hdoj2544 最短路（Dijkstra || Floyd || SPFA）

题目链接

http://acm.hdu.edu.cn/showproblem.php?pid=2544

思路

最短路算法模板题，求解使用的Dijkstra算法、Floyd算法、SPFA算法可以当做求解最短路问题的模板使用。

代码

Dijkstra算法：

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;

const int INF = 0x3f3f3f;
const int N = 100 + 10;
int map[N][N];
int dist[N];
int visit[N];
int n, m;

void dijkstra()
{
    memset(visit, 0, sizeof(visit));
    for (int i = 1; i <= n; i++)
        dist[i] = map[1][i];
    dist[1] = 0;
    int min_dist, now;
    for (int i = 1; i <= n; i++)
    {
        min_dist = INF;
        for (int j = 1; j <= n; j++)
        {
            if (!visit[j] && dist[j] < min_dist)
            {
                min_dist = dist[j];
                now = j;
            }
        }
        if (min_dist == INF) break;
        visit[now] = 1;
        for (int j = 1; j <= n; j++)    //“松弛”操作
        {
            if (dist[now] + map[now][j] < dist[j])
                dist[j] = dist[now] + map[now][j];
        }
    }
    printf("%d
", dist[n]);
}

int main()
{
    //freopen("hdoj2544.txt", "r", stdin);
    while (scanf("%d%d", &n, &m) == 2 && n)
    {
        memset(map, INF, sizeof(map));
        int a, b, c;
        for (int i = 0; i < m; i++)
        {
            scanf("%d%d%d", &a, &b, &c);
            map[a][b] = map[b][a] = c;
        }
        dijkstra();
    }
    return 0;
}

Floyd算法：

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;

const int INF = 0x3f3f3f;
const int N = 100 + 10;
int map[N][N];
int n, m;

void floyd()
{
    for (int k = 1; k <= n; k++)
        for (int i = 1; i <= n; i++)
            for (int j = 1;j <= n; j++)
                map[i][j] = min(map[i][j], map[i][k] + map[k][j]);
    printf("%d
", map[1][n]);
}

int main()
{
    //freopen("hdoj2544.txt", "r", stdin);
    while (scanf("%d%d", &n, &m) == 2 && n)
    {
        memset(map, INF, sizeof(map));
        int a, b, c;
        for (int i = 0; i < m; i++)
        {
            scanf("%d%d%d", &a, &b, &c);
            map[a][b] = map[b][a] = c;
        }
        floyd();
    }
    return 0;
}

SPAF算法：

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>
#include <vector>
using namespace std;

struct Edge
{
    int s, e, dist;    //边的起点、终点、长度

    Edge() {}
    Edge(int s, int e, int d) :s(s), e(e), dist(d) {}
};

const int INF = 0x3f3f3f;
const int N = 100 + 10;
vector<Edge> v[N];    //使用邻接表存储图
int dist[N];
int visit[N];
int n, m;

void spfa(int s)
{
    queue<int> q;
    memset(dist, INF, sizeof(dist));
    memset(visit, 0, sizeof(visit));
    q.push(s);
    visit[s] = 1;
    dist[s] = 0;

    while (!q.empty())
    {
        int s = q.front();
        q.pop();
        visit[s] = 0;
        for (int i = 0; i < v[s].size(); i++)
        {
            int e = v[s][i].e;
            if (dist[e] > dist[s] + v[s][i].dist)
            {
                dist[e] = dist[s] + v[s][i].dist;
                if (visit[e] == 0)
                {
                    visit[e] = 1;
                    q.push(e);
                }
            }
        }
    }
    printf("%d
", dist[n]);
}

int main()
{
    //freopen("hdoj2544.txt", "r", stdin);
    while (scanf("%d%d", &n, &m) == 2 && n)
    {
        for (int i = 1;i <= n; i++)
            v[i].clear();
        int a, b, c;
        for (int i = 0; i < m; i++)
        {
            scanf("%d%d%d", &a, &b, &c);
            v[a].push_back(Edge(a, b, c));
            v[b].push_back(Edge(b, a, c));
        }
        spfa(1);    //求结点1到其余各点的最短路径
    }
    return 0;
}