洛谷P4779 【模板】单源最短路径（标准版）
P4779 【模板】单源最短路径（标准版） $Dijkstra$ 模板，求解单源最短路，复杂度 $O(m \log(n))$，其中 $n$ 为点数，$m$ 为边数。 思想是把已经求出最短距离的点加入到集合中，然后把其它点到起点的距离加入到最小堆中，每次从堆顶取出元素 $i$，用它去做松弛操作，如果能够更新相邻点 $j$，那么把 $j$ 的距离加入到最小堆中。可以保证每次从堆顶取出元素之后，这个元素的最短距离就已经被确定，可以直接把它加入到集合中。 算法要求边权值都是正数。 // Date: Fri Dec 29 11:33:23 2023 #include <climits> #include <cmath> #include <cstdio> #include <cstdlib> #include <cstring> #include <algorithm> #include <functional> #include <iomanip> #include <iostream> #include <map> #include <queue> #include <set> #include <sstream> #include <stack> #include <string> #include <utility> #include <vector> using namespace std; const int INF = 0x3f3f3f3f, MOD = 1e9 + 7; const double eps = 1e-8; const int dir[8][2] = { {0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1}, }; typedef long long ll; typedef unsigned long long ull; typedef vector<int> VI; typedef pair<int, int> PII; const ull Pr = 131; #define For(i, a, b) for (int i = int(a); i < int(b); ++i) #define Rof(i, a, b) for (int i = int(b) - 1; i >= int(a); --i) #define For1(i, a, b) for (int i = int(a); i <= int(b); ++i) #define Rof1(i, a, b) for (int i = int(b); i >= int(a); --i) #define ForE(i, j) for (int i = h[j]; i != -1; i = ne[i]) #define f1 first #define f2 second #define pb push_back #define has(a, x) (a.find(x) != a.end()) #define nemp(a) (!a.empty()) #define all(a) (a).begin(), (a).end() #define SZ(a) int((a).size()) template <typename t> istream &operator>>(istream &in, vector<t> &vec) { for (t &x : vec) in >> x; return in; } template <typename t> ostream &operator<<(ostream &out, vector<t> &vec) { int n = SZ(vec); For(i, 0, n) { out << vec[i]; if (i < n - 1) out << ' '; } return out; } #ifdef _DEBUG #define debug1(x) cout << #x " = " << x << endl; #define debug2(x, y) cout << #x " = " << x << " " #y " = " << y << endl; #define debug3(x, y, z) \ cout << #x " = " << x << " " #y " = " << y << " " #z " = " << z << endl; #else #define debug1 #define debug2 #define debug3 #endif const int N = 100100, M = 200100; int n, m, s, h[N], st[N], dis[N]; int idx, e[M], ne[M], w[M]; void Init() { idx = 0; memset(h, -1, sizeof h); memset(st, 0, sizeof st); memset(dis, 0x3f, sizeof dis); } void Add(int a, int b, int c) { e[idx] = b, w[idx] = c, ne[idx] = h[a], h[a] = idx++; } void dijkstra(int s) { dis[s] = 0; priority_queue<PII, vector<PII>, greater<PII>> q; q.push({0, s}); while (nemp(q)) { auto t = q.top(); q.pop(); int base = t.f1, ver = t.f2; if (st[ver]) continue; st[ver] = true; ForE(i, ver) { int j = e[i], tmp = base + w[i]; if (tmp < dis[j]) { dis[j] = tmp; q.push({tmp, j}); } } } } int main(void) { #ifdef _DEBUG freopen("4779.in", "r", stdin); #endif std::ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> n >> m >> s; Init(); For1(i, 1, m) { int a, b, c; cin >> a >> b >> c; Add(a, b, c); } dijkstra(s); For1(i, 1, n) { int tmp = dis[i]; if (tmp == INF) cout << ((1LL << 31) - 1) << ' '; else cout << tmp << ' '; } cout << '\n'; return 0; }