E

E - Elevator
http://codeforces.com/gym/241680/problem/E
同余最短路，从0~a-1中每一个i向(i+b)%a连一条权值为b的边，向(i+c)%a连一条权值为c的边，然后跑spfa最短路，此时d[i]表示达到x%a花费的最小的距离，这里放的只有b,c，（解释一下，b,c组合出的实际大小为x,因为x过大，数组存不下，所以表示为x%a
最后统计答案的时候ans+=1+(h-d[i])/a;当前只有b,c组合出的d[i]算一个答案,然后剩下可以用a来填充

//用最小的来做同余系比较快

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<queue>
  4 #include<algorithm>
  5 #include<cmath>
  6 #include<ctime>
  7 #include<set>
  8 #include<map>
  9 #include<stack>
 10 #include<cstring>
 11 #define inf 2147483647
 12 #define INF 9187201950435737471
 13 #define ls rt<<1
 14 #define rs rt<<1|1
 15 #define lson ls,nl,mid,l,r
 16 #define rson rs,mid+1,nr,l,r
 17 #define N 100010
 18 #define For(i,a,b) for(long long i=a;i<=b;i++)
 19 #define p(a) putchar(a)
 20 #define g() getchar()
 21 
 22 using namespace std;
 23 long long h;
 24 long long a,b,c,ans;
 25 long long d[1000010];
 26 queue<long long>q;
 27 bool vis[1000010];
 28 
 29 struct node{
 30     long long v;
 31     long long n;
 32     node *next;
 33 }*e[10000010];
 34 
 35 void in(long long &x){
 36     long long y=1;
 37     char c=g();x=0;
 38     while(c<'0'||c>'9'){
 39         if(c=='-')y=-1;
 40         c=g();
 41     }
 42     while(c<='9'&&c>='0'){
 43         x=(x<<1)+(x<<3)+c-'0';c=g();
 44     }
 45     x*=y;
 46 }
 47 void o(long long x){
 48     if(x<0){
 49         p('-');
 50         x=-x;
 51     }
 52     if(x>9)o(x/10);
 53     p(x%10+'0');
 54 }
 55 
 56 void push(long long x,long long y,long long v){
 57     node *p;
 58     p=new node();
 59     p->n=y;
 60     p->v=v;
 61     if(e[x]==0)
 62         e[x]=p;
 63     else{
 64         p->next=e[x]->next;
 65         e[x]->next=p;
 66     }
 67 }
 68 
 69 void spfa(){
 70      For(i,0,a)
 71          d[i]=INF;
 72     q.push(1%a);
 73     d[1%a]=1;
 74     while(!q.empty()){
 75         long long t=q.front();
 76         q.pop();
 77         vis[t]=true;
 78 
 79         for(node *i=e[t];i;i=i->next){
 80             if(d[i->n]>d[t]+i->v){
 81                 d[i->n]=d[t]+i->v;
 82                 if(!vis[i->n]){
 83                     q.push(i->n);
 84                     vis[i->n]=true;
 85                 }
 86             }
 87         }
 88         vis[t]=false;
 89     }
 90 }
 91 
 92 int main(){
 93      freopen("elevator.in","r",stdin);
 94      freopen("elevator.out","w",stdout);
 95     in(h);
 96     in(a);in(b);in(c);
 97     if(a>b) swap(a,b);
 98     if(a>c) swap(a,c);
 99     For(i,0,a-1){
100         push(i,(i+b)%a,b);
101         push(i,(i+c)%a,c);
102     }
103     spfa();
104     For(i,0,a-1)
105         if(h>=d[i])
106             ans+=1+(h-d[i])/a;
107     o(ans);
108     return 0;
109 }

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