解題區/解題區 - UVa

UVa 1013 - Island Hopping

contents

  1. 1. Problem
  2. 2. Sample Input
  3. 3. Sample Output
  4. 4. Solution

Problem

島嶼居民要建造網路連到本島，假設現在島嶼跟島嶼之間都沒有架設網路線，現在開始建造網路，使得每一個島嶼都可以與本島或者是間接相連。

請問平均等待時間需要多少。

所有的路線，在同一時刻開始建造，以每一天一公里的速度建造所有的邊，而每一條邊都以歐幾里得距離為路線長度。

Sample Input

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11 12 2500
14 17 1500
9 9 750
7 15 600
19 16 500
8 18 400
15 21 250
0

Sample Output

1
Island Group: 1 Average 3.20

Solution

一開始沒有注意到同時建造，發現這條規則後，將所有邊的長度由小到大排序，使用并查集去紀錄，找到第一個時刻連到本島的時間。

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#include <stdio.h> 
#include <math.h>
#include <vector>
#include <algorithm>
using namespace std;
const int MAXN = 64;
double X[MAXN], Y[MAXN], M[MAXN];
struct Edge {
    int x, y;
    double v;
    Edge(int a = 0, int b = 0, double c = 0):
        x(a), y(b), v(c) {}
    bool operator<(const Edge &x) const {
        return v < x.v;
    }
};
vector<Edge> E;
int parent[MAXN], weight[MAXN];
double weight2[MAXN];
int findp(int x) {
    return parent[x] == x ? x : parent[x] = findp(parent[x]);
}
int joint(int x, int y) {
    x = findp(x), y = findp(y);
    if (x == y)	
        return 0;
    if (weight[x] > weight[y]) {
        parent[y] = x, weight[x] += weight[y];
        weight2[x] += weight2[y];
    } else {
        parent[x] = y, weight[y] += weight[x];
        weight2[y] += weight2[x];
    }
    return 1;
}
double solve(int n) {
    sort(E.begin(), E.end());
    double div = 0, sum = 0;
    int u, v;
    for (int i = 0; i < n; i++)
        parent[i] = i, weight[i] = 1, weight2[i] = M[i], div += M[i];
        
    for (int i = 0; i < E.size(); i++) {
        u = E[i].x, v = E[i].y;
        if (findp(u) != findp(v)) {
            if (findp(u) == findp(0))
                sum += weight2[findp(v)] * E[i].v;
            if (findp(v) == findp(0))
                sum += weight2[findp(u)] * E[i].v;
            joint(u, v);
        }
    }
    return sum / div;
}
int main() {
    int n, cases = 0;
    while (scanf("%d", &n) == 1 && n) {
        for (int i = 0; i < n; i++)
            scanf("%lf %lf %lf", &X[i], &Y[i], &M[i]);
        E.clear();
        for (int i = 0; i < n; i++) {
            for (int j = i+1; j < n; j++) {
                double v = hypot(X[i] - X[j], Y[i] - Y[j]);
                E.push_back(Edge(i, j, v));
            }
        }
        
        double ret = solve(n);
        
        printf("Island Group: %d Average %.2lf\n", ++cases, ret);
        
        puts("");
    }
    return 0;
}
/*
7
11 12 2500
14 17 1500
9 9 750
7 15 600
19 16 500
8 18 400
15 21 250
0
*/