问题
This is my code for Dijkstra's algorithm:
#include<iostream>
#include<cstdio>
#include<vector>
#include<queue>
#define pp pair<int,int>
using namespace std;
struct pri
{
int operator() (const pair<int,int>&p1,const pair<int,int>&p2)
{
return p1.second<p2.second;
}
}p;
int main()
{
priority_queue<pp,vector<pp>,pri> q;
int n;
cin>>n;
vector<pp> g[n+1];
int e,u,v,w,i;
cin>>e;
for(i=0;i<e;i++)
{
cin>>u>>v>>w;
g[u].push_back(pp(v,w));
g[v].push_back(pp(u,w));
}
int s;
cin>>s;
int d[n+1];
for(i=1;i<=n;i++)
d[i]=999;
d[s]=0;
q.push(pp(s,d[s]));
while(!q.empty())
{
u=q.top().first;
q.pop();
int size=g[u].size();
for(int i=0;i<size;i++)
{
v=g[u][i].first;
w=g[u][i].second;
cout<<u<<" "<<" "<<w<<endl;
if(d[v]>d[u]+w)
{
d[v]=d[u]+w;
q.push(pp(v,d[v]));
}
}
}
for(i=1;i<=n;i++)
printf("node %d,min weight=%d\n",i,d[i]);
return 0;
}
In this I can't understand the working of
priority_queue<pp,vector<pp>,pri> q;
That is related to:
struct pri
{
int operator() (const pair<int,int>&p1,const pair<int,int>&p2)
{
return p1.second<p2.second;
}
}p;
What is the use of () operator in this? I mean how it functions in this code?
Also why are we using & in operator()?
Also, how does this comparator work in priority queue definition? And why are we using constant in operator definition?
i mean to say how is exactly this comparison in operator working and cant we use any other symbol as = * @ or any other instead of ()
回答1:
I think the compare function you write is wrong.
int operator() (const pair<int,int>&p1,const pair<int,int>&p2)
{
return p1.second<p2.second;
}
which the correct one should be
int operator() (const pair<int,int>&p1,const pair<int,int>&p2)
{
return p1.second>p2.second;
}
Because in priority_quequeyou can find that The expression comp(a,b), where comp is an object of this type and a and b are elements in the container, shall return true if a is considered to go before b in the strict weak ordering the function defines.
Because in the Dijkstra algorithm, the node with smaller value should has higher priority, thus the operator we used here should be
p1.second>p2.second
(By using your code to solve a problem, it took me a long time to figure out this problem that my program's results were always different with the correct one.) (By the way, in the Dijkstra algorithm itself, I think once a node was pop as the smallest one, there is no need to pop it again and update all the nodes that connected to it. This could save a lot of time.)
回答2:
struct pri {
int operator() (const pair<int,int>&p1,const pair<int,int>&p2)
{
return p1.second<p2.second;
}
}p;
Creates a function object by overloading () operator
This is passed to the priority_queue as the compare class
& is used to pass the pair as constant reference, making sure that no copying of actual arguments take place, (by passing them as reference), at same time the function can't modify their values (by using const keyword)
With the use of this function object, the queue determines how to insert the values (pair).
In this case the second value of pair is used for comparison.
回答3:
When declaring variables (including function arguments), the & is to mark the variable as a reference. It's very basic and common thing to use references for some types of arguments, partly because it passes the arguments without creating copies (so good for e.g. a std::vector) and it also allows non-const references to be changed in the function as a form of output argument.
As for the use of operator() in a structure like this, it makes instances of the structure function objects, in other words, objects that can be invoked like a function.
回答4:
I think your question is about the line priority_queue<pp,vector<pp>,pri> q;?
This declares a variable q of type priority_queue<pp,vector<pp>,pri>. priority_queue is defined as
template<class T,
class Container = vector<T>,
class Compare = less<typename Container::value_type> >
class priority_queue;
So, pp is the type of the elements, vector<pp> is the container (the same as the default), and pri is a function object which is used to compare items in the queue (Compare). The priority_queue uses Compare to order its elements. If the elements cannot be compared directly, or the default is not appropriate, then you can supply your own. In this case, the elements will be order by second member in each element pair.
回答5:
Basically the same as the other answers, just a little more detail -- the operator() code is what defines how the priority queue should do comparisons to determine item priority in the queue. Using this type of framework, you can have a priority queue defined to store any type of objects, and the priority queue can be ordered according to any kind of custom ordering you want on the objects.
回答6:
I refactored this code and checked it with hackerrank.
#include <cstdio>
#include <vector>
#include <queue>
#include <iostream>
#include <vector>
#include <deque>
#include <set>
#include <limits>
#include <iterator>
#include <algorithm>
#include <functional>
using namespace std;
struct pri
{
typedef pair<int,int> pp;
typedef deque<pri::pp > list;
typedef vector< pri::list > graph;
int operator() (pp&p1,const pp&p2)
{
return p1.second>p2.second;
}
typedef priority_queue< pri::pp, pri::list, pri > queue;
};
static int f1(const int x){ return x==std::numeric_limits<int>().max()?-1:x; }
int main()
{
int t;
cin>>t;
while(t--){
int n,e;
cin>>n>>e;
pri::graph g(n+1);
for(int i(0);i<e;i++){
int u,v,w;
cin>>u>>v>>w;
g[u].push_back(pri::pp(v,w));
g[v].push_back(pri::pp(u,w));
}
vector<int> d(n+1,std::numeric_limits<int>().max());
int s; cin>>s;
d[s]=0;
pri::queue q;
q.push(pri::pp(s,d[s]));
set<int> vs;
while(!q.empty()) {
const int u(q.top().first);
const pri::list& gu(g[u]);
q.pop();
vs.insert(u);
for( pri::list::const_iterator i(gu.begin()); i != gu.end(); ++i ) {
const int v(i->first), w(i->second);
if( vs.find(v)==vs.end() ){
// cout<<u<<" "<<v<<" "<<w<<endl;
if( d[v]>d[u]+w ) {
d[v]=d[u]+w;
q.push(pri::pp(v,d[v]));
}
}
}
}
copy_if(d.begin()+1,d.end(),d.begin(),std::bind2nd(std::not_equal_to<int>(),0));
transform(d.begin(),d.end()-2,ostream_iterator<int>(cout," "),f1);
cout<<endl;
}
return 0;
}
来源：https://stackoverflow.com/questions/17898342/priority-queue-in-dijkstras-algorithm