SPFA 算法

洛谷 P3371 【模板】单源最短路径（弱化版）

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using p = pair<int, int>;
const double pi(acos(-1));
const int inf(0x3f3f3f3f);
const ll _inf(0x3f3f3f3f3f3f3f3f);
const int mod(1e9 + 7);
const int maxn(1e4 + 10);
const int maxm(5e5 + 10);
int ecnt, head[maxn];
ll dis[maxn];
bool vis[maxn];

struct edge {
    int to, wt, nxt;
} edges[maxm];

template<typename T = int>
inline const T read()
{
    T x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-') f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
        x = (x << 3) + (x << 1) + ch - '0';
        ch = getchar();
    }
    return x * f;
}

template<typename T>
inline void write(T x, char c)
{
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10, false);
    putchar(x % 10 + '0');
    if (c) putchar(c);
}

void addEdge(int u, int v, int w)
{
    edges[ecnt].to = v;
    edges[ecnt].wt = w;
    edges[ecnt].nxt = head[u];
    head[u] = ecnt++;
}

void spfa(int src)
{
    queue<int> q;
    q.push(src);
    dis[src] = 0;
    vis[src] = true;
    while (not q.empty()) {
        int u = q.front();
        q.pop();
        vis[u] = false;
        for (int i = head[u]; ~i; i = edges[i].nxt) {
            int v = edges[i].to, w = edges[i].wt;
            if (dis[v] > dis[u] + w) {
                dis[v] = dis[u] + w;
                if (not vis[v]) {
                    q.push(v);
                    vis[v] = true;
                }
            }
        }
    }
}

int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("input.txt", "r", stdin);
#endif
    memset(head, -1, sizeof head);
    memset(dis, 0x3f, sizeof dis);
    int n = read(), m = read(), s = read();
    while (m--) {
        int u = read(), v = read(), w = read();
        addEdge(u, v, w);
    }
    spfa(s);
    for (int i = 1; i <= n; ++i) {
        write(dis[i] == _inf ? INT_MAX : dis[i], i == n ? '\n' : ' ');
    }
    return 0;
}

洛谷 P4779 【模板】单源最短路径（标准版）

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using p = pair<int, int>;
const double pi(acos(-1));
const int inf(0x3f3f3f3f);
const ll _inf(0x3f3f3f3f3f3f3f3f);
const int mod(1e9 + 7);
const int maxn(1e5 + 10);
const int maxm(2e5 + 10);
int ecnt, head[maxn];
ll dis[maxn];
bool vis[maxn];

struct edge {
    int to, wt, nxt;
} edges[maxm];

template<typename T = int>
inline const T read()
{
    T x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-') f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
        x = (x << 3) + (x << 1) + ch - '0';
        ch = getchar();
    }
    return x * f;
}

template<typename T>
inline void write(T x, char c)
{
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10, false);
    putchar(x % 10 + '0');
    if (c) putchar(c);
}

void addEdge(int u, int v, int w)
{
    edges[ecnt].to = v;
    edges[ecnt].wt = w;
    edges[ecnt].nxt = head[u];
    head[u] = ecnt++;
}

void spfa(int src)
{
    queue<int> q;
    q.push(src);
    dis[src] = 0;
    vis[src] = true;
    while (not q.empty()) {
        int u = q.front();
        q.pop();
        vis[u] = false;
        for (int i = head[u]; ~i; i = edges[i].nxt) {
            int v = edges[i].to, w = edges[i].wt;
            if (dis[v] > dis[u] + w) {
                dis[v] = dis[u] + w;
                if (not vis[v]) {
                    q.push(v);
                    vis[v] = true;
                }
            }
        }
    }
}

int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("input.txt", "r", stdin);
#endif
    memset(head, -1, sizeof head);
    memset(dis, 0x3f, sizeof dis);
    int n = read(), m = read(), s = read();
    while (m--) {
        int u = read(), v = read(), w = read();
        addEdge(u, v, w);
    }
    spfa(s);
    for (int i = 1; i <= n; ++i) {
        write(dis[i] == _inf ? INT_MAX : dis[i], i == n ? '\n' : ' ');
    }
    return 0;
}

玄学优化 https://www.luogu.com.cn/blog/xhhkwy/spfa-hacker-orzorz

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using p = pair<int, int>;
const double pi(acos(-1));
const int inf(0x3f3f3f3f);
const int mod(1e9 + 7);
const int maxn(1e5 + 10);
const int maxm(1e6 + 10);
int ecnt, head[maxn];
int dis[maxn];
bool vis[maxn];
deque<int> q;

struct edge {
    int to, wt, nxt;
} edges[maxm];

template<typename T = int>
inline const T read()
{
    T x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-') f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
        x = (x << 3) + (x << 1) + ch - '0';
        ch = getchar();
    }
    return x * f;
}

template<typename T>
inline void write(T x, char c)
{
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10, false);
    putchar(x % 10 + '0');
    if (c) putchar(c);
}

void addEdge(int u, int v, int w)
{
    edges[ecnt].to = v;
    edges[ecnt].wt = w;
    edges[ecnt].nxt = head[u];
    head[u] = ecnt++;
}

void swap_slf()
{
    if (q.size() > 2 and dis[q.front()] > dis[q.back()]) {
        swap(q.front(), q.back());
    }
}

void spfa(int src)
{
    dis[src] = 0;
    q.push_back(src);
    vis[src] = true;
    while (not q.empty()) {
        int u = q.front();
        q.pop_front();
        swap_slf();
        vis[u] = false;
        for (int i = head[u]; compl i; i = edges[i].nxt) {
            int v = edges[i].to, w = edges[i].wt;
            if (dis[v] > dis[u] + w) {
                dis[v] = dis[u] + w;
                if (not vis[v]) {
                    q.push_back(v);
                    swap_slf();
                    vis[v] = true;
                }
            }
        }
    }
}

int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("input.txt", "r", stdin);
#endif
    memset(head, -1, sizeof head);
    memset(dis, 0x3f, sizeof dis);
    int n = read(), m = read(), s = read();
    while (m--) {
        int u = read(), v = read(), w = read();
        addEdge(u, v, w);
    }
    spfa(s);
    for (int i = 1; i <= n; ++i) {
        if (dis[i] == inf) {
            puts("NO PATH");
        } else {
            write(dis[i], i == n ? 10 : 32);
        }
    }
    return 0;
}

