Little Wish~ lyrical step~
Time Limit: 5000/2500 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 417 Accepted Submission(s): 109
Problem Description
N children are living in a tree with exactly N nodes, on each node there lies either a boy or a girl.
A girl is said to be protected, if the distance between the girl and her nearest boy is no more than D.
You want to do something good, so that each girl on the tree will be protected. On each step, you can choose two nodes, and swap the children living on them.
What is the minimum number of steps you have to take to fulfill your wish?
Input
The first line has a number T (T <= 150) , indicating the number of test cases.
In a case, the first line contain two number n (1 <= n <= 50), D (1 <= D <= 10000000), Which means the number of the node and the distance between the girls and boys.
The next lines contains n number. The ith number means the ith node contains a girl or a boy. (0 means girl 1 means boy), The follow n - 1 lines contains a, b, w, means a edge connect ath node and bth node, and the
length of the edge is w (1 <= w <= 10000000).
Output
For every case, you should output "Case #t: " at first, without quotes. The
t is the case number starting from 1.
Then follows the answer, -1 meas you can‘t comlete it, and others means the minimum number of the times.
Sample Input
1 3 1 0 0 1 1 2 1 1 3 1
Sample Output
Case #1: 1
Source
2013 ACM/ICPC Asia Regional Chengdu Online
一棵树n个节点，每一个节点或者有男孩，或者有女孩，每一个男孩可以保护距离他D范围之内的男孩，问最少通过多少次交换可以使得所有女孩受到保护。
男孩与男孩，女孩与女孩之间的交换显然毫无意义，只用考虑男孩与女孩之间的交换，可以DP做，也可以DLX爆搜，只考虑男孩，女孩毫无意义，可以先DLX爆搜得到解，然后判断需要多少次交换，当搜到一组解时，里面的女孩个数就是需要交换的次数，我们只需要把女孩全部移走，换成男孩，就可以保证把所有点覆盖。
代码：
/* ***********************************************
Author :_rabbit
Created Time :2014/5/1 22:56:26
File Name :12.cpp
************************************************ */
#pragma comment(linker, "/STACK:102400000,102400000")
#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <sstream>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <string>
#include <time.h>
#include <math.h>
#include <queue>
#include <stack>
#include <set>
#include <map>
using namespace std;
#define INF 0x3f3f3f3f
#define eps 1e-8
#define pi acos(-1.0)
typedef long long ll;
int boys,boy[100],d[60][60];
struct DLX{
const static int maxn=7500;
#define FF(i,A,s) for(int i = A[s];i != s;i = A[i])
int L[maxn],R[maxn],U[maxn],D[maxn];
int size,col[maxn],row[maxn],s[maxn],H[100];
bool vis[100];
int ans[maxn],cnt;
void init(int m){
for(int i=0;i<=m;i++){
L[i]=i-1;R[i]=i+1;U[i]=D[i]=i;s[i]=0;
}
memset(H,-1,sizeof(H));
L[0]=m;R[m]=0;size=m+1;
}
void link(int r,int c){
U[size]=c;D[size]=D[c];U[D[c]]=size;D[c]=size;
if(H[r]<0)H[r]=L[size]=R[size]=size;
else {
L[size]=H[r];R[size]=R[H[r]];
L[R[H[r]]]=size;R[H[r]]=size;
}
s[c]++;col[size]=c;row[size]=r;size++;
}
void del(int c){//精确覆盖
L[R[c]]=L[c];R[L[c]]=R[c];
FF(i,D,c)FF(j,R,i)U[D[j]]=U[j],D[U[j]]=D[j],--s[col[j]];
}
void add(int c){ //精确覆盖
R[L[c]]=L[R[c]]=c;
FF(i,U,c)FF(j,L,i)++s[col[U[D[j]]=D[U[j]]=j]];
}
bool dfs(int k){//精确覆盖
if(!R[0]){
cnt=k;return 1;
}
int c=R[0];FF(i,R,0)if(s[c]>s[i])c=i;
del(c);
FF(i,D,c){
FF(j,R,i)del(col[j]);
ans[k]=row[i];if(dfs(k+1))return true;
FF(j,L,i)add(col[j]);
}
add(c);
return 0;
}
void remove(int c){//重复覆盖
FF(i,D,c)L[R[i]]=L[i],R[L[i]]=R[i];
}
void resume(int c){//重复覆盖
FF(i,U,c)L[R[i]]=R[L[i]]=i;
}
int A(){//估价函数
int res=0;
memset(vis,0,sizeof(vis));
FF(i,R,0)if(!vis[i]){
res++;vis[i]=1;
FF(j,D,i)FF(k,R,j)vis[col[k]]=1;
}
return res;
}
void dfs(int now,int &lim){//重复覆盖
if(now+A()>boys)return;int tt=0;
for(int i=0;i<now;i++)tt+=boy[ans[i]];
if(now-tt>=lim)return;
if(!R[0]){
lim=now-tt;
return;
}
int temp=INF,c;
FF(i,R,0)if(temp>=s[i])temp=s[i],c=i;
FF(i,D,c){
ans[now]=row[i];
remove(i);FF(j,R,i)remove(j);
dfs(now+1,lim);
FF(j,L,i)resume(j);resume(i);
}
}
}dlx;
int main()
{
//freopen("data.in","r",stdin);
//freopen("data.out","w",stdout);
int T;
cin>>T;
for(int t=1;t<=T;t++){
int n,D;boys=0;
scanf("%d%d",&n,&D);
dlx.init(n);
for(int i=1;i<=n;i++)scanf("%d",&boy[i]),boys+=boy[i];
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
d[i][j]=i==j?0:INF;
for(int i=1;i<n;i++){
int u,v,p;
scanf("%d%d%d",&u,&v,&p);
d[u][v]=d[v][u]=p;
}
for(int k=1;k<=n;k++)
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
if(d[i][j]>d[i][k]+d[k][j])d[i][j]=d[i][k]+d[k][j];
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
if(d[i][j]<=D)dlx.link(i,j);
int ans=INF;
dlx.dfs(0,ans);
if(ans>boys)ans=-1;
printf("Case #%d: %d\n",t,ans);
}
return 0;
}