HDU2489 Minimal Ratio Tree 【DFS】+【最小生成樹Prim】
阿新 • • 發佈:2017-05-19
mini note 推斷 sym hash %d ted n) lin
Problem Description For a tree, which nodes and edges are all weighted, the ratio of it is calculated according to the following equation.
Given a complete graph of n nodes with all nodes and edges weighted, your task is to find a tree, which is a sub-graph of the original graph, with m nodes and whose ratio is the smallest among all the trees of m nodes in the graph.
Input Input contains multiple test cases. The first line of each test case contains two integers n (2<=n<=15) and m (2<=m<=n), which stands for the number of nodes in the graph and the number of nodes in the minimal ratio tree. Two zeros end the input. The next line contains n numbers which stand for the weight of each node. The following n lines contain a diagonally symmetrical n×n connectivity matrix with each element shows the weight of the edge connecting one node with another. Of course, the diagonal will be all 0, since there is no edge connecting a node with itself.
All the weights of both nodes and edges (except for the ones on the diagonal of the matrix) are integers and in the range of [1, 100].
The figure below illustrates the first test case in sample input. Node 1 and Node 3 form the minimal ratio tree.
Output For each test case output one line contains a sequence of the m nodes which constructs the minimal ratio tree. Nodes should be arranged in ascending order. If there are several such sequences, pick the one which has the smallest node number; if there‘s a tie, look at the second smallest node number, etc. Please note that the nodes are numbered from 1 .
Sample Input
Sample Output
Source 2008 Asia Regional Beijing ⊙﹏⊙‖∣在推斷兩浮點數大小時應該這樣比較:a-b<-(1e-8);我由於不知道這個WA了6次。
Minimal Ratio Tree
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 2382 Accepted Submission(s): 709Problem Description For a tree, which nodes and edges are all weighted, the ratio of it is calculated according to the following equation.
Given a complete graph of n nodes with all nodes and edges weighted, your task is to find a tree, which is a sub-graph of the original graph, with m nodes and whose ratio is the smallest among all the trees of m nodes in the graph.
Input Input contains multiple test cases. The first line of each test case contains two integers n (2<=n<=15) and m (2<=m<=n), which stands for the number of nodes in the graph and the number of nodes in the minimal ratio tree. Two zeros end the input. The next line contains n numbers which stand for the weight of each node. The following n lines contain a diagonally symmetrical n×n connectivity matrix with each element shows the weight of the edge connecting one node with another. Of course, the diagonal will be all 0, since there is no edge connecting a node with itself.
All the weights of both nodes and edges (except for the ones on the diagonal of the matrix) are integers and in the range of [1, 100].
The figure below illustrates the first test case in sample input. Node 1 and Node 3 form the minimal ratio tree.
Output For each test case output one line contains a sequence of the m nodes which constructs the minimal ratio tree. Nodes should be arranged in ascending order. If there are several such sequences, pick the one which has the smallest node number; if there‘s a tie, look at the second smallest node number, etc. Please note that the nodes are numbered from 1 .
Sample Input
3 2 30 20 10 0 6 2 6 0 3 2 3 0 2 2 1 1 0 2 2 0 0 0
Sample Output
1 3 1 2
Source 2008 Asia Regional Beijing ⊙﹏⊙‖∣在推斷兩浮點數大小時應該這樣比較:a-b<-(1e-8);我由於不知道這個WA了6次。
題意:求一個稍微變形的“最小生成樹”,其值為邊權和除以點權和。
題解:用深搜在n個點裏選出m個點。再求這m個點的“最小生成樹”就可以。
#include <stdio.h> #include <string.h> #include <limits.h> #define maxn 16 int map[maxn][maxn], node[maxn]; int n, m, store[maxn], vis[maxn]; double ans; bool visted[maxn]; //hash to vis array double prim() { int i, j, u, count = 0, tmp, vnv = 0, vne = 0; for(i = 1; i <= m; ++i) vnv += node[vis[i]]; memset(visted, 0, sizeof(visted)); visted[1] = 1; while(count < m - 1){ for(i = 1, tmp = INT_MAX; i <= m; ++i){ if(!visted[i]) continue; for(j = 1; j <= m; ++j){ if(!visted[j] && map[vis[i]][vis[j]] < tmp){ tmp = map[vis[i]][vis[j]]; u = j; } } } if(tmp != INT_MAX){ visted[u] = 1; vne += tmp; ++count; } } return vne * 1.0 / vnv; } void DFS(int k, int id) { if(id > m){ double tmp = prim(); if(tmp - ans < -(1e-8)){ ans = tmp; memcpy(store, vis, sizeof(vis)); } return; } for(int i = k; i <= n; ++i){ vis[id] = i; DFS(i + 1, id + 1); } } int main() { int i, j; while(scanf("%d%d", &n, &m), n || m){ for(i = 1; i <= n; ++i) scanf("%d", &node[i]); for(i = 1; i <= n; ++i) for(j = 1; j <= n; ++j) scanf("%d", &map[i][j]); ans = INT_MAX; DFS(1, 1); for(i = 1; i <= m; ++i) if(i != m) printf("%d ", store[i]); else printf("%d\n", store[i]); } return 0; }
HDU2489 Minimal Ratio Tree 【DFS】+【最小生成樹Prim】