Candies

Time Limit: 1500ms

Memory Limit: 131072KB

This problem will be judged on 

PKU. Original ID: 

64-bit integer IO format: %lld      Java class name: Main

 

 

During the kindergarten days, flymouse was the monitor of his class. Occasionally the head-teacher brought the kids of flymouse’s class a large bag of candies and had flymouse distribute them. All the kids loved candies very much and often compared the numbers of candies they got with others. A kid A could had the idea that though it might be the case that another kid B was better than him in some aspect and therefore had a reason for deserving more candies than he did, he should never get a certain number of candies fewer than B did no matter how many candies he actually got, otherwise he would feel dissatisfied and go to the head-teacher to complain about flymouse’s biased distribution.

snoopy shared class with flymouse at that time. flymouse always compared the number of his candies with that of snoopy’s. He wanted to make the difference between the numbers as large as possible while keeping every kid satisfied. Now he had just got another bag of candies from the head-teacher, what was the largest difference he could make out of it?

Input

The input contains a single test cases. The test cases starts with a line with two integers N and M not exceeding 30 000 and 150 000 respectively. N is the number of kids in the class and the kids were numbered 1 through N. snoopy and flymouse were always numbered 1 and N. Then follow M lines each holding three integers A, B and c in order, meaning that kid A believed that kid B should never get over c candies more than he did.

 

Output

Output one line with only the largest difference desired. The difference is guaranteed to be finite.

 

Sample Input

2 21 2 52 1 4

Sample Output

5

Source

 

解题：一个很裸的差分约束问题！直接求1到n的最短路

 

至于为什么spfa要用栈而不是队列，因为一直超时！vector没法用，用了就超时！

 

1 #include 
        
          2 #include 
         
           3 #include 
          
            4 #include 
           
             5 #include 
            
              6 #include 
             
               7 #include 
              
                8 #include 
               
                 9 #include 
                
                 10 #include 
                 
                  11 #include 
                  
                   12 #include 
                   
                    13 #define LL long long14 #define INF 0x3f3f3f3f15 using namespace std;16 struct arc{17 int to,w,next;18 };19 arc g[200000];20 int head[30010],tot,n,m;21 int d[30010];22 bool done[30010];23 void add(int u,int v,int w){24 g[tot].to = v;25 g[tot].w = w;26 g[tot].next = head[u];27 head[u] = tot++;28 }29 stack
                    
                     stk;30 void spfa(int s){31 d[s] = 0;32 while(!stk.empty()) stk.pop();33 done[s] = true;34 stk.push(s);35 int u,i;36 while(!stk.empty()){37 u = stk.top();38 stk.pop();39 done[u] = false;40 for(i = head[u]; i != -1; i = g[i].next){41 if(d[g[i].to] > d[u] + g[i].w){42 d[g[i].to] = d[u] + g[i].w;43 if(!done[g[i].to]){44 done[g[i].to] = true;45 stk.push(g[i].to);46 }47 }48 }49 }50 }51 int main(){52 int i,j,u,v,w;53 while(~scanf("%d %d",&n,&m)){54 for(i = 0; i <= n; i++){55 done[i] = false;56 head[i] = -1;57 d[i] = INF;58 }59 for(tot = i = 0; i < m; i++){60 scanf("%d %d %d",&u,&v,&w);61 add(u,v,w);62 }63 spfa(1);64 printf("%d\n",d[n]);65 }66 return 0;67 }
                    
                   
                  
                 
                
               
              
             
            
           
          
         
        

 

好吧，加个优先队列版的Dijkstra吧

 

1 #include 
        
          2 #include 
         
           3 #include 
          
            4 #include 
           
             5 #include 
            
              6 #include 
             
               7 #include 
              
                8 #include 
               
                 9 #include 
                
                 10 #include 
                 
                  11 #include 
                  
                   12 #include 
                   
                    13 #define LL long long14 #define INF 0x3f3f3f3f15 #define pii pair
                    
                     16 using namespace std;17 struct arc{18 int to,w,next;19 };20 arc g[200000];21 int head[30010],d[30010],tot,n,m;22 bool done[30010];23 void add(int u,int v,int w){24 g[tot].to = v;25 g[tot].w = w;26 g[tot].next = head[u];27 head[u] = tot++;28 }29 priority_queue
                     
                      < pii >,greater< pii > >q;30 void dijkstra(int s,int t){31 while(!q.empty()) q.pop();32 d[s] = 0;33 q.push(make_pair(d[s],s));34 while(!q.empty()){35 int u = q.top().second;36 q.pop();37 if(done[u]) continue;38 done[u] = true;39 for(int i = head[u]; i != -1; i = g[i].next){40 if(d[g[i].to] > d[u] + g[i].w){41 d[g[i].to] = d[u] + g[i].w;42 q.push(make_pair(d[g[i].to],g[i].to));43 }44 }45 if(done[t]) return;46 }47 }48 int main(){49 int i,u,v,w;50 while(~scanf("%d %d",&n,&m)){51 for(i = 0; i <= n; i++){52 head[i] = -1;53 done[i] = false;54 d[i] = INF;55 }56 for(tot = i = 0; i < m; i++){57 scanf("%d %d %d",&u,&v,&w);58 add(u,v,w);59 }60 dijkstra(1,n);61 printf("%d\n",d[n]);62 }63 return 0;64 }