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Here
典中之典!!
解题思路
- 可选k条边代价为0
- 如何决策?
- 将到当前位置选择了几条代价为0的边放入状态,即
- 若当前状态选的边数小于,则可以进行决策,是否选择当前边,
- 若选,则,否则
- 若当前状态选的边数等于,则只能
- 考虑分层图,建k层
- (实际上就是将上一种方法中多一维记录来区别状态),改为用点的标号区分)
- 对于每条边,向层连一条相同但代价为0的边
- 同层连代价为的边
- 最终输出第k层的
for(int i=1;i<=m;++i){int x=read(),y=read(),w=read();for(int j=0;j<=k;++j){Lian(x+j*n,y+j*n,w);Lian(y+j*n,x+j*n,w);if(j==k)continue;Lian(x+j*n,y+(j+1)*n,0);Lian(y+j*n,x+(j+1)*n,0);}}
- 由于代价具有单调性(代价低的,花费更高代价一定也行)
- 二分答案
- 对于每条边的边权有小到大排序去重 ,将边权视为答案进行
- 时,对大于当前所选答案的边,视作代价为1的边,小于的视作代价为0
- 判断最终,即为可能解,接着往小进行尝试
- 否则,往大进行尝试
//二分答案
import java.io.*;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Objects;
import java.util.PriorityQueue;
import java.util.Stack;
import java.util.StringTokenizer;//implements Runnable
public class Main{static long md=(long)20020219;static long Linf=Long.MAX_VALUE/2;static int inf=Integer.MAX_VALUE/2;static int M=10000;static int N=1000;static int n=0;static int m=0;static int k=0;static class Edge{int fr,to,val,nxt;public Edge(int u,int v,int w) {fr=u;to=v;val=w;}}static Edge[] e=new Edge[2*M+1];static int[] head=new int[N+1];static int cnt=0;static void addEdge(int fr,int to,int val) {cnt++;e[cnt]=new Edge(fr, to, val);e[cnt].nxt=head[fr];head[fr]=cnt;}staticclass Node{int x;int y;public Node(int u,int v) {x=u;y=v;}}static boolean Dij(int s,int lim) {int[] dis=new int[N+1];Arrays.fill(dis, inf);boolean[] vis=new boolean[N+1];PriorityQueue<Node> q=new PriorityQueue<Node>((o1,o2)->{return o1.y-o2.y;});q.add(new Node(s, 0));dis[s]=0;while(!q.isEmpty()) {Node now=q.peek();q.poll();int x=now.x;if(vis[x])continue;vis[x]=true;for(int i=head[x];i>0;i=e[i].nxt) {int v=e[i].to;if(vis[v])continue;int w=e[i].val;if(w>lim) {if(dis[x]+1<dis[v]) {dis[v]=dis[x]+1;q.add(new Node(v, dis[v]));}}else {if(dis[x]<dis[v]) {dis[v]=dis[x];q.add(new Node(v, dis[v]));}}}}if(dis[n]<=k)return true;else return false;}public static void main(String[] args) throws Exception{AReader input=new AReader();PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out)); n=input.nextInt();m=input.nextInt();k=input.nextInt();int[] a=new int[m+1];int aa=0;int[] b=new int[m+1];int bb=0;for(int i=1;i<=m;++i) {int u=input.nextInt();int v=input.nextInt();int w=input.nextInt();addEdge(u, v, w);addEdge(v, u, w);aa++;a[aa]=w;}Arrays.sort(a,1,aa+1);for(int i=1;i<=aa;++i) {if(a[i]!=a[i-1]) {bb++;b[bb]=a[i];}}int l=1,r=bb;int ans=-1;while(l<=r) {int mid=(l+r)>>1;if(Dij(1, b[mid])) {ans=b[mid];r=mid-1;}else l=mid+1;}out.print(ans);out.flush();out.close();}
// public static final void main(String[] args) throws Exception {
// new Thread(null, new Main(), "线程名字", 1 << 27).start();
// }
// @Override
// public void run() {
// try {
// //原本main函数的内容
// solve();
//
// } catch (Exception e) {
// }
// }
// static
// class Node{
// int x;
// int y;
// public Node(int u,int v) {
// x=u;
// y=v;
// }
// @Override
// public boolean equals(Object o) {
// if (this == o) return true;
// if (o == null || getClass() != o.getClass()) return false;
// Node may = (Node) o;
// return x == may.x && y==may.y;
// }
//
// @Override
// public int hashCode() {
// return Objects.hash(x, y);
// }
// }staticclass AReader{ BufferedReader bf;StringTokenizer st;BufferedWriter bw;public AReader(){bf=new BufferedReader(new InputStreamReader(System.in));st=new StringTokenizer("");bw=new BufferedWriter(new OutputStreamWriter(System.out));}public String nextLine() throws IOException{return bf.readLine();}public String next() throws IOException{while(!st.hasMoreTokens()){st=new StringTokenizer(bf.readLine());}return st.nextToken();}public char nextChar() throws IOException{//确定下一个token只有一个字符的时候再用return next().charAt(0);}public int nextInt() throws IOException{return Integer.parseInt(next());}public long nextLong() throws IOException{return Long.parseLong(next());}public double nextDouble() throws IOException{return Double.parseDouble(next());}public float nextFloat() throws IOException{return Float.parseFloat(next());}public byte nextByte() throws IOException{return Byte.parseByte(next());}public short nextShort() throws IOException{return Short.parseShort(next());}public BigInteger nextBigInteger() throws IOException{return new BigInteger(next());}public void println() throws IOException {bw.newLine();}public void println(int[] arr) throws IOException{for (int value : arr) {bw.write(value + " ");}println();}public void println(int l, int r, int[] arr) throws IOException{for (int i = l; i <= r; i ++) {bw.write(arr[i] + " ");}println();}public void println(int a) throws IOException{bw.write(String.valueOf(a));bw.newLine();}public void print(int a) throws IOException{bw.write(String.valueOf(a));}public void println(String a) throws IOException{bw.write(a);bw.newLine();}public void print(String a) throws IOException{bw.write(a);}public void println(long a) throws IOException{bw.write(String.valueOf(a));bw.newLine();}public void print(long a) throws IOException{bw.write(String.valueOf(a));}public void println(double a) throws IOException{bw.write(String.valueOf(a));bw.newLine();}public void print(double a) throws IOException{bw.write(String.valueOf(a));}public void print(char a) throws IOException{bw.write(String.valueOf(a));}public void println(char a) throws IOException{bw.write(String.valueOf(a));bw.newLine();}}}
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