最短路算法

最新推荐文章于 2024-09-10 20:00:52 发布

2inf

最新推荐文章于 2024-09-10 20:00:52 发布

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本文链接：https://blog.youkuaiyun.com/AbelYang1/article/details/89199999

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博客分享了Dijkstra、Floyd、Bellman - Ford和SPFA算法相关资源，其中Dijkstra算法有堆优化及matlab相关内容，每个算法都给出了对应的博客链接。

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Dijkstra

https://www.cnblogs.com/fzl194/p/8728018.html

const int N = 1e5 + 5;
int mp[N][N];
int d[N];
bool vis[N];
int V;      //顶点数

void dijkstra(int s)
{
    fill(d, d + V, INF);
    fill(vis, vis + V, false);
    d[s] = 0;

    while(1) {
        int v = -1;
        //从未选择的点中选一个距离最小的顶点
        for (int i = 0; i < V; ++i) {
            if (!vis[i] && (v == -1 || d[i] < d[v])) v = i;
        }
        if (v == -1) break;
        vis[v] = 1;
        for (int u = 0; u < V; ++u) {
            d[u] = min(d[u], d[v] + mp[v][u]);
        }
    }
}

堆优化

priority_queue<pii > q;

struct Edge
{
    int next, to, w;
}e[M];

inline void add(int x, int y, int z)
{
    e[++tot].w = z;
    e[tot].next = head[x];
    e[tot].to = y;
    head[x] = tot;
}

void dijkstra()
{
    d[s] = 0;
    q.push(mp(0, s));
    while (!q.empty()) {
        int x = q.top().second;
        q.pop();
        if (vis[x]) continue;
        vis[x] = 1;
        for (int i = head[x]; i; i = e[i].next) {
            int y = e[i].to;
            if (d[y] > d[x] + e[i].w) {
                d[y] = d[x] + e[i].w;
                q.push(mp(-d[y], y));
            }
        }
    }
}

matlab

clc
clear all
function [d path] = dijkstra(A, s, t)
%Dijkstra最短算法实现, A为图的赋权邻接矩阵
%当输入参数含有s和t时, 求s到t的最短路
if nargin==2
	flag=0;
elseif nargin==3
	flag=1;
end
n=length(A);%节点数
for i=1:n
	A(i,j)=inf;
end;
V=zeros(1,n);
D=zeros(1,n);
T=A+inf;
T(s,:)=A(s,:);
A(:,s)=inf

path =[];
 
for k=1:n-1
    [p,q] = min(T);
    q1=q;
    [p,q] = min(p);
    v(q)=q1(q);
    if flag
    
    [value,index] = min(temp);
   
    visit(index) = 0;
    
    %更新 如果经过index节点，从起点到每个节点的路径长度更小，则更新，记录前趋节点，方便后面回溯循迹
    for k=1:n
        if D(k)>D(index)+W(index,k)
           D(k) = D(index)+W(index,k);
           parent(k) = index;
        end
    end
    
   
end
 
distance = D(e);%最短距离
%回溯法  从尾部往前寻找搜索路径
t = e;
while t~=st && t>0
 path =[t,path];
  p=parent(t);t=p;
end
path =[st,path];%最短路径
 
 
end

Floyd

https://www.cnblogs.com/fzl194/p/8729340.html

void floyd()
{
    for (int k = 0; k < n; ++k) {
        for (int i = 0; i < n; ++i) {
            for(int j = 0; j < n; ++j) {
                mp[i][j] = min(mp[i][j], mp[i][k] + mp[k][j]);
}

Bellman-Ford

https://www.cnblogs.com/fzl194/p/8728529.html

SPFA

https://www.cnblogs.com/fzl194/p/8728883.html

struct Edge
{
    int next, to, w;
}edge[M];

void add(int x, int y, int z)
{
    edge[++tot].next = head[x];
    edge[tot].to = y;
    edge[tot].w = z;
    head[x] = tot;
}

void spfa()
{
    queue<int> q;
    for (int i = 1; i <= n; ++i) {
        d[i] = INF;
        vis[i] = 0;
    }
    q.push(s);
    d[s] = 0, vis[s] = 1;
    while (!q.empty()) {
        int u = q.front();
        q.pop();
        vis[u] = 0;
        for (int i = head[u]; i; i = edge[i].next) {
            int v = edge[i].to;
            if (d[v] > d[u] + edge[i].w) {
                d[v] = d[u] + edge[i].w;
                if (!vis[v]) q.push(v), vis[v] = 1;
            }
        }
    }
}