【问题描述】编程实现K-means算法，对平面坐标上的点进行聚类 【输入形式】输入有多行，第1行3个整数，依次是N，M，K，N为点的个数，M为坐标数，K为聚类数，下面N行输入N个点的坐标，最后1行输入K个点的编号，这K个点作为初始的聚类中心 【输出形式】输出有K行，每行输出该类中的点的编号 【样例输入】 11 2 3 2 10 2 5 8 4 5 8 7 5 6 4 1 2 4 9 7 3 1 3 3 9 1 4 7 【样例输出】 cluster1:1,4,8,11 cluster2:3,5,6,9 cluster3:2,7,10用c++编写

以下是使用 C++ 实现 K-means 算法的代码，可以参考一下：

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>

using namespace std;

// Calculate Euclidean distance between two points
double distance(const vector<double>& x, const vector<double>& y) {
    double d = 0.0;
    for (int i = 0; i < x.size(); i++) {
        d += pow(x[i] - y[i], 2);
    }
    return sqrt(d);
}

// Assign each data point to nearest centroid
void assign_cluster(const vector<vector<double>>& data, const vector<vector<double>>& centroids, vector<int>& labels) {
    for (int i = 0; i < data.size(); i++) {
        double min_dist = INFINITY;
        int min_index = 0;
        for (int j = 0; j < centroids.size(); j++) {
            double d = distance(data[i], centroids[j]);
            if (d < min_dist) {
                min_dist = d;
                min_index = j;
            }
        }
        labels[i] = min_index;
    }
}

// Update centroids based on current cluster labels
void update_centroids(const vector<vector<double>>& data, const vector<int>& labels, vector<vector<double>>& centroids) {
    vector<vector<double>> new_centroids(centroids.size(), vector<double>(data[0].size(), 0.0));
    vector<int> counts(centroids.size(), 0);

    for (int i = 0; i < data.size(); i++) {
        int c = labels[i];
        for (int j = 0; j < data[i].size(); j++) {
            new_centroids[c][j] += data[i][j];
        }
        counts[c]++;
    }

    for (int i = 0; i < centroids.size(); i++) {
        if (counts[i] > 0) {
            for (int j = 0; j < centroids[i].size(); j++) {
                centroids[i][j] = new_centroids[i][j] / counts[i];
            }
        }
    }
}

// K-means clustering algorithm
void kmeans(const vector<vector<double>>& data, int k, vector<int>& labels, vector<vector<double>>& centroids) {
    // Initialize centroids randomly
    centroids = vector<vector<double>>(k, vector<double>(data[0].size(), 0.0));
    for (int i = 0; i < k; i++) {
        centroids[i] = data[rand() % data.size()];
    }

    // Initialize cluster labels
    labels = vector<int>(data.size(), 0);

    while (true) {
        // Assign each data point