最短路径 Dijkstra+priority_queue优化+bellman_ford+Floyd

#include<iostream>
#include<cstring>
#include<algorithm>
#include<queue>
#include<vector>
using namespace std;
const int maxn = 1005;
const int inf = 0x3f3f3f3f;
struct HeapNode {
int d, u;
HeapNode() = default;
HeapNode(int a, int b) :d(a), u(b) {}
bool operator<(const HeapNode& b)const {
return d > b.d;
}
};
struct Edge {
int to, dist;
Edge(int v,int d):to(v),dist(d){}
};
int arc[maxn][maxn],vis[maxn],n,d[maxn],pre[maxn],cnt[maxn],f[maxn][maxn];
//vector表示图
vector<Edge> G[maxn];
//
void Dij(int s) {
memset(vis, 0, sizeof(vis));
for (int i = 0; i < n; ++i)
d[i] = inf;
d[s] = 0;
for (int i = 0; i < n; ++i) {
int x, m = inf;
for (int y = 0; y < n; ++y)
if (!vis[y] && d[y] <= m) m = d[x = y];
vis[x] = 1;
//邻接矩阵的写法
/*for (int y = 0; y < n; ++y)
d[y] = min(d[y], d[x] + arc[x][y]);*/
//vector表示图的写法
for (auto &y : G[x])
d[y.to] = min(d[y.to], d[x] + y.dist), pre[y.to] = x;
}
}
void Dij_pri(int s) {
memset(vis, 0, sizeof(vis));
priority_queue <HeapNode> Q;
for (int i = 0; i < n; ++i)
d[i] = inf;
d[s] = 0;
Q.push(HeapNode(0, s));
while (!Q.empty()) {
HeapNode x = Q.top(); Q.pop();
if (x.d != d[x.u]) continue;//由于priority_queue不提供修改优先级操作，故冗余加入，老的跳过
for (auto &y : G[x.u]) {
if (d[y.to] > d[x.u] + y.dist)
d[y.to] = d[x.u] + y.dist, pre[y.to] = x.u,Q.push(HeapNode(d[y.to],y.to));
}
}
}
bool bellman_ford(int s) {
queue<int> Q;
memset(vis, 0, sizeof(vis));
memset(cnt, 0, sizeof(cnt));
for (int i = 0; i < n; ++i)
d[i] = inf;
d[s] = 0, vis[s] = 1, Q.push(s);
while (!Q.empty()) {
int u = Q.front(); Q.pop();
vis[u] = 0;
for (auto y : G[u]) {
if (d[u]<inf && d[y.to]>d[u] + y.dist) {
d[y.to] = d[u] + y.dist, pre[y.to] = u;
if (!vis[y.to]) {
Q.push(y.to), vis[y.to] = 1;
if (++cnt[y.to] > n) return false;
}
}
}
}
return true;
}
void Floyd() {
memcpy(f, arc, sizeof(arc));
for (int k = 0; k < n; ++k)
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
f[i][j] = min(f[i][j], f[i][k] + f[k][j]);
}
int main() {
n = 5;
G[0].push_back(Edge(1, 1));
G[1].push_back(Edge(2, 1)), G[1].push_back(Edge(3, 3));
G[2].push_back(Edge(4, 3)), G[2].push_back(Edge(3, 1));
G[3].push_back(Edge(4, 2));
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j)
arc[i][j] = i==j?0:inf;
arc[0][1] = arc[1][2] = arc[2][3] = 1;
arc[3][4] = 2;
arc[1][3] = arc[2][4] = 3;
Dij(0);
Dij_pri(0);
bellman_ford(0);
Floyd();
cout << 5;
}