merge_sort(int file_count) { if(file_count <= 0) return; //归并临时文件 FILE *fout = fopen(m_out_file, "wt"); FILE* *farray = new FILE*[file_count]; int i; for(i = 0; i < file_count; ++i) { char* fileName = temp_filename(i); farray[i] = fopen(fileName, "rt"); free(fileName); } int *data = http://www.mamicode.com/new int[file_count];//存储每个文件当前的一个数字 "%d", &data[i]) == EOF)//读每个文件的第一个数到data数组 hasNext[i] = false; } while(true) //循环读取和输出,选择最小数的方法是简单遍历选择法 { //求data中可用的最小的数字,并记录对应文件的索引 int min = data[0]; int j = 0; while (j < file_count && !hasNext[j]) //顺序跳过已读取完毕的文件 j++; if (j >= file_count) //没有可取的数字,终止归并 break; for(i = j +1; i < file_count; ++i) //选择最小数,这里应该是i=j吧!但结果是一样的! { if(hasNext[i] && min > data[i]) { min = data[i]; j = i; } } if(fscanf(farray[j], "%d", &data[j]) == EOF) //读取文件的下一个元素 hasNext[j] = false; fprintf(fout, "%d ", min); } delete [] hasNext; delete [] data; for(i = 0; i < file_count; ++i) { fclose(farray[i]); } delete [] farray; fclose(fout); } */}; #endif //测试主函数文件 /* * 大文件排序 * 数据不能一次性全部装入内存 * 排序文件里有多个整数,整数之间用空格隔开 */ const unsigned int count = 10000000; // 文件里数据的行数 const unsigned int number_to_sort = 100000; //在内存中一次排序的数量 const char *unsort_file = "unsort_data.txt"; //原始未排序的文件名 const char *sort_file = "sort_data.txt"; //已排序的文件名 void init_data(unsigned int num); //随机生成数据文件 int main(int argc, char* *argv) { srand(time(NULL)); init_data(count); ExternSort extSort(unsort_file, sort_file, number_to_sort); extSort.sort(); system("pause"); return 0; } void init_data(unsigned int num) { FILE* f = fopen(unsort_file, "wt"); for(int i = 0; i < num; ++i) fprintf(f, "%d ", rand()); fclose(f); }
五、字符串回文结构判断
class Solution{ //http://blog.csdn.net/v_july_v/article/details/6712171public: /** *check weather s is a palindrome, n is the length of string s *Copyright(C) fairywell 2011 */ bool IsPalindrome(const char *s, int n) { if (s == 0 || n < 1) return false; // invalid string char *front, *back; front = s; back = s + n - 1; // set front and back to the begin and endof the string while (front < back) { if (*front != *back) return false; // not a palindrome ++front; --back; } return true; // check over, it‘s a palindrome } /** *check weather s is a palindrome, n is the length of string s *Copyright(C) fairywell 2011 */ bool IsPalindrome2(const char *s, int n) { if (s == 0 || n < 1) return false; // invalid string char *first, *second; int m = ((n>>1) - 1) >= 0 ? (n>>1) - 1 : 0; // m is themiddle point of s first = s + m; second = s + n - 1 - m; while (first >= s) if (s[first--] !=s[second++]) return false; // not equal, so it‘s not apalindrome return true; // check over, it‘s a palindrome } /** *find the longest palindrome in a string, n is the length of string s *Copyright(C) fairywell 2011 */ int LongestPalindrome(const char *s, int n) { int i, j, max; if (s == 0 || n < 1) return 0; max = 0; for (i = 0; i < n; ++i) { // i is the middle point of the palindrome for (j = 0; (i-j >= 0) && (i+j < n); ++j) // if the lengthof the palindrome is odd if (s[i-j] != s[i+j]) break; if (j*2+1 > max) max = j * 2 + 1; for (j = 0; (i-j >= 0) && (i+j+1 < n); ++j) // for theeven case if (s[i-j] != s[i+j+1]) break; if (j*2+2 > max) max = j * 2 + 2; } return max; } int LongestPalindrome(const char *s, int n) { int max = 0; int i,j; for ( i = 0; i < n ; i++ ) {//以i为中心开始计算回文子串 //计算奇数回问子串长度 for ( j = 0; (i-j) >= 0 && (i+j) < n; j++ ) { if ( s[i-j] != s[i+j] ) { break; } else { max = GETMAX(max, (2 * j + 1)); } } //计算偶数回问子串长度 for ( j = 0; (i-j) >= 0 && i + j + 1< n; j++ ) { if ( s[i-j] != s[i+j+1]) { break; } else { max = GETMAX(max, ( 2 * j + 2) ); } } } return max; } }
Dijkstra算法以及各种海量数据排序算法
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