题目链接:点击打开链接
题意:
给定n个点的有根树(0为根),
下面给出边和边权
一个整数q表示q个询问
每个询问一个数字x ,表示有一个人从根开始走,行走距离不超过x且使得走过不相同的点最多。
问最多能走多少个点。
思路:
dp[i][j][0]表示以i为根的子树,以i为起点走了j个不同点且回到i的最小花费。
dp[i][j][1]表示不需要回到i的最小花费。
转移的时候就是一个背包
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;
import java.util.Queue;
public class Main {
int n, q;
int[] siz = new int[N];
int[][][] dp = new int[N][N][2];//dp[i][j][0]表示以i为子树 走了j个点后回到i的最小花费,1表示不回到i
int[][] tmp = new int[N][2];
void input(){
init_edge();
for(int i = 1, u, v, dis; i < n; i++){
u = cin.nextInt(); v = cin.nextInt(); dis = cin.nextInt();
add(u, v, dis);
add(v, u, dis);
}
q = cin.nextInt();
}
void dfs(int u, int fa){
dp[u][1][0] = dp[u][1][1] = 0;
siz[u] = 1;
for(int i = head[u]; i != -1; i = edge[i].nex){
int v = edge[i].to; if(v == fa)continue;
dfs(v, u);
siz[u] += siz[v];
for(int j = siz[u]; j > 1; j--){
for(int k = 1; k <= siz[v] && j-k>=0; k++)
{
dp[u][j][0] = min(dp[u][j][0], dp[u][j-k][0]+dp[v][k][0]+edge[i].dis*2);
dp[u][j][1] = min(dp[u][j][1], dp[u][j-k][0]+dp[v][k][1]+edge[i].dis);
dp[u][j][1] = min(dp[u][j][1], dp[u][j-k][1]+dp[v][k][0]+edge[i].dis*2);
}
}
}
// out.print(u+" back:"); for(int i = 1; i <= siz[u]; i++)out.print(dp[u][i][0]+ " "); out.println();out.print(u+" not back:"); for(int i = 1; i <= siz[u]; i++)out.print(dp[u][i][1]+ " "); out.println();
}
void work() {
int Cas = 1;
while(true){
n = cin.nextInt(); if(n == 0)break;
input();
for(int i = 0; i <= n; i++) for(int j = 0; j <= n; j++)dp[i][j][0] = dp[i][j][1] = inf;
dfs(0, 0);
out.println("Case "+(Cas++)+":");
while(q-->0){
int x = cin.nextInt(), ans = 1;
for(int i = 2; i <= n; i++)
if(x>=dp[0][i][1])
ans = i;
out.println(ans);
}
}
}
Main() {
cin = new Scanner(System.in);
out = new PrintWriter(System.out);
}
public static void main(String[] args) {
Main e = new Main();
e.work();
out.close();
}
public Scanner cin;
public static PrintWriter out;
static int N = 505;
static int M = 505;
DecimalFormat df=new DecimalFormat("0.0000");
static int inf = (int) 1e9 + 7;
static long inf64 = (long) 1e18;
static double eps = 1e-8;
static int mod = 1000000007 ;
class Edge{
int from, to, dis, nex;
Edge(){}
Edge(int from, int to, int dis, int nex){
this.from = from;
this.to = to;
this.dis = dis;
this.nex = nex;
}
}
Edge[] edge = new Edge[M<<1];
int[] head = new int[N];
int edgenum;
void init_edge(){for(int i = 0; i < N; i++)head[i] = -1; edgenum = 0;}
void add(int u, int v, int dis){
edge[edgenum] = new Edge(u, v, dis, head[u]);
head[u] = edgenum++;
}/*
int upper_bound(int[] A, int l, int r, int val) {// upper_bound(A+l,A+r,val)-A;
int pos = r;
r--;
while (l <= r) {
int mid = (l + r) >> 1;
if (A[mid] <= val) {
l = mid + 1;
} else {
pos = mid;
r = mid - 1;
}
}
return pos;
}/**/
int Pow(int x, int y) {
int ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
y >>= 1;
x = x * x;
}
return ans;
}
double Pow(double x, int y) {
double ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
y >>= 1;
x = x * x;
}
return ans;
}
int Pow_Mod(int x, int y, int mod) {
int ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
ans %= mod;
y >>= 1;
x = x * x;
x %= mod;
}
return ans;
}
long Pow(long x, long y) {
long ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
y >>= 1;
x = x * x;
}
return ans;
}
long Pow_Mod(long x, long y, long mod) {
long ans = 1;
while (y > 0) {
if ((y & 1) > 0)
ans *= x;
ans %= mod;
y >>= 1;
x = x * x;
x %= mod;
}
return ans;
}
int gcd(int x, int y){
if(x>y){int tmp = x; x = y; y = tmp;}
while(x>0){
y %= x;
int tmp = x; x = y; y = tmp;
}
return y;
}
int max(int x, int y) {
return x > y ? x : y;
}
int min(int x, int y) {
return x < y ? x : y;
}
double max(double x, double y) {
return x > y ? x : y;
}
double min(double x, double y) {
return x < y ? x : y;
}
long max(long x, long y) {
return x > y ? x : y;
}
long min(long x, long y) {
return x < y ? x : y;
}
int abs(int x) {
return x > 0 ? x : -x;
}
double abs(double x) {
return x > 0 ? x : -x;
}
long abs(long x) {
return x > 0 ? x : -x;
}
boolean zero(double x) {
return abs(x) < eps;
}
}