[AHOI2002]哈利·波特与魔法石

最新推荐文章于 2024-10-28 15:57:13 发布

转载最新推荐文章于 2024-10-28 15:57:13 发布 · 140 阅读

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原文链接：http://www.cnblogs.com/ac-evil/p/10309035.html

本文深入探讨了Dijkstra算法的原理与应用，通过具体实例展示了如何使用该算法解决最短路径问题。代码中详细解释了算法的每一步操作，包括节点的定义、边的添加以及优先队列的使用。

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这道题比较简单，就是一个最短路（SSSP）。数据水，用Floyd即可AC。这里用了Dijkstra。

  1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <algorithm>
  5 #include <queue>
  6 
  7 using namespace std;
  8 
  9 #define re register
 10 #define rep(i, a, b) for (re int i = a; i <= b; ++i)
 11 #define repd(i, a, b) for (re int i = a; i >= b; --i)
 12 #define maxx(a, b) a = max(a, b);
 13 #define minn(a, b) a = min(a, b);
 14 #define LL long long
 15 #define inf (1 << 30)
 16 
 17 inline int read() {
 18     int w = 0, f = 1; char c = getchar();
 19     while (!isdigit(c)) f = c == '-' ? -1 : f, c = getchar();
 20     while (isdigit(c)) w = (w << 3) + (w << 1) + (c ^ '0'), c = getchar();
 21     return w * f;
 22 }
 23 
 24 const int maxn = 100 + 5, maxm = 1e4 + 5;
 25 
 26 struct Edge {
 27     int u, v, w, pre;
 28 };
 29 
 30 struct Node {
 31     int u, d;
 32     bool operator < (const Node &rhs) const {
 33         return d > rhs.d;
 34     }
 35 };
 36 
 37 int way[8] = {0, 2, 6, 4, 8, 6, 10, 14};
 38 
 39 priority_queue<Node> Q;
 40 
 41 struct Graph {
 42 #define iter(i, u) for (re int i = G[u]; i; i = edges[i].pre)
 43     Edge edges[maxm << 1];
 44     int n, m;
 45     int G[maxn];
 46     int dis[maxn], vis[maxn];
 47     void init(int n) {
 48         this->n = n;
 49         m = 0;
 50         memset(G, 0, sizeof(G));
 51     }
 52     void AddEdge(int u, int v, int w) {
 53         edges[++m] = (Edge){u, v, way[w], G[u]};
 54         G[u] = m;
 55         edges[++m] = (Edge){v, u, way[w], G[v]};
 56         G[v] = m;
 57     }
 58     void dijkstra(int s) {
 59         memset(vis, 0, sizeof(vis));
 60         memset(dis, 0x3f, sizeof(dis));
 61         dis[s] = 0;
 62         Q.push((Node){s, 0});
 63         while (!Q.empty()) {
 64             int u = Q.top().u; Q.pop();
 65             if (vis[u]) continue;
 66             vis[u] = 1;
 67             iter(i, u) {
 68                 Edge &e = edges[i];
 69                 if (dis[u] + e.w < dis[e.v]) {
 70                     dis[e.v] = dis[u] + e.w;
 71                     Q.push((Node){e.v, dis[e.v]});
 72                 }
 73             }
 74         }
 75     }
 76 } G;
 77 
 78 int s, t, m;
 79 
 80 int main() {
 81     freopen("ques.in", "r", stdin);
 82     freopen("ques.out", "w", stdout);
 83 
 84     rep(i, 1, 7) 
 85         if (read()) way[i] >>= 1;
 86 
 87     s = read(), t = read();
 88 
 89     G.init(100);
 90 
 91     m = read();
 92 
 93     rep(i, 1, m) {
 94         int u = read(), v = read(), w = read();
 95         G.AddEdge(u, v, w);
 96     }
 97 
 98     G.dijkstra(s);
 99 
100     printf("%d", G.dis[t]);
101 
102     return 0;
103 }

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <queue>
using namespace std;
#define re register#define rep(i, a, b) for (re int i = a; i <= b; ++i)#define repd(i, a, b) for (re int i = a; i >= b; --i)#define maxx(a, b) a = max(a, b);#define minn(a, b) a = min(a, b);#define LL long long#define inf (1 << 30)
inline int read() {int w = 0, f = 1; char c = getchar();while (!isdigit(c)) f = c == '-' ? -1 : f, c = getchar();while (isdigit(c)) w = (w << 3) + (w << 1) + (c ^ '0'), c = getchar();return w * f;}
const int maxn = 100 + 5, maxm = 1e4 + 5;
struct Edge {int u, v, w, pre;};
struct Node {int u, d;bool operator < (const Node &rhs) const {return d > rhs.d;}};
int way[8] = {0, 2, 6, 4, 8, 6, 10, 14};

priority_queue<Node> Q;
struct Graph {#define iter(i, u) for (re int i = G[u]; i; i = edges[i].pre)Edge edges[maxm << 1];int n, m;int G[maxn];int dis[maxn], vis[maxn];void init(int n) {this->n = n;m = 0;memset(G, 0, sizeof(G));}void AddEdge(int u, int v, int w) {edges[++m] = (Edge){u, v, way[w], G[u]};G[u] = m;edges[++m] = (Edge){v, u, way[w], G[v]};G[v] = m;}void dijkstra(int s) {memset(vis, 0, sizeof(vis));memset(dis, 0x3f, sizeof(dis));dis[s] = 0;Q.push((Node){s, 0});while (!Q.empty()) {int u = Q.top().u; Q.pop();if (vis[u]) continue;vis[u] = 1;iter(i, u) {Edge &e = edges[i];if (dis[u] + e.w < dis[e.v]) {dis[e.v] = dis[u] + e.w;Q.push((Node){e.v, dis[e.v]});}}}}} G;
int s, t, m;
int main() {freopen("ques.in", "r", stdin);freopen("ques.out", "w", stdout);
rep(i, 1, 7) if (read()) way[i] >>= 1;
s = read(), t = read();
G.init(100);
m = read();
rep(i, 1, m) {int u = read(), v = read(), w = read();G.AddEdge(u, v, w);}
G.dijkstra(s);
printf("%d", G.dis[t]);
return 0;}

转载于:https://www.cnblogs.com/ac-evil/p/10309035.html