问题
#include <bits/stdc++.h>
using namespace std;
#define fast ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define LL long long int
#define pb push_back
#define mp make_pair
#define PI pair<int,int>
#define PL pair<LL,LL>
#define PIS pair< int,string>
#define test int t;cin>>t;while(t--)
#define ff first
#define ss second
#define INF 1000000000
#define input(a,n) for(i=1;i<=n;i++)cin>>a[i];
#define output(a,n) for(i=1;i<=n;i++)cout<<a[i]<<" ";
vector< vector<LL> >v(3002, vector<LL>(3002,-1));
priority_queue<PI, vector<PI> ,greater<PI> > pp;
LL w=0;
int vis[3002]={0};
/*void deck(int a ,int b, int *k)
{
while(!pp.empty())
{
i=pp.top.ss;
if(i==a)
pp.top
}
}*/
void prim(LL s, LL *k, LL *p,LL n)
{
pp.push(mp(0,s));
k[s]=0;
LL i,x,a,b,c=0;
vector<PI >::iterator it;
while(true)
{
if(c==n)
break;
i=pp.top().ss;
//cout<<i<<" ";
if(vis[i]!=1)
w=w+pp.top().ff;
vis[i]=1;
c++;
pp.pop();
for(x=1;x<=n;x++)
{
if(v[i][x]!=-1)
{
a=x;
b=v[i][x];
if(!vis[a] && b<k[a])
{
k[a]=b;
p[a]=i;
pp.push(mp(b,a));
}
}
}
}
}
int main()
{
fast
LL n,m,x,i,j,r,s;
/*pp.push(mp(2,3));
pp.push(mp(3,4));*/
cin>>n>>m;
LL k[n+1],p[n+1];
v.resize(n+1);
for(x=1;x<n+1;x++)
{
k[x]=INF;
p[x]=-1;
}
for(x=0;x<m;x++)
{
cin>>i>>j>>r;
/*v[i].pb(mp(j,r));
v[j].pb(mp(i,r));*/
if(v[i][j]!=-1)
{
if(v[i][j]>r)
{
v[i][j]=r;
v[j][i]=r;
}
}
else
{
v[i][j]=r;
v[j][i]=r;
}
}
cin>>s;
prim(s,k,p,n);
cout<<w;
//cout<<pp.top().ss;
}
I was not able to implement the function which searches a particular value i.e the vertex and changes it's key value instead I pushed the changed pair, using
pp.push(mp(b,a));
I was able to get some test cases right by using the if statement
if(c==n)
break;
where 'c' represents the count of vertexes visited.
回答1:
The standard std::priority_queue does not allow to peak inside of it so changing priority keys is not possible. It is a classic queue implementation with pushing elements at one side and popping them back at the other. So probably you should look for a more general implementation of the heap data structure.
If you insist on using std::priority_queue you might need to do something as ugly as popping the full queue content to a vector, updating elements and restoring the queue.
回答2:
There are three ways I know of.
If you insist on using the standard library's
priority_queue, you can insert each vertex multiple times, but ignore it every time you see it except the first. In your code, you can changeif(vis[i]!=1) w=w+pp.top().ff;intoif(vis[i]==1) continue;(perhaps; didn't test). The downside is that yourpriority_queuecan grow to O(|E|) memory.You can also use the standard library's
setinstead ofpriority_queue. Then, whenever you want to insert a pair(distance, vertex), first you have to find and remove the pair(old_distance, vertex)if it is in the set. To knowold_distanceto eachvertexat all times, you have to maintain an array (or vector) with the current distances. This way, you keep memory to O(|V|), butsethas a greater constant factor thanpriority_queue.Finally, you can implement a priority queue which allows deletion. Let's say you implement the priority queue as a binary heap. Then, you will have to maintain an inverse permutation of elements in the priority queue: for each element
v, store and track what is the current heap index ofv. One of the other answers looks like it implements this approach, the inverse permutation beingindex_map.
回答3:
priority_queue in C++ does not provide the functionality of decrease key operation which means we cannot find a key in priority_queue and decrease its value. One way I know to achieve this is to implement a priority queue ourselves and then maintain another structure (a vector or a map) which would store the indices of keys in the priority queue. Try to understand the code below which uses this idea.
// C++11 code
#include <iostream>
#include <vector>
#include <cstring>
#define SIZE 5 // number of vertices.
#define INF 100000000
/* This vector will contain a pair of integers where the first integer in
the pair is value(cost) and the second is the vertex.
This will be our priority queue.
*/
std::vector <std::pair <int, int> > pq (SIZE);
int size = SIZE; // size of priority queue
int index_map[SIZE];
// Shift up the key with lower value.
void sift_up(int index) {
int parent = (index-1)/2;
while(index >= 0 && pq[index].first < pq[parent].first) {
index_map[pq[index].second] = parent;
index_map[pq[parent].second] = index;
std::swap(pq[index], pq[parent]);
index = parent;
parent = (index - 1)/2;
}
}
// Shift down the key with higher value.
void sift_down(int index) {
int left = 2*index+1, right = 2*index+2;
int min_index = index;
if(left < size && pq[left].first < pq[min_index].first)
min_index = left;
if(right < size && pq[right].first < pq[min_index].first)
min_index = right;
if(min_index != index) {
index_map[pq[index].second] = min_index;
index_map[pq[min_index].second] = index;
std::swap(pq[index], pq[min_index]);
sift_down(min_index);
}
}
// Extract the minimum element from priority queue.
std::pair <int, int> extract_min() {
index_map[pq[0].second] = size-1;
index_map[pq[size-1].second] = 0;
std::swap(pq[0], pq[size-1]);
size -= 1;
sift_down(0);
return pq[size];
}
// Change the value at index 'index' to 'value'.
void decrease_key(int index, int value) {
int temp = pq[index].first;
pq[index].first = value;
if(value < temp)
sift_up(index);
else
sift_down(index);
}
// Initialise and heapify the priority queue.
void make_heap(int start_index) {
for(int i = 0; i < SIZE; i++) {
pq[i].first = INF;
pq[i].second = i;
}
pq[0].first = 0;
pq[start_index].second = start_index;
for(int i = SIZE-1; i >= 0; i--)
sift_down(i);
}
int main() {
/* Graph is represent using adjacency list. It takes the following form:
graph[u] = {{v_1, c_1}, {v_2, c_2}, ..., {v_n, c_n}};
The above line means that there is an undirected edge
between vertices 'u' and 'v_1' with cost 'c_1'.
Similarly for (u, v_2, c_2), ..., (u, v_n, c_n).
*/
std::vector <std::vector <std::pair <int, int> > > graph (SIZE);
graph[0] = {{1, 20}, {2, 50}, {3, 70}, {4, 90}};
graph[1] = {{0, 20}, {2, 30}};
graph[2] = {{0, 50}, {1, 30}, {3, 40}};
graph[3] = {{0, 70}, {2, 40}, {4, 60}};
graph[4] = {{0, 90}, {3, 60}};
int visited[SIZE];
memset(visited, 0, sizeof(visited));
visited[0] = 1;
make_heap(0); // Assuming algorithm to start from vertex 0.
for(int i = 0; i < SIZE; i++)
index_map[pq[i].second] = i;
int answer = 0;
while(size != 0) {
std::pair <int, int> p = extract_min();
/* p.first will contain the cost of the next edge to be added in our
answer and p.second will give the vertex number.
*/
visited[p.second] = 1;
answer += p.first;
for(int i = 0; i < graph[p.second].size(); i++) {
if(!visited[graph[p.second][i].first]) {
if(graph[p.second][i].second < pq[index_map[graph[p.second][i].first]].first) {
decrease_key(index_map[graph[p.second][i].first], graph[p.second][i].second);
}
}
}
}
std::cout << answer << "\n";
}
回答4:
I found a way to implement the algorithm using
std::priority_queue
By changing approach, would like to share my code
#include<iostream>
#include<algorithm>
#include<vector>
#include<set>
#include<limits.h>
#include<map>
#include<stack>
#include<stdio.h>
#include<queue>
#include<cmath>
#include<string.h>
using namespace std;
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define PII pair<int,int>
vector<PII> v[3001];
bool vis[3001];
int sum=0;
void prim(int s)
{
int y,x,i;
PII p;
priority_queue<PII, vector<PII> , greater<PII> > q;
q.push(mp(0,s));
while(!q.empty())
{
p = q.top();
q.pop();
x = p.ss;
if(vis[x]==true)
continue;
sum+=p.ff;
vis[x]=true;
for(i=0;i<v[x].size();i++)
{
y = v[x][i].ss;
if(vis[y]==false)
q.push(v[x][i]);
}
}
}
int main() {
fast
int f1=0,max=0,y,a1,x,j,w=0,f=0,l,m,b,c1=0,r=0;
char t,a[4][4],c;
int n,i=0,d=1,k;
cin>>n>>k;
for(x=0;x<k;x++)
{
cin>>i>>j>>r;
v[i].pb(mp(r,j));
v[j].pb(mp(r,i));
}
cin>>i;
prim(i);
cout<<sum;
return 0;
}
来源：https://stackoverflow.com/questions/38422444/how-to-decrease-key-for-a-particular-edge-in-a-priority-queuepi-vectorpi-gr