次短路
找了好半天才找到两个比较好理解的代码，暂时放到这，之后再来改。
点击打开链接
次短路[v]=最短路[u]+边[u,v] 或者 次短路[v]=次短路[u]+边[u,v] ，不同于普通最短路，我们需要维护两个数组：最短路+次短路。
我这里采用 邻接表+dijkstra，不断更新最短路和次短路。
#include
#include
#include
#include
#include
#define INF 0xfffffff
using namespace std;
struct Edge{
int to,cost;
};
int n,r;
vector edge[5005];
typedef pair P;//first是最短距离，second是顶点编号
int dis1[5005];//最短距离
int dis2[5005];//次短距离
void solve(){
priority_queue,greater > q;//递增的优先队列
for(int i = 0; i <= n; i++){
dis1[i] = INF;
dis2[i] = INF;
}
dis1[1] = 0;
q.push(P(0,1));
while(!q.empty()){
P p = q.top();
q.pop();
int v = p.second,d = p.first;
if(dis2[v] < d)
continue;
for(int i = 0; i < edge[v].size(); i++){
Edge &e = edge[v][i];
int d2 = d + e.cost;
//最短距离的更新，入队
if(dis1[e.to] > d2){
printf("dis1[e.to]=%d > d2=%d ?\n",e.to,d2);
swap(dis1[e.to],d2);
q.push(P(dis1[e.to],e.to));
}
//新的次短距离 应该 大于最短距离&&小于原来的次短距离
if(dis2[e.to] > d2 && dis1[e.to] < d2){
printf("dis2[e.to]=%d > d2=%d ?\n",e.to,d2);
dis2[e.to] = d2;
q.push(P(dis2[e.to],e.to));//入队
}
}
}
printf("%d\n",dis2[n]);
}
int main(){
while(~scanf("%d%d",&n,&r)){
for(int i = 0; i <= n; i++)
edge[i].clear();
int u,v,cost;
Edge tmp;
for(int i = 0; i < r; i++){
scanf("%d%d%d",&u,&v,&cost);
tmp.to = v;tmp.cost = cost;
edge[u].push_back(tmp);
tmp.to = u;
edge[v].push_back(tmp);
}
solve();
}
return 0;
}
点击打开链接http://blog.csdn.net/qq_21899803/article/details/52192736
先算出每个点到1的最短路dis[i]，再算出每个点到n点的最短路disr[i]，然后枚举所有边，计算次短路dis[u]+disr[v]+edge[u][v]
#include
#include
#include
#include
#include
#include
#define MAXN 5010
#define MAXM 101000
#define INF 0x3f3f3f3f
using namespace std;
struct node
{
int v, w, next;
} edge[MAXM * 2];
int n, m, e, p, q;
int vis[MAXN], dis[MAXN], disr[MAXN], head[MAXN];
void insert(int x, int y, int w)
{
edge[e].v = y;
edge[e].w = w;
edge[e].next = head[x];
head[x] = e++;
}
void spfa(int src, int d[])
{
memset(vis, 0, sizeof(vis));
vis[src] = 1;
d[src] = 0;
queue Q;
Q.push(src);
while(!Q.empty())
{
p = Q.front();
Q.pop();
vis[p] = 0;
for(int i = head[p]; i != -1; i = edge[i].next)
{
int v = edge[i].v;
int w = edge[i].w;
if(d[v] > d[p] + w)
{
d[v] = d[p] + w;
if(!vis[v])
{
vis[v] = 1;
Q.push(v);
}
}
}
}
}
int main()
{
int a, b, c;
while(scanf("%d%d", &n, &m) != EOF)
{
e = 0;
memset(head, -1, sizeof(head));
memset(dis, 0x3f, sizeof(dis));
memset(disr, 0x3f, sizeof(dis));
for(int i = 0; i < m; i++)
{
scanf("%d%d%d", &a, &b, &c);
insert(a, b, c);
insert(b, a, c);
}
spfa(1, dis);
spfa(n, disr);
int mini = dis[n];
int ans = INF;
for(int i = 1; i <= n; i++)
{
for(int j = head[i]; j != -1; j = edge[j].next)
{
int v = edge[j].v;
int w = edge[j].w;
if(dis[i] + disr[v] + w > mini && dis[i] + disr[v] + w < ans)
ans = dis[i] + disr[v] + w;
}
}
printf("%d\n",ans);
}
return 0;
}