Dijkstra

特点：权值非负、单源、有向和无向、无优化O(n²)，使用优先队列优化O(mlogn)

图片来源：http://www.cnblogs.com/biyeymyhjob/archive/2012/07/31/2615833.html

//
//  main.cpp
//  Dijkstra无优化
//
//  Created by Haoying Zhao on 17/8/28.
//  Copyright © 2017年 Haoying Zhao. All rights reserved.
//

#include <iostream>

using namespace std;
#define N 6
#define MAX 101

int find_min_position(int* mindis, int* flag) {
    int min = MAX;
    int pos = -1;
    for(int i = 0; i < N; i++) {
        if(flag[i] == 1)
            continue;
        if(mindis[i] < min) {
            min = mindis[i];
            pos = i;
        }
    }
    return pos;
}

int main(int argc, const char * argv[]) {
    int a[N][N];
    for(int i = 0; i < N; i++)
        for(int j = 0; j < N; j++)
            if(i != j) a[i][j] = MAX;
            else a[i][j] = 0;
    a[0][1] = 6; a[1][0] = 6;a[0][2] = 3; a[2][0] = 3;
    a[1][2] = 2; a[2][1] = 2;a[1][3] = 5; a[3][1] = 5;
    a[2][3] = 3; a[3][2] = 3;a[2][4] = 4; a[4][2] = 4;
    a[3][5] = 3; a[5][3] = 3;a[3][4] = 2; a[4][3] = 2;
    a[4][5] = 5; a[5][4] = 5;
    int flag[N];
    memset(flag, 0, sizeof(flag));
    int mindis[N];
    for(int i = 0; i < N; i++)
        mindis[i] = MAX;
    int parent[N];
    memset(parent, 0 , sizeof(parent));
    mindis[0] = 0;
    for(int j = 0; j < N; j++) {
        int pos = find_min_position(mindis, flag);
        flag[pos] = 1;
        int dis = mindis[pos];
        for(int i = 0 ; i < N; i++) {
            if(flag[i] == 1)
                continue;
            if(a[pos][i] == MAX)
                continue;
            if(mindis[i] > dis + a[pos][i]) {
                 mindis[i] = dis + a[pos][i];
                parent[i] = pos;
            }
        }
    }
    cout << "mindis: " << endl;
    for(int i = 0; i < N; i++)
        cout << mindis[i] << " ";
    cout << endl << "parent: " << endl;
    for(int i = 0; i < N; i++)
        cout << parent[i] << " ";
    cout << endl << "track: " << endl;
    for(int i = 0; i < N; i++) {
        cout << (char)('A'+i);
        int j = i;
        while(1) {
            if(j == 0)
                break;
            cout << "<---" << (char)('A'+parent[j]);
            j = parent[j];
        }
        cout << endl;
    return 0;
}

输出结果：

mindis: 
0 5 3 6 7 9 
parent: 
0 2 0 2 2 3 
track: 
A
B<---C<---A
C<---A
D<---C<---A
E<---C<---A
F<---D<---C<---A