洛谷 P3385 【模板】负环

判断存在负环的条件：1、当前点入列达到 $n$ 次；2、源点到当前点的最短（长）路径达到 $n$ 。

两种玄学优化：1、入列计数 tot >= n * 2 跳出；2、使用 stack 代替 queue。

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using p = pair<int, int>;
const double pi(acos(-1));
const int inf(0x3f3f3f3f);
const ll _inf(0x3f3f3f3f3f3f3f3f);
const int mod(1e9 + 7);
const int maxn(2e3 + 10);
const int maxm(3e3 + 10);
bool vis[maxn];
int ecnt, head[maxn], cnt[maxn], dis[maxn];

struct edge {
    int to, wt, nxt;
} edges[maxm << 1];

template<typename T = int>
inline const T read()
{
    T x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-') f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
        x = (x << 3) + (x << 1) + ch - '0';
        ch = getchar();
    }
    return x * f;
}

template<typename T>
inline void write(T x, char c)
{
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10, false);
    putchar(x % 10 + '0');
    if (c) putchar(c);
}

void addEdge(int u, int v, int w)
{
    edges[ecnt].to = v;
    edges[ecnt].wt = w;
    edges[ecnt].nxt = head[u];
    head[u] = ecnt++;
}

bool spfa(int tot)
{
    queue<int> q;
    vis[1] = true;
    dis[1] = 0;
    q.push(1);
    while (not q.empty()) {
        int u = q.front();
        q.pop();
        vis[u] = false;
        for (int i = head[u]; ~i; i = edges[i].nxt) {
            int v = edges[i].to, w = edges[i].wt;
            if (dis[v] > dis[u] + w) {
                dis[v] = dis[u] + w;
                if (not vis[v]) {
                    cnt[v] = cnt[u] + 1;
                    if (cnt[v] >= tot) {
                        return true;
                    }
                    vis[v] = true;
                    q.push(v);
                }
            }
        }
    }
    return false;
}

int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("input.txt", "r", stdin);
#endif
    int t = read();
    while (t--) {
        ecnt = 0;
        memset(head, -1, sizeof head);
        memset(dis, 0x3f, sizeof dis);
        memset(vis, false, sizeof vis);
        memset(cnt, 0, sizeof cnt);
        int n = read(), m = read();
        while (m--) {
            int u = read(), v = read(), w = read();
            addEdge(u, v, w);
            if (w >= 0) {
                addEdge(v, u, w);
            }
        }
        printf("%s\n", spfa(n) ? "YES" : "NO");
    }
    return 0;
}

洛谷 P5960 【模板】差分约束算法

差分约束：求最小值→最长路，求最大值→最短路

#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using p = pair<int, int>;
const double pi(acos(-1));
const int inf(0x3f3f3f3f);
const int mod(1e9 + 7);
const int maxn(5e3 + 10);
const int maxm(1e4 + 10);
bool vis[maxn];
int ecnt, head[maxn], cnt[maxn], dis[maxn];

struct edge {
    int to, wt, nxt;
} edges[maxm];

template<typename T = int>
inline const T read()
{
    T x = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {
        if (ch == '-') f = -1;
        ch = getchar();
    }
    while (ch >= '0' && ch <= '9') {
        x = (x << 3) + (x << 1) + ch - '0';
        ch = getchar();
    }
    return x * f;
}

template<typename T>
inline void write(T x, char c)
{
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) write(x / 10, false);
    putchar(x % 10 + '0');
    if (c) putchar(c);
}

void addEdge(int u, int v, int w)
{
    edges[ecnt].to = v;
    edges[ecnt].wt = w;
    edges[ecnt].nxt = head[u];
    head[u] = ecnt++;
}

bool spfa(int n)
{
    memset(dis, 0x3f, sizeof dis);
    dis[0] = 0;
    queue<int> q;
    q.push(0);
    vis[0] = true;
    while (not q.empty()) {
        int u = q.front();
        q.pop();
        vis[u] = false;
        for (int i = head[u]; compl i; i = edges[i].nxt) {
            int v = edges[i].to, w = edges[i].wt;
            if (dis[v] > dis[u] + w) {
                dis[v] = dis[u] + w;
                if (not vis[v]) {
                    vis[v] = true;
                    q.push(v);
                    cnt[v] = cnt[u] + 1;
                    if (cnt[v] >= n + 1) {
                        return false;
                    }
                }
            }
        }
    }
    return true;
}

int main()
{
#ifdef ONLINE_JUDGE
#else
    freopen("input.txt", "r", stdin);
#endif
    ios::sync_with_stdio(false);
    memset(head, -1, sizeof head);
    int n = read(), m = read();
    while (m--) {
        int u = read(), v = read(), w = read();
        addEdge(v, u, w);
    }
    for (int i = 0; i <= n; ++i) {
        addEdge(0, i, 0);
    }
    if (spfa(n)) {
        for (int i = 1; i <= n; ++i) {
            write(dis[i], " \n"[i == n]);
        }
    } else {
        printf("NO\n");
    }
    return 0;
}

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