Floyd,Dijkstra,SPFA模板整理(以[HDU2544-最短路]为例 )

复习了一下三大基础最短路算法

随说只有三种,但实际上由于情况不同,

有Dijkstra,Dijkstra-堆优化,SPFA-邻接矩阵,SPFA-链式前向星,Floyd-邻接矩阵,Floyd-邻接表等更多种写法...

至于Bellmen-Ford算法.SPFA就是它的队列优化形式,不再赘述.

用一道最基本的最短路算法问题来写一下我常用的四种吧.

原题链接:http://acm.split.hdu.edu.cn/showproblem.php?pid=2544

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Time limit:          1000 ms

Memory limit:     32768 kB

OS:                      Windows

Input

输入包括多组数据。每组数据第一行是两个整数N、M（N<=100，M<=10000），N表示节点数目，标号为1为源节点，标号为N为汇节点，M为边的数目.

N=M=0表示输入结束。接下来M行，每行包括3个整数A，B，C（1<=A,B<=N,1<=C<=1000）,表示在节点A与节点B之间有一条双向边，经过一次该边的花费是C。
输入的图保证至少有1条从源点到汇点的路径。

Output

对于每组输入，输出一行,含有一个数字，表示从源点到汇点的最小花费

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Sample Input

2 11 2 33 31 2 52 3 53 1 20 0

Sample Output

3
2

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 (所有代码已通过全部测试数据)

spfa + 链式前向星:

/***********************@Name: hdu 2544 spfa**@Author: Nervending*@Describtion: spfa link *@DateTime: 2017-10-04 14:00:39***********************/#include <queue>#include <string.h>#include <iostream>using namespace std;typedef long long ll;typedef unsigned long long ull;const int maxn = 1e4 + 100;const int INF = 0x3f3f3f3f;const int DINF = 0xc0c0c0c0;int a, b, c;int n, m, k, T;int t, ans;int x, y, z;struct node {int to, cost, next;} e[maxn];int head[maxn];bool vis[maxn];int dis[maxn], nume;void init() {memset(e, 0, sizeof e);memset(head, -1, sizeof head);memset(vis, false, sizeof vis);memset(dis, 0x3f, sizeof dis);ans = 0;nume = 0;}void add(int a, int b , int c) {node t = {b, c, head[a]};e[nume] = t;head[a] = nume++;}void spfa(int st, int ed) {queue <int> q;q.push(st);dis[st] = 0;while (!q.empty()) {int now = q.front();q.pop();vis[now] = false;for (int i = head[now]; ~i; i = e[i].next) {int to = e[i].to;int cost = e[i].cost;if (dis[to] > dis[now] + cost) {dis[to] = dis[now] + cost;if (!vis[to]) {vis[to] = true;q.push(to);}}}}ans = dis[ed];}int main() {while (cin >> n >> m, n || m) {init();for (int i = 0; i < m; i++) {cin >> a >> b >> c;add(a, b, c);add(b, a, c);}spfa(1, n);cout << ans << endl;}return 0;}

dijkstra+邻接矩阵

/***********************@Name: hdu 2544 dijkstra**@Author: Nervending*@Describtion: Dijkstra*@DateTime: 2017-10-04 14:00:39***********************/#include <string.h>#include <iostream>using namespace std;typedef long long ll;typedef unsigned long long ull;const int maxn = 1e2 + 10;const int INF = 0x3f3f3f3f;const int DINF = 0xc0c0c0c0;int a, b, c;int n, m, k, T;int t, ans;int x, y, z;int cost[maxn][maxn];bool vis[maxn];int dis[maxn];void init() {fill(dis, dis + maxn, INF);fill(vis, vis + maxn, false);memset(cost, INF, sizeof cost);ans = 0;}void dijkstra(int st, int ed) {for (int i = 1; i <= n; i++) {cost[i][i] = 0;dis[i] = cost[st][i];}vis[st] = true;int now;// dis[st]=0;for (int i = 1; i <= n; i++) {int mini = INF;for (int j = 1; j <= n; j++) {if (vis[j] == 0 && dis[j] < mini) {now = j;mini = dis[j];}}vis[now] = 1;for (int j = 1; j <= n; j++) {if (vis[j] == 0)if (cost[now][j] < INF && dis[now] + cost[now][j] < dis[j])dis[j] = dis[now] + cost[now][j];}}ans = dis[ed];}int main() {while (cin >> n >> m, n || m) {init();for (int i = 0; i < m; i++) {cin >> a >> b >> c;cost[a][b] = cost[b][a] = c;}dijkstra(1, n);printf("%d\n", ans);}}

dijkstra + heap

/***********************@Name: hdu 2544 dijkstra heap**@Author: Nervending*@Describtion: Dijkstra  heap*@DateTime: 2017-10-04 14:00:39***********************/#include <queue>#include <string.h>#include <iostream>#include <vector>using namespace std;typedef long long ll;typedef unsigned long long ull;const int maxn = 1e2 + 10;const int INF = 0x3f3f3f3f;const int DINF = 0xc0c0c0c0;int a, b, c;int n, m, k, T;int t, ans;int x, y, z;vector<pair<int, int>> e[maxn];int dis[maxn];bool vis[maxn];void init() {for (int i = 0; i < maxn; i++) e[i].clear();memset(dis, INF, sizeof dis);ans = 0;}void dijkstra(int st, int ed) {priority_queue<pair<int, int> > q;q.push(make_pair(-INF, st));dis[st] = 0;while (!q.empty()) {int now = q.top().second;q.pop();int size = e[now].size();for (int i = 0; i < size; i++) {int to = e[now][i].first;int cost = e[now][i].second;if (dis[to] > dis[now] + cost) {dis[to] = dis[now] + e[now][i].second;q.push(make_pair(-dis[to], to));}}}ans = dis[ed];}int main() {while (cin >> n >> m, n || m) {init();for (int i = 0; i < m; i++) {cin >> a >> b >> c;e[a].push_back(make_pair(b, c));e[b].push_back(make_pair(a, c));}dijkstra(1, n);cout << ans << endl;}}

Floyd+邻接矩阵

/***********************@Name: hdu 2544 Floyd**@Author: Nervending*@Describtion: Floyd*@DateTime: 2017-10-04 14:00:39***********************/#include <string.h>#include <iostream>using namespace std;typedef long long ll;typedef unsigned long long ull;const int maxn = 1e2 + 10;const int INF = 0x3f3f3f3f;const int DINF = 0xc0c0c0c0;int a, b, c;int n, m, k, T;int t, ans;int x, y, z;int dis[maxn][maxn];void init() {memset(dis, INF, sizeof dis);for (int i = 0; i < maxn; i++) {dis[i][i] = 0;}ans = 0;}void floyd(int st , int ed) {for (int i = 1; i <= n; i++) {for (int j = 1; j <= n; j++) {for (int k = 1; k <= n; k++) {if (dis[j][k] > dis[j][i] + dis[i][k]) {dis[j][k] = dis[j][i] + dis[i][k];}}}}ans = dis[st][ed];}int main() {while (cin >> n >> m, n || m) {init();for (int i = 0; i < m; i++) {cin >> a >> b >> c;dis[a][b] = dis[b][a] = c;}floyd(1, n);cout << ans << endl;}}