bellman-ford & SPFA

bellman-ford 求限定走k条边的最短路

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 510, M = 10010;

struct node
{
    int x, y, z;
} e[M];

int n, m, k;
int dis[N], last[N];

void bellman_ford(int u)
{
    memset(dis, 0x3f, sizeof dis);
    dis[u] = 0;
    for (int i = 1; i <= k; i++)
    {
        memcpy(last, dis, sizeof dis);
        for (int j = 1; j <= m; j++)
        {
            int x = e[j].x;
            int y = e[j].y;
            int z = e[j].z;
            dis[y] = min(dis[y], last[x] + z);
        }
    }
}

int main()
{
    scanf("%d%d%d", &n, &m, &k);
    for (int i = 1; i <= m; i++)
    {
        int x, y, z;
        scanf("%d%d%d", &x, &y, &z);
        e[i] = {x, y, z};
    }

    bellman_ford(1);
    
    if (dis[n] > 0x3f3f3f3f / 2)
        printf("impossible\n");
    else
        printf("%d", dis[n]);
        
    return 0;
}

spfa

#include <algorithm>
#include <cstring>
#include <queue>
#include <iostream>
using namespace std;
typedef pair<int, int> PII;
const int N = 1e5 + 10;
int dis[N], ne[N], e[N], h[N], w[N];
int n, m, len;
bool vis[N];

void add(int a, int b, int c)
{
    e[len] = b;
    w[len] = c;
    ne[len] = h[a];
    h[a] = len++;
}

void spfa(int u)
{
    memset(dis, 0x3f, sizeof dis);
    queue<int> q;
    q.push(u);
    dis[u] = 0;
    vis[u] = true;
    while (q.size())
    {
        int x = q.front();
        q.pop();
        vis[x] = false;
        for (int i = h[x]; ~i; i = ne[i])
        {
            int y = e[i];
            int c = w[i];
            if (dis[y] > dis[x] + c)
            {
                dis[y] = dis[x] + c;
                if (!vis[y])
                {
                    q.push(y);
                    vis[y] = true;
                }
            }
        }
    }
}
int main()
{
    scanf("%d%d", &n, &m);
    memset(h, -1, sizeof h);
    for (int i = 1; i <= m; i++)
    {
        int x, y, z;
        scanf("%d%d%d", &x, &y, &z);
        add(x, y, z);
    }

    spfa(1);
    
    if (dis[n] == 0x3f3f3f3f)
        printf("impossible\n");
    else
        printf("%d", dis[n]);
    return 0;
}

spfa判断是否存在负环

#include <algorithm>
#include <cstring>
#include <queue>
#include <iostream>
using namespace std;
typedef pair<int, int> PII;
const int N = 10010;
int dis[N], ne[N], e[N], h[N], w[N];
int n, m, len, cnt[N];
bool vis[N];

void add(int a, int b, int c)
{
    e[len] = b;
    w[len] = c;
    ne[len] = h[a];
    h[a] = len++;
}

bool spfa()
{
    queue<int> q;
    for (int i = 1; i <= n; i++)
    {
        q.push(i);
        vis[i] = true;
        cnt[i] = 1;
    }
    while ((q.size()))
    {
        int x = q.front();
        q.pop();
        vis[x] = false;
        for (int i = h[x]; ~i; i = ne[i])
        {
            int y = e[i];
            int z = w[i];
            if (dis[y] > dis[x] + z)
            {
                dis[y] = dis[x] + z;
                cnt[y] = cnt[x] + 1;
                if (cnt[y] > n)
                    return true;
                if (!vis[y])
                    q.push(y);
            }
        }
    }
    return false;
}
int main()
{
    scanf("%d%d", &n, &m);
    memset(h, -1, sizeof h);
    for (int i = 1; i <= m; i++)
    {
        int x, y, z;
        scanf("%d%d%d", &x, &y, &z);
        add(x, y, z);
    }

    if (spfa())
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
    return 0;
}