1003. Emergency (25)(Dijkstra + DFS)

最新推荐文章于 2019-05-01 00:00:07 发布

原创最新推荐文章于 2019-05-01 00:00:07 发布 · 228 阅读

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本文通过一个具体的案例，对比了Dijkstra算法和DFS算法在寻找最短路径及最大团队人数问题上的应用。通过源代码详细展示了两种算法的实现过程，并讨论了它们的时间和空间复杂度。

这一题算是我对于 Dijkstra 和 DFS 的初步认识吧，学习水准还是比较低的。
贴代码！

#include <cstdio>

#define INF 65535
#define MX 501

int mp[MX][MX];
int v[MX];
int dist[MX];
int teams[MX];
int amount[MX];
int pathcount[MX];
int N,M,start,en;

int main()
{

    scanf("%d %d %d %d", &N,&M,&start,&en);
    for (int i = 0; i < N; i++)
    {
        scanf("%d", &teams[i]);
    }
    for (int i=0; i<N; i++)
    {
        dist[i] = INF;
        for (int j=0; j<N; j++)
            mp[i][j] = INF;
    }
    for (int i=0; i<M; i++)
    {
        int c1, c2, L;
        scanf("%d %d %d", &c1,&c2,&L);
        mp[c1][c2] = mp[c2][c1] = L;
    }

    for (int i = 0; i < N; i++)
    {
        v[i] = 0;
        dist[i] = mp[start][i];

    }

    pathcount[start] = 1;
    dist[start] = 0;
    amount[start] = teams[start];

    for (int i = 0; i < N; i++)
    {
        int k = 0,min = INF;
        for (int j = 0; j < N; j++)
        {
            if (!v[j] && dist[j] < min)
            {
                k = j;
                min = dist[j];
            }
        }
        if (min==INF || k==en) break;

        v[k] = 1;
        for (int j = 0; j < N; j++)
        {
            if (!v[j])
            {
                if (min + mp[k][j] < dist[j])
                {
                    dist[j] = min + mp[k][j];
                    pathcount[j] = pathcount[k];
                    amount[j] = amount[k] + teams[j];
                }
                else if (min + mp[k][j] == dist[j])
                {
                    if (amount[j] < amount[k] + teams[j])
                        amount[j] = amount[k] + teams[j];
                    pathcount[j] += pathcount[k];
                }
            }
        }
    }

    printf("%d %d\n", pathcount[en], amount[en]);
    return 0;
}

这一题的 Dijkstra 还是有一点的变形，觉得真是一个神奇的算法。
接着就是 DFS 用这种法子觉得很暴力，在 pat 里也发现时间和空间都相比 Dijkstra 比较大。
贴代码

#include <cstdio>

#define MX 501

int N,M,C1,C2;
int teams[MX] = {0};
int mp[MX][MX] = {0};
bool boolDfs[MX] = {false};

int minDistance = 65535;
int shortPath = 0;
int maxTeams = 0;

void dfs(int start, int distance, int team)
{
    if (start == C2)
    {
        if (distance < minDistance)
        {
            minDistance = distance;
            shortPath = 1;
            maxTeams = team;
        }
        else if (distance == minDistance)
        {
            shortPath++;
            if (team > maxTeams)
                maxTeams = team;
        }
        return;
    }

    boolDfs[start] = true;
    for (int i = 0; i < N; i++)
    {
        if (boolDfs[i] == false && mp[start][i] > 0)
        {
            dfs(i,distance + mp[start][i],team + teams[i]);
        }
    }
    boolDfs[start] = false;
}

int main()
{
    scanf("%d %d %d %d",&N,&M,&C1,&C2);

    for (int i = 0; i < N; i++)
    {
        scanf("%d",&teams[i]);
    }
    for (int i = 0; i < M; i++)
    {
        int c1,c2,tmp;
        scanf("%d %d %d",&c1,&c2,&tmp);
        mp[c1][c2] = mp[c2][c1] = tmp;
    }
    dfs(C1,0,teams[C1]);

    printf("%d %d",shortPath,maxTeams);
    return 0;
}