2017 Multi-University Training Contest 10 1011 Two Paths HDU 6181 (次短路)

题意：给你一个有向图，问你他的次短路长度（与最短路至少有一条边不同即可）

思路：如果最短路有多条，那答案就是最短路，否则就是次短路

求次短路（见点击打开链接）：

1.     思路： 
2.         把求最短路时更新最短路的那部分改一下。 
3.         dis1，dis2数组分别记录到该点的最短路和次短路 
4.         分三种情况： 
5.             1.若该点最短路+下一条边比到下个点的最短路短，则更新下个点的最短路，同时更新次短路为原最短路 
6.             2.若该点次短路+下一条边比到下个点的次短路短，则更新下个点的次短路 
7.             3.若该点最短路+下一条边比到下个点的最短路长同时比下个点的次短路短，则更新下个点的次短路 

代码：

#include<iostream>#include<cstdio>#include<queue>#include<cstring>#include<algorithm>using namespace std;typedef long long ll;const int maxn = 2e5+5;const ll INF = 0x3f3f3f3f3f3f3f3f;int n, m, k, head[maxn];ll cnt[maxn];ll dis1[maxn], dis2[maxn], dis[maxn];bool book[maxn];struct node{    int v, w, next;}edge[maxn];void addEdge(int u, int v, int w){    edge[k].v = v;    edge[k].w = w;    edge[k].next = head[u];    head[u] = k++;}void spfa(int u){    for(int i = 1; i <= n; i++) dis1[i] = INF;    for(int i = 1; i <= n; i++) dis2[i] = INF;    memset(book, 0, sizeof(book));    queue<int> q;    q.push(u);    dis1[u] = 0;    book[u] = 1;    while(!q.empty())    {        u = q.front(); q.pop();        book[u] = 0;        for(int i = head[u]; i != -1; i = edge[i].next)        {            int v = edge[i].v;            int w = edge[i].w;            if(dis1[v] > dis1[u]+w)            {                dis2[v] = dis1[v];                dis1[v] = dis1[u]+w;                if(!book[v]) book[v] = 1, q.push(v);            }            if(dis2[v] > dis2[u]+w)            {                dis2[v] = dis2[u]+w;                if(!book[v]) book[v] = 1, q.push(v);            }            if(dis1[v] < dis1[u]+w && dis2[v] > dis1[u]+w)            {                dis2[v] = dis1[u]+w;                if(!book[v]) book[v] = 1, q.push(v);            }        }    }}void spfa2(int u){    for(int i = 1; i <= n; i++) dis[i] = INF;    memset(book, 0, sizeof(book));    queue<int> q;    q.push(u);    book[u] = cnt[u] = 1;    dis[u] = 0;    while(!q.empty())    {        u = q.front(); q.pop();        book[u] = 0;        for(int i = head[u]; i != -1; i = edge[i].next)        {            int v = edge[i].v;            int w = edge[i].w;            if(dis[u]+w < dis[v])            {                dis[v] = dis[u]+w;                if(!book[v]) book[v] = 1, q.push(v);                cnt[v] = cnt[u];            }            else if(dis[u]+w == dis[v])            {                cnt[v] += cnt[u];            }        }    }}int main(void){    int t;    cin >> t;    while(t--)    {        k = 0;        memset(cnt, 0, sizeof(cnt));        memset(head, -1, sizeof(head));        scanf("%d%d", &n, &m);        for(int i = 1; i <= m; i++)        {            int u, v, w;            scanf("%d%d%d", &u, &v, &w);            addEdge(u, v, w);            addEdge(v, u, w);        }        spfa(1);        spfa2(1);        if(cnt[n] > 1) printf("%lld\n", dis1[n]);        else printf("%lld\n", dis2[n]);    }    return 0;}