dijkstra和spfa区别 ：
dikstra是基于贪心的思想，每次选择最近的点去更新其它点，过后就不再访问。而在spfa算法中，只要有某个点的距离被更新了，就把它加到队列中，去更新其它点，所有每个点有被重复加入队列的可能。
或者跟具体的说区别在于diikstra总是要找到dist最小的元素来作为父节点更新其他点，而不是直接取队头元素(当然如果是优先队列也是取队头元素) :更新的顺序不同主要导致的差异是算法时间复杂度上的不同;功能上当然也造成了一定的区别，比如由于dikstra严格要求每次取的元素都是队列中最小的，这也导致了队头元素的dist值是单调递增的，从而一旦出现负权边就会破坏这个性质，从而导致找不到最优解。
图结构练习——最短路径 | SDUT OnlineJudge
#include <bits/stdc++.h>
using namespace std;
#define xx first
#define yy second
#define endl "\n"
#define int long long
#define pb push_back
typedef pair<int, int> PII;
#define Yshanqian ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
const int N = 1e6 + 10, M = 1010, inf = 0x3f3f3f3f;
int n, m;
int g[M][M];
void floyd()
{
for (int k = 1; k <= n; k++)
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++)
g[i][j] = min(g[i][k] + g[k][j], g[i][j]);
}
signed main()
{
Yshanqian;
while (cin >> n >> m)
{
memset(g, inf, sizeof g);
for (int i = 1; i <= n; i++)
g[i][i] = 0;
for (int i = 1; i <= m; i++)
{
int a, b, c;
cin >> a >> b >> c;
if (c < g[a][b])
g[a][b] = g[b][a] = c;
}
floyd();
cout << g[1][n] << endl;
}
return 0;
}
#include <bits/stdc++.h>
using namespace std;
#define xx first
#define yy second
#define endl "\n"
#define int long long
#define pb push_back
typedef pair<int, int> PII;
#define Yshanqian ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
const int N = 1e4 + 10, M = 1010, inf = 0x3f3f3f3f;
int n, m;
int dis[N], st[N];
vector<PII> g[N];
void spfa()
{
queue<int> q;
for (int i = 1; i <= n; i++)
dis[i] = 1e18;
memset(st, 0, sizeof st);
dis[1] = 0;
q.push(1);
st[1] = 1;
while (q.size())
{
int u = q.front();
q.pop();
st[u] = 0;
for (auto ed : g[u])
{
int v = ed.xx, w = ed.yy;
if (dis[v] > dis[u] + w)
{
dis[v] = dis[u] + w;
if (!st[v])
q.push(v);
}
}
}
}
signed main()
{
Yshanqian;
while (cin >> n >> m)
{
for (int i = 1; i <= n; i++)
g[i].clear();
for (int i = 1; i <= m; i++)
{
int a, b, c;
cin >> a >> b >> c;
g[a].pb({b, c});
g[b].pb({a, c});
}
spfa();
cout << dis[n] << endl;
}
return 0;
}#include <bits/stdc++.h>
using namespace std;
#define xx first
#define yy second
#define endl "\n"
#define int long long
#define pb push_back
typedef pair<int, int> PII;
#define Yshanqian ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
const int N = 1e6 + 10, M = 1010, inf = 0x3f3f3f3f;
int n, m;
int dis[N], st[N];
vector<PII> g[N];
void dijkstra()
{
priority_queue<PII, vector<PII>, greater<PII>> q;
memset(dis, inf, sizeof dis);
memset(st, 0, sizeof st);
dis[1] = 0;
q.push({0, 1});
while (q.size())
{
int u = q.top().yy;
q.pop();
if (st[u])
continue;
st[u] = 1;
for (auto ed : g[u])
{
int v = ed.xx, w = ed.yy;
if (dis[v] > dis[u] + w)
{
dis[v] = dis[u] + w;
q.push({dis[v], v});
}
}
}
}
signed main()
{
Yshanqian;
while (cin >> n >> m)
{
for (int i = 1; i <= n; i++)
g[i].clear();
for (int i = 1; i <= m; i++)
{
int a, b, c;
cin >> a >> b >> c;
g[a].pb({b, c});
g[b].pb({a, c});
}
dijkstra();
cout << dis[n] << endl;
}
return 0;
}数据结构实验之图论七：驴友计划
#include <bits/stdc++.h>
using namespace std;
#define xx first
#define yy second
#define endl "\n"
#define int long long
#define pb push_back
typedef pair<int, int> PII;
#define Yshanqian ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
const int N = 1e6 + 10, M = 1010, inf = 0x3f3f3f3f;
int n, m, s, t;
int dis[N], st[N], mon[N];
struct node
{
int v, w, cost;
};
vector<node> g[N];
void dijkstra()
{
priority_queue<PII, vector<PII>, greater<PII>> q;
memset(dis, inf, sizeof dis);
memset(st, 0, sizeof st);
dis[s] = 0;
q.push({0, s});
while (q.size())
{
int u = q.top().yy;
q.pop();
if (st[u])
continue;
st[u] = 1;
for (auto ed : g[u])
{
int v = ed.v, w = ed.w, cost = ed.cost;
if (dis[v] > dis[u] + w)
{
dis[v] = dis[u] + w;
mon[v] = mon[u] + cost;
q.push({dis[v], v});
}
else if (dis[v] == dis[u] + w)
{
if (mon[v] > mon[u] + cost)
{
mon[v] = mon[u] + cost;
q.push({dis[v], v});
}
}
}
}
}
signed main()
{
Yshanqian;
int T;
cin >> T;
while (T--)
{
cin >> n >> m >> s >> t;
for (int i = 0; i <= n; i++)
g[i].clear();
for (int i = 1; i <= m; i++)
{
int a, b, c, d;
cin >> a >> b >> c >> d;
g[a].pb({b, c, d});
g[b].pb({a, c, d});
}
dijkstra();
cout << dis[t] << " " << mon[t] << endl;
}
return 0;
}人活着系列之芳姐和芳姐的猪
#include <bits/stdc++.h>
using namespace std;
#define xx first
#define yy second
#define endl "\n"
#define int long long
#define pb push_back
typedef pair<int, int> PII;
#define Yshanqian ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
const int N = 1e6 + 10, M = 1010, inf = 0x3f3f3f3f;
int n, m, k;
int a[N], g[M][M];
void floyd()
{
for (int k = 1; k <= m; k++)
for (int i = 1; i <= m; i++)
for (int j = 1; j <= m; j++)
g[i][j] = min(g[i][j], g[i][k] + g[k][j]);
}
signed main()
{
Yshanqian;
cin >> n >> m >> k;
for (int i = 1; i <= n; i++)
cin >> a[i];
memset(g, inf, sizeof g);
for (int i = 1; i <= m; i++)
g[i][i] = 0;
for (int i = 1; i <= k; i++)
{
int a, b, c;
cin >> a >> b >> c;
if (c < g[a][b])
g[a][b] = g[b][a] = c;
}
floyd();
int ans = 1e18;
for (int i = 1; i <= m; i++)
{
int tmp = 0;
for (int j = 1; j <= n; j++)
{
int s = a[j];
tmp += g[i][s];
}
ans = min(ans, tmp);
}
cout << ans << endl;
return 0;
}
