HDU1162-Eddy's picture（最小生成树）

Posted 2020-08-25 Pic

Problem Description

Eddy begins to like painting pictures recently ,he is sure of himself to become a painter.Every day Eddy draws pictures in his small room, and he usually puts out his newest pictures to let his friends appreciate. but the result it can be imagined, the friends are not interested in his picture.Eddy feels very puzzled,in order to change all friends ‘s view to his technical of painting pictures ,so Eddy creates a problem for the his friends of you.
Problem descriptions as follows: Given you some coordinates pionts on a drawing paper, every point links with the ink with the straight line, causes all points finally to link in the same place. How many distants does your duty discover the shortest length which the ink draws?

Input

The first line contains 0 < n <= 100, the number of point. For each point, a line follows; each following line contains two real numbers indicating the (x,y) coordinates of the point.
Input contains multiple test cases. Process to the end of file.

Output

Your program prints a single real number to two decimal places: the minimum total length of ink lines that can connect all the points.

Sample Input

3
1.0 1.0
2.0 2.0
2.0 4.0

Sample Output

3.41

Author

eddy

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JGShining

这是一个最小生成树的模板题目

下面的代码用了Kruskal算法

#include <cstdio>
#include <vector>
#include <algorithm>
#include <cmath>

using namespace std;

const int N = 105;

struct Edge
{
    int x, y;
    double w;
};

struct Point
{
    double x;
    double y;
};

int pre[N];
Point point[N];
Edge edges[N * N / 2];

int i_p, i_e, cnt;
double res;

int root(int x)
{
    if (x != pre[x])
    {
        pre[x] = root(pre[x]);
    }
    return pre[x];
}

bool merge(int x, int y)
{
    int fx = root(x);
    int fy = root(y);

    bool ret = false;

    if (fx != fy)
    {
        pre[fx] = pre[fy];
        ret = true;
        --cnt;
    }
    return ret;
}

void init(int n)
{
    cnt = n;
    res = 0;

    for (int i = 0; i <= n; ++i)
    {
        pre[i] = i;
    }
}

bool cmp(const Edge &a, const Edge &b)
{
    return a.w < b.w;
}

int main()
{
    int n;
    double dx, dy;

    while (scanf("%d", &n) != EOF)
    {
        init(n);

        i_e = i_p = 0;

        for (int i = 0; i < n; ++i)
        {
            scanf("%lf %lf", &dx, &dy);
            point[i_p].x = dx;
            point[i_p].y = dy;
            ++i_p;
        }

        for (int i = 0; i < n; ++i)
        {
            for (int j = i + 1; j < n; ++j)
            {
                edges[i_e].x = i;
                edges[i_e].y = j;
                double dd = (point[i].x - point[j].x) * (point[i].x - point[j].x);
                dd += (point[i].y - point[j].y) * (point[i].y - point[j].y);
                edges[i_e].w = sqrt(dd);
                ++i_e;
            }
        }

        sort(edges, edges + i_e, cmp);

        //the cnt == 1 indicates that the mixnum spanning tree is builded sucessfully.
        for (int i = 0; i < i_e && cnt != 1; ++i)
        {
            if (merge(edges[i].x, edges[i].y))res += edges[i].w;
        }

        printf("%.2lf\n", res);
    }
    return 0;
}