http://acm.hdu.edu.cn/showproblem.php?pid=3191

求次短路的长度和个数

相关分析在这里http://blog.csdn.net/u012774187/article/details/40681515

  1. #pragma comment(linker, "/STACK:36777216")
  2. #pragma GCC optimize ("O2")
  3. #include <cstdio>
  4. #include <cstdlib>
  5. #include <cmath>
  6. #include <cstring>
  7. #include <string>
  8. #include <queue>
  9. #include <map>
  10. #include <iostream>
  11. #include <algorithm>
  12. using namespace std;
  13. #define RD(x) scanf("%d",&x)
  14. #define RD2(x,y) scanf("%d%d",&x,&y)
  15. #define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)
  16. #define clr0(x) memset(x,0,sizeof(x))
  17. #define clr1(x) memset(x,-1,sizeof(x))
  18. #define eps 1e-9
  19. const double pi = acos(-1.0);
  20. typedef long long LL;
  21. typedef unsigned long long ULL;
  22. const int modo = 1e9 + 7;
  23. const int INF = 0x3f3f3f3f;
  24. const int inf = 0x3fffffff;
  25. const LL _inf = 1e18;
  26. const int maxn = 55,maxm = 10005;
  27. struct edge{
  28.     int v,w,next;
  29.     edge(){};
  30.     edge(int vv,int ww,int nnext):v(vv),w(ww),next(nnext){};
  31. }e[maxn*maxn*2];
  32. int head[maxn],inq[maxn][2],dist[maxn][2],cnt[maxn][2];//0最短1次短
  33. int n,m,ecnt;
  34. void init()
  35. {
  36.     clr1(head);
  37.     ecnt = 0;
  38.     for(int i = 1;i <= maxn;++i)
  39.         dist[i][0] = dist[i][1] = inf;
  40.     //fill(dist,dist+maxn*2,inf);
  41.     clr0(inq),clr0(cnt);
  42. }
  43. void add(int u,int v,int w)
  44. {
  45.     e[ecnt] = edge(v,w,head[u]);
  46.     head[u] = ecnt++;
  47. //    e[ecnt] = edge(u,w,head[v]);
  48. //    head[v] = ecnt++;
  49. }
  50. typedef pair<int,int> p2;
  51. struct cmp {
  52.      bool operator() (const p2 &a, const p2 &b)
  53.      {
  54.         if(dist[a.first][a.second] != dist[b.first][b.second])
  55.             return dist[a.first][a.second] > dist[b.first][b.second];
  56.         else
  57.             return a.first > b.first;
  58.      }
  59. };
  60. void spfa(int src,int dst)
  61. {
  62.     priority_queue<p2 , vector<p2> , cmp> q;
  63.     q.push(make_pair(src,0));
  64.     dist[src][0] = 0,cnt[src][0] = 1;
  65.     while(!q.empty()){
  66.         int u = q.top().first,flag = q.top().second;
  67.         q.pop();
  68.         if(inq[u][flag])    continue;
  69.         inq[u][flag] = 1;
  70.         for(int i = head[u];i != -1;i = e[i].next){
  71.             int v = e[i].v,w = e[i].w;
  72.             if(!inq[v][0] && dist[v][0] > dist[u][flag] + e[i].w){
  73.                 if(dist[v][0] != inf){
  74.                     dist[v][1] = dist[v][0];
  75.                     cnt[v][1] = cnt[v][0];
  76.                     q.push(make_pair(v,1));
  77.                 }
  78.                 dist[v][0] = dist[u][flag] + e[i].w;
  79.                 cnt[v][0] = cnt[u][flag];
  80.  
  81.                 q.push(make_pair(v,0));
  82.             }else if(!inq[v][0] && dist[v][0] == dist[u][flag] + e[i].w){
  83.                 cnt[v][0] += cnt[u][flag];
  84.             }else if(!inq[v][1] && dist[v][1] > dist[u][flag] + e[i].w){
  85.                 dist[v][1] = dist[u][flag] + e[i].w;
  86.                 cnt[v][1] = cnt[u][flag];
  87.  
  88.                 q.push(make_pair(v,1));
  89.             }else if(!inq[v][1] && dist[v][1] == dist[u][flag] + e[i].w){
  90.                 cnt[v][1] += cnt[u][flag];
  91.             }
  92.         }
  93.     }
  94.     printf("%d %d\n",dist[dst][1],cnt[dst][1]);
  95. }
  96.  
  97. int main(){
  98.     int u,v,w,s,t;
  99.     while(~RD2(n,m)){
  100.         RD2(s,t);s++,t++;
  101.         init();
  102.         while(m--){
  103.             RD3(u,v,w);u++,v++;
  104.             add(u,v,w);
  105.         }
  106.         spfa(s,t);
  107.     }
  108.     return 0;
  109. }

