poj 3013 Big Christmas Tree
Time Limit: 3000MS | Memory Limit: 131072K | |
Total Submissions: 20974 | Accepted: 4535 |
Description
Christmas is coming to KCM city. Suby the loyal civilian in KCM city is preparing a big neat Christmas tree. The simple structure of the tree is shown in right picture.
The tree can be represented as a collection of numbered nodes and some edges. The nodes are numbered 1 through n. The root is always numbered 1. Every node in the tree has its weight. The weights can be different from each other. Also the shape of every available edge between two nodes is different, so the unit price of each edge is different. Because of a technical difficulty, price of an edge will be (sum of weights of all descendant nodes) × (unit price of the edge).
Suby wants to minimize the cost of whole tree among all possible choices. Also he wants to use all nodes because he wants a large tree. So he decided to ask you for helping solve this task by find the minimum cost.
Input
The input consists of T test cases. The number of test cases T is given in the first line of the input file. Each test case consists of several lines. Two numbers v, e (0 ≤ v, e ≤ 50000) are given in the first line of each test case. On the next line, v positive integers wi indicating the weights of v nodes are given in one line. On the following e lines, each line contain three positive integers a, b, c indicating the edge which is able to connect two nodes a and b, and unit price c.
All numbers in input are less than 216.
Output
For each test case, output an integer indicating the minimum possible cost for the tree in one line. If there is no way to build a Christmas tree, print “No Answer” in one line.
Sample Input
2 2 1 1 1 1 2 15 7 7 200 10 20 30 40 50 60 1 2 1 2 3 3 2 4 2 3 5 4 3 7 2 3 6 3 1 5 9
Sample Output
15 1210
Source
1 /* 2 * Author: Joshua 3 * Created Time: 2014年10月06日 星期一 20时39分47秒 4 * File Name: poj3013.cpp 5 */ 6 #include<cstdio> 7 #include<queue> 8 #include<cstring> 9 #include<iostream> 10 #include<algorithm> 11 using namespace std; 12 #define maxn 50005 13 #define LLinf 0x7f7f7f7f7f7f7f7f 14 typedef long long LL; 15 struct edge 16 { 17 int v,w,next; 18 } e[maxn<<1]; 19 struct node 20 { 21 LL d; 22 int num; 23 bool operator < (const node& pp) const 24 { 25 return d<pp.d; 26 } 27 } heap[maxn]; 28 int T,n,m,tot,heapSize; 29 int c[maxn],head[maxn],map[maxn]; 30 bool vis[maxn]; 31 void Read(int &ret){ 32 ret = 0; 33 bool ok = 0; 34 for( ; ;){ 35 int c = getchar(); 36 if (c >= '0' && c <= '9') ret = (ret << 3) + (ret << 1) + c - '0', ok = 1; 37 else if (ok) return; 38 } 39 } 40 41 void createEdge(int u,int v,int w) 42 { 43 edge& temp=e[++tot]; 44 temp.v=v; 45 temp.w=w; 46 temp.next=head[u]; 47 head[u]=tot; 48 } 49 50 void heap_swap(int x,int y) 51 { 52 swap(heap[x],heap[y]); 53 map[heap[x].num]=x; 54 map[heap[y].num]=y; 55 } 56 57 void heap_up(int x) 58 { 59 while (x!=1 && heap[x]<heap[x>>1]) 60 { 61 heap_swap(x,x>>1); 62 x>>=1; 63 } 64 } 65 66 void heap_down(int x) 67 { 68 while ((x<<1)<=heapSize) 69 { 70 x<<=1; 71 if (x+1<=heapSize && heap[x+1]<heap[x]) x++; 72 if (heap[x]<heap[x>>1]) 73 heap_swap(x,x>>1); 74 else break; 75 } 76 } 77 78 void heap_del() 79 { 80 heap_swap(1,heapSize); 81 heapSize--; 82 heap_down(1); 83 } 84 85 void init() 86 { 87 int u,v,w; 88 Read(n);Read(m); 89 for (int i=1;i<=n;++i) 90 Read(c[i]); 91 memset(head,-1,(n+1)<<2); 92 tot=0; 93 for (int i=1;i<=m;++i) 94 { 95 Read(u);Read(v);Read(w); 96 createEdge(u,v,w); 97 createEdge(v,u,w); 98 } 99 } 100 101 void updata(int x,LL y) 102 { 103 if (heap[x].d<=y) return; 104 heap[x].d=y; 105 heap_up(x); 106 } 107 108 void solve() 109 { 110 bool flag=false; 111 LL td,ans=0; 112 int tn; 113 for (int i=2;i<=n;++i) 114 { 115 heap[i-1].d=LLinf; 116 heap[i-1].num=i; 117 map[i]=i-1; 118 } 119 heap[n].d=0; 120 heap[n].num=1; 121 map[1]=n; 122 heapSize=n; 123 heap_up(n); 124 memset(vis,1,n+1); 125 for (int i=1;i<=n;++i) 126 { 127 td=heap[1].d; 128 tn=heap[1].num; 129 vis[tn]=false; 130 if (td==LLinf) 131 { 132 flag=true; 133 break; 134 } 135 heap_del(); 136 ans+=td*c[tn]; 137 for (int i=head[tn];~i;i=e[i].next) 138 if (vis[e[i].v]) 139 updata(map[e[i].v],td+e[i].w); 140 } 141 if (flag) printf("No Answer\n"); 142 else cout<<ans<<endl; 143 } 144 145 int main() 146 { 147 Read(T); 148 for (int i=1;i<=T;++i) 149 { 150 init(); 151 solve(); 152 } 153 return 0; 154 }