2015
04-14

# Find Metal Mineral

Humans have discovered a kind of new metal mineral on Mars which are distributed in point�\like with paths connecting each of them which formed a tree. Now Humans launches k robots on Mars to collect them, and due to the unknown reasons, the landing site S of all robots is identified in advanced, in other word, all robot should start their job at point S. Each robot can return to Earth anywhere, and of course they cannot go back to Mars. We have research the information of all paths on Mars, including its two endpoints x, y and energy cost w. To reduce the total energy cost, we should make a optimal plan which cost minimal energy cost.

There are multiple cases in the input.
In each case:
The first line specifies three integers N, S, K specifying the numbers of metal mineral, landing site and the number of robots.
The next n�\1 lines will give three integers x, y, w in each line specifying there is a path connected point x and y which should cost w.
1<=N<=10000, 1<=S<=N, 1<=k<=10, 1<=x, y<=N, 1<=w<=10000.

There are multiple cases in the input.
In each case:
The first line specifies three integers N, S, K specifying the numbers of metal mineral, landing site and the number of robots.
The next n�\1 lines will give three integers x, y, w in each line specifying there is a path connected point x and y which should cost w.
1<=N<=10000, 1<=S<=N, 1<=k<=10, 1<=x, y<=N, 1<=w<=10000.

3 1 1
1 2 1
1 3 1
3 1 2
1 2 1
1 3 1

3
2

HintIn the first case: 1->2->1->3 the cost is 3;
In the second case: 1->2; 1->3 the cost is 2;


/*

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杩欐牱鐨勮瘽锛屽鏋滄渶鍚庝互i涓烘牴缁撶偣鐨勬爲涓病鏈夋満鍣ㄤ汉锛岄偅涔堝彧鍙兘鏄淳涓�涓満鍣ㄤ汉涓嬪幓閬嶅巻瀹屽悗鍐嶅洖鏉�
*/
#include<stdio.h>
#include<string.h>
#include<iostream>
using namespace std;

const __int64 maxn=11000;
const __int64 maxm=21000;
struct edge
{
__int64 u,v,w,next;
}e[maxm];
__int64 edgeNum,first[maxn],dp[maxn][15];

{
e[edgeNum].u=u,e[edgeNum].v=v,e[edgeNum].w=w,e[edgeNum].next=first[u],first[u]=edgeNum++;
e[edgeNum].u=v,e[edgeNum].v=u,e[edgeNum].w=w,e[edgeNum].next=first[v],first[v]=edgeNum++;
}

void DFS(__int64 t,__int64 p)
{
__int64 ii,i,j,k;
for(k=first[t];k!=-1;k=e[k].next)
{
i=e[k].v;
if(i==p) continue;
DFS(i,t);
}
/* 璧嬪垵鍊�0鏃讹紝鍙笉鐢ㄧ鍙跺瓙缁撶偣浜�
//first[t]=-1鏃惰鏄庢爲涓彧鏈変竴涓粨鐐�
if(first[t]==-1||(e[first[t]].next==-1&&p!=-1))//鍙跺瓙缁撶偣,娉ㄦ剰涓�瀹氳鎶婃牴缁撶偣鎺掗櫎銆�
{
for(i=0;i<=10;i++)
dp[t][i]=0;
return;
}*/
for(k=first[t];k!=-1;k=e[k].next)
{
i=e[k].v;
if(i==p) continue;
for(j=10;j>=0;j--)//璺�01鑳屽寘绫讳技锛屾柟鍚戜笉鑳芥崲銆�
{//姝ゆ椂鐨刣p[i][j]琛ㄧず浠涓烘牴缁撶偣鐨勫瓙鏍戜腑鍓嶉潰鐨勫瓙鏍�(鍖呮嫭杩欐５瀛愭爲)鎬诲垎閰嶄簡j涓満鍣ㄤ汉鐨勬渶灏戞潈鍊煎拰
/*if(!dp[t][j])//绗竴妫靛瓙鏍�
{
if(j)
{//鏈�澶氭斁j涓湪璇ュ瓙鏍戜腑锛屼笉涓�瀹氳鍏ㄩ儴鍒拌瀛愭爲涓�(鏈変竴浜涙満鍣ㄤ汉灏卞仠鍦ㄨ繖涓粨鐐逛笂)銆傚綋鐒朵竴涓笉鏀捐偗瀹氫笉鏄渶濂界殑
for(ii=1;ii<=j;ii++)
if(dp[t][j]==0||dp[t][j]>dp[i][ii]+ii*e[k].w)
dp[t][j]=dp[i][ii]+ii*e[k].w;
}
else dp[t][0]=dp[i][0]+2*e[k].w;//鏀句笅涓�涓張閫�鍥炴潵
continue;
}
else//鍚﹀垯锛岃嫢璇ュ瓙鏍戞斁0涓満鍣ㄤ汉*///杩欎竴娈典篃鍙互涓嶈
dp[t][j]+=dp[i][0]+2*e[k].w;
for(ii=1;ii<=j;ii++)//璇ュ瓙鏍戞斁[1,j]涓満鍣ㄤ汉
{
if(dp[t][j]>dp[t][j-ii]+dp[i][ii]+ii*e[k].w)
dp[t][j]=dp[t][j-ii]+dp[i][ii]+ii*e[k].w;
}
}
}
}
int main()
{
__int64 n,s,k,i,u,v,w;
while(scanf("%I64d%I64d%I64d",&n,&s,&k)!=EOF)
{
memset(first,-1,sizeof(first));
for(edgeNum=0,i=1;i<n;i++)
{
scanf("%I64d%I64d%I64d",&u,&v,&w);
}
memset(dp,0,sizeof(dp));
DFS(s,-1);
printf("%I64d\n",dp[s][k]);
}
return 0;
}

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