上面是错误代码

经过筛查，发现是 

  1. if(dist[a.first][a.second] != dist[b.first][b.second])
  2.             return dist[a.first][a.second] > dist[b.first][b.second];

有问题，因为不同的路径到达同一个点的同一个状态的值不一样，所有比较和更新穿插在一起就会出错了

可是每次更新dist数组都是向小了更新，所以不应该有影响啊..?

以下是AC代码，谁能清楚一点地告诉为啥上面的程序就不对呢？

  1. #pragma comment(linker, "/STACK:36777216")
  2. #pragma GCC optimize ("O2")
  3. #include <cstdio>
  4. #include <cstdlib>
  5. #include <cmath>
  6. #include <cstring>
  7. #include <string>
  8. #include <queue>
  9. #include <map>
  10. #include <iostream>
  11. #include <algorithm>
  12. using namespace std;
  13. #define RD(x) scanf("%d",&x)
  14. #define RD2(x,y) scanf("%d%d",&x,&y)
  15. #define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)
  16. #define clr0(x) memset(x,0,sizeof(x))
  17. #define clr1(x) memset(x,-1,sizeof(x))
  18. #define eps 1e-9
  19. const double pi = acos(-1.0);
  20. typedef long long LL;
  21. typedef unsigned long long ULL;
  22. const int modo = 1e9 + 7;
  23. const int INF = 0x3f3f3f3f;
  24. const int inf = 0x3fffffff;
  25. const LL _inf = 1e18;
  26. const int maxn = 55,maxm = 10005;
  27. struct edge{
  28.     int v,w,next;
  29.     edge(){};
  30.     edge(int vv,int ww,int nnext):v(vv),w(ww),next(nnext){};
  31. }e[maxn*maxn*2];
  32. int head[maxn],inq[maxn][2],dist[maxn][2],cnt[maxn][2];//0最短1次短
  33. int n,m,ecnt;
  34. struct node{
  35.     int v,flag,dis;
  36.     node(int a,int b,int c):v(a),flag(b),dis(c){};
  37.     bool operator < (const node & a) const{
  38.         if(a.dis == dis)
  39.             return a.v < v;
  40.         return a.dis < dis;
  41.     }
  42. };
  43. void init()
  44. {
  45.     clr1(head);
  46.     ecnt = 0;
  47.     for(int i = 0;i <= n;++i)
  48.         dist[i][0] = dist[i][1] = inf;
  49.     //fill(dist,dist+maxn*2,inf);
  50.     clr0(inq),clr0(cnt);
  51. }
  52. void add(int u,int v,int w)
  53. {
  54.     e[ecnt] = edge(v,w,head[u]);
  55.     head[u] = ecnt++;
  56. //    e[ecnt] = edge(u,w,head[v]);
  57. //    head[v] = ecnt++;
  58. }
  59. void spfa(int src,int dst)
  60. {
  61.     priority_queue<node> q;
  62.     q.push(node(src,0,0));
  63.     dist[src][0] = 0,cnt[src][0] = 1;
  64.     while(!q.empty()){
  65.         int u = q.top().v,flag = q.top().flag,dis = q.top().dis;
  66.         q.pop();
  67.         if(inq[u][flag])    continue;
  68.         inq[u][flag] = 1;
  69.         for(int i = head[u];i != -1;i = e[i].next){
  70.             int v = e[i].v,w = e[i].w;
  71.             if(!inq[v][0] && dist[v][0] > dis + e[i].w){
  72.                 if(dist[v][0] != inf){
  73.                     dist[v][1] = dist[v][0];
  74.                     cnt[v][1] = cnt[v][0];
  75.                     q.push(node(v,1,dist[v][1]));
  76.                 }
  77.                 dist[v][0] = dis + e[i].w;
  78.                 cnt[v][0] = cnt[u][flag];
  79.  
  80.                 q.push(node(v,0,dist[v][0]));
  81.             }else if(!inq[v][0] && dist[v][0] == dis + e[i].w){
  82.                 cnt[v][0] += cnt[u][flag];
  83.             }else if(!inq[v][1] && dist[v][1] > dis + e[i].w){
  84.                 dist[v][1] = dis + e[i].w;
  85.                 cnt[v][1] = cnt[u][flag];
  86.  
  87.                 q.push(node(v,1,dist[v][1]));
  88.             }else if(!inq[v][1] && dist[v][1] == dis+ e[i].w){
  89.                 cnt[v][1] += cnt[u][flag];
  90.             }
  91.         }
  92.     }
  93.     printf("%d %d\n",dist[dst][1],cnt[dst][1]);
  94. }
  95.  
  96. int main(){
  97.     int u,v,w,s,t;
  98.     while(~RD2(n,m)){
  99.         RD2(s,t);s++,t++;
  100.         init();
  101.         while(m--){
  102.             RD3(u,v,w);u++,v++;
  103.             add(u,v,w);
  104.         }
  105.         spfa(s,t);
  106.     }
  107.     return 0;
  108. }

