Bzoj 3627 jloi 2014 route planning hierarchy chart spfa + heap

N points and m are undirected edges. Each point may have traffic lights, gas stations, or just one point. If there are too many traffic lights, it will be annoying. If you do not need to refuel for a long time, the car will not be able to drive. You can ask how much traffic will be consumed from the "Start" to "end" at most.

Idea: you can only use up to k traffic lights to create a layered chart based on this. F [I] [J] is the minimum cost of after I traffic lights have passed. This is just the general idea. Whether it is implemented or there are other minor issues.

There is a limit in the question, indicating that the distance from a gas station to another gas station cannot exceed this distance. Think about it. In fact, those that are not gas stations are meaningless to us. After simple processing, they can be processed. Start with a gas station and calculate the distance between the node and other nodes and the number of traffic lights. Add the information to the New Graph and run the spfa command from the start point to the end point to get the answer.

In addition, the waiting time for the traffic lights is a mathematical expectation. For a simple image, you can get time = (red * red)/(2 * (Red + green ))

Code:

#include <map>#include <queue>#include <cstdio>#include <string>#include <iomanip>#include <cstring>#include <iostream>#include <algorithm>#define MAX 100010#define INF 0x7f7f7f7fusing namespace std;map<string,int> G;map<int,int> gas_num;double f[11][MAX];bool v[11][MAX];struct Complex{int pos,step;Complex(int _step,int _pos):pos(_pos),step(_step) {}Complex() {}bool operator <(const Complex& a)const {return f[step][pos] > f[a.step][a.pos];}};int points,edges,k,limit,cost;int st,ed;int total_gas;double expection[MAX];bool stop[MAX],is_gas[MAX];int head[MAX],total;int next[MAX],aim[MAX];double length[MAX];int _head[MAX],_total;int _next[MAX],_aim[MAX];int lights[MAX];double _length[MAX];string temp;inline void Add(int x,int y,double len);inline void _Add(int x,int y,double _len,int l);inline void _SPFA(int start);void SPFA();int main(){cin >> points >> edges >> k >> limit >> cost;for(int x,y,i = 1;i <= points; ++i) {cin >> temp;G[temp] = i;if(temp == "start")st = i,is_gas[i] = true;if(temp == "end")ed = i,is_gas[i] = true;if(temp.find("gas") != string::npos)is_gas[i] = true;scanf("%d%d",&x,&y);if(x) {expection[i] = (double)(x * x) / (2.0 * (x + y));stop[i] = true;}}for(int x,y,len,i = 1;i <= edges; ++i) {cin >> temp; x = G[temp];cin >> temp; y = G[temp];cin >> temp >> len;Add(x,y,(double)len + expection[y]),Add(y,x,(double)len + expection[x]);}for(int i = 1;i <= points; ++i)if(is_gas[i])_SPFA(i);SPFA();double ans = INF;for(int i = 0;i <= k; ++i)ans = min(ans,f[i][ed]);cout << fixed << setprecision(3) << ans - cost;return 0;}inline void Add(int x,int y,double len){next[++total] = head[x];aim[total] = y;length[total] = len;head[x] = total;}inline void _Add(int x,int y,double len,int l){_next[++_total] = _head[x];_aim[_total] = y;_length[_total] = len;lights[_total] = l;_head[x] = _total;}inline void _SPFA(int start){static priority_queue<Complex> q;while(!q.empty())q.pop();memset(f,0x43,sizeof(f));memset(v,false,sizeof(v));f[0][start] = 0;q.push(Complex(0,start));while(!q.empty()) {Complex temp = q.top(); q.pop();int x = temp.pos,step = temp.step;v[step][x] = false;for(int i = head[x];i;i = next[i]) {bool detla = stop[aim[i]];if(step + detla <= k && f[step + detla][aim[i]] > f[step][x] + length[i]) {f[step + detla][aim[i]] = f[step][x] + length[i];if(!v[step + detla][aim[i]]) {v[step + detla][aim[i]] = true;q.push(Complex(step + detla,aim[i]));}}}}for(int i = 0;i <= k; ++i)for(int j = 1;j <= points; ++j)if(j != start && f[i][j] <= limit && is_gas[j])_Add(start,j,f[i][j] + cost,i);}void SPFA(){static priority_queue<Complex> q;memset(f,0x43,sizeof(f));memset(v,false,sizeof(v));f[0][st] = 0;q.push(Complex(0,st));while(!q.empty()) {Complex temp = q.top(); q.pop();int x = temp.pos,step = temp.step;v[step][x] = false;for(int i = _head[x];i;i = _next[i])if(step + lights[i] <=k && f[step + lights[i]][_aim[i]] > f[step][x] + _length[i]) {f[step + lights[i]][_aim[i]] = f[step][x] + _length[i];if(!v[step + lights[i]][_aim[i]]) {v[step + lights[i]][_aim[i]] = true;q.push(Complex(step + lights[i],_aim[i]));}}}}

Bzoj 3627 jloi 2014 route planning hierarchy chart spfa + heap