AC代码2

  1. #pragma comment(linker, "/STACK:36777216")
  2. #pragma GCC optimize ("O2")
  3. #include <cstdio>
  4. #include <cstdlib>
  5. #include <cmath>
  6. #include <cstring>
  7. #include <string>
  8. #include <queue>
  9. #include <map>
  10. #include <iostream>
  11. #include <algorithm>
  12. using namespace std;
  13. #define RD(x) scanf("%d",&x)
  14. #define RD2(x,y) scanf("%d%d",&x,&y)
  15. #define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)
  16. #define clr0(x) memset(x,0,sizeof(x))
  17. #define clr1(x) memset(x,-1,sizeof(x))
  18. #define eps 1e-9
  19. const double pi = acos(-1.0);
  20. typedef long long LL;
  21. typedef unsigned long long ULL;
  22. const int modo = 1e9 + 7;
  23. const int INF = 0x3f3f3f3f;
  24. const int inf = 0x3fffffff;
  25. const LL _inf = 1e18;
  26. const int maxn = 55,maxm = 10005;
  27. struct edge{
  28.     int v,w,next;
  29.     edge(){};
  30.     edge(int vv,int ww,int nnext):v(vv),w(ww),next(nnext){};
  31. }e[maxn*maxn*2];
  32. int head[maxn],inq[maxn][2],dist[maxn][2],cnt[maxn][2];//0最短1次短
  33. int n,m,ecnt;
  34. struct node{
  35.     int v,flag,dis;
  36.     node(int a,int b,int c):v(a),flag(b),dis(c){};
  37.     bool operator < (const node & a) const{
  38.         if(a.dis == dis)
  39.             return a.v < v;
  40.         return a.dis < dis;
  41.     }
  42. };
  43. void init()
  44. {
  45.     clr1(head);
  46.     ecnt = 0;
  47.     for(int i = 0;i <= n;++i)
  48.         dist[i][0] = dist[i][1] = inf;
  49.     //fill(dist,dist+maxn*2,inf);
  50.     clr0(inq),clr0(cnt);
  51. }
  52. void add(int u,int v,int w)
  53. {
  54.     e[ecnt] = edge(v,w,head[u]);
  55.     head[u] = ecnt++;
  56. //    e[ecnt] = edge(u,w,head[v]);
  57. //    head[v] = ecnt++;
  58. }
  59. void spfa(int src,int dst)
  60. {
  61.     priority_queue<node> q;
  62.     q.push(node(src,0,0));
  63.     dist[src][0] = 0,cnt[src][0] = 1;
  64.     while(!q.empty()){
  65.         int u = q.top().v,flag = q.top().flag;//dis = q.top().dis;
  66.         q.pop();
  67.         if(inq[u][flag])    continue;
  68.         inq[u][flag] = 1;
  69.         for(int i = head[u];i != -1;i = e[i].next){
  70.             int v = e[i].v,w = e[i].w;
  71.             if(!inq[v][0] && dist[v][0] > dist[u][flag] + e[i].w){
  72.                 if(dist[v][0] != inf){
  73.                     dist[v][1] = dist[v][0];
  74.                     cnt[v][1] = cnt[v][0];
  75.                     q.push(node(v,1,dist[v][1]));
  76.                 }
  77.                 dist[v][0] = dist[u][flag] + e[i].w;
  78.                 cnt[v][0] = cnt[u][flag];
  79.  
  80.                 q.push(node(v,0,dist[v][0]));
  81.             }else if(!inq[v][0] && dist[v][0] == dist[u][flag] + e[i].w){
  82.                 cnt[v][0] += cnt[u][flag];
  83.             }else if(!inq[v][1] && dist[v][1] > dist[u][flag] + e[i].w){
  84.                 dist[v][1] = dist[u][flag] + e[i].w;
  85.                 cnt[v][1] = cnt[u][flag];
  86.  
  87.                 q.push(node(v,1,dist[v][1]));
  88.             }else if(!inq[v][1] && dist[v][1] == dist[u][flag] + e[i].w){
  89.                 cnt[v][1] += cnt[u][flag];
  90.             }
  91.         }
  92.     }
  93.     printf("%d %d\n",dist[dst][1],cnt[dst][1]);
  94. }
  95.  
  96. int main(){
  97.     int u,v,w,s,t;
  98.     while(~RD2(n,m)){
  99.         RD2(s,t);s++,t++;
  100.         init();
  101.         while(m--){
  102.             RD3(u,v,w);u++,v++;
  103.             add(u,v,w);
  104.         }
  105.         spfa(s,t);
  106.     }
  107.     return 0;
  108. }

#pragma comment(linker, "/STACK:36777216")#pragma GCC optimize ("O2")#include <cstdio>#include <cstdlib>#include <cmath>#include <cstring>#include <string>#include
<queue>#include <map>#include <iostream>#include <algorithm>using namespace std;#define RD(x) scanf("%d",&x)#define RD2(x,y) scanf("%d%d",&x,&y)#define RD3(x,y,z) scanf("%d%d%d",&x,&y,&z)#define clr0(x) memset(x,0,sizeof(x))#define clr1(x) memset(x,-1,sizeof(x))#define
eps 1e-9const double pi = acos(-1.0);typedef long long LL;typedef unsigned long long ULL;const int modo = 1e9 + 7;const int INF = 0x3f3f3f3f;const int inf = 0x3fffffff;const LL _inf = 1e18;const int maxn = 55,maxm = 10005;struct edge{ int v,w,next; edge(){};
edge(int vv,int ww,int nnext):v(vv),w(ww),next(nnext){};}e[maxn*maxn*2];int head[maxn],inq[maxn][2],dist[maxn][2],cnt[maxn][2];//0最短1次短int n,m,ecnt;void init(){ clr1(head); ecnt = 0; for(int i = 0;i < maxn;++i) dist[i][0] = dist[i][1] = inf; //fill(dist,dist+maxn*2,inf);
clr0(inq),clr0(cnt);}void add(int u,int v,int w){ e[ecnt] = edge(v,w,head[u]); head[u] = ecnt++;// e[ecnt] = edge(u,w,head[v]);// head[v] = ecnt++;}typedef pair<int,int> p2;struct cmp { bool operator() (const p2 &a, const p2 &b) { if(dist[a.first][a.second]
!= dist[b.first][b.second]) return dist[a.first][a.second] > dist[b.first][b.second]; else return a.first > b.first; }};void spfa(int src,int dst){ priority_queue<p2 , vector<p2> , cmp> q; q.push(make_pair(src,0)); dist[src][0] = 0,cnt[src][0] = 1; while(!q.empty()){
int u = q.top().first,flag = q.top().second; q.pop(); if(inq[u][flag]) continue; inq[u][flag] = 1; for(int i = head[u];i != -1;i = e[i].next){ int v = e[i].v,w = e[i].w; if(!inq[v][0] && dist[v][0] > dist[u][flag] + e[i].w){ if(dist[v][0] != inf){ dist[v][1]
= dist[v][0]; cnt[v][1] = cnt[v][0]; q.push(make_pair(v,1)); } dist[v][0] = dist[u][flag] + e[i].w; cnt[v][0] = cnt[u][flag]; q.push(make_pair(v,0)); }else if(!inq[v][0] && dist[v][0] == dist[u][flag] + e[i].w){ cnt[v][0] += cnt[u][flag]; }else if(!inq[v][1]
&& dist[v][1] > dist[u][flag] + e[i].w){ dist[v][1] = dist[u][flag] + e[i].w; cnt[v][1] = cnt[u][flag]; q.push(make_pair(v,1)); }else if(!inq[v][1] && dist[v][1] == dist[u][flag] + e[i].w){ cnt[v][1] += cnt[u][flag]; } } } printf("%d %d\n",dist[dst][1],cnt[dst][1]);}int
main(){ int u,v,w,s,t; while(~RD2(n,m)){ RD2(s,t);s++,t++; init(); while(m--){ RD3(u,v,w);u++,v++; add(u,v,w); } spfa(s,t); } return 0;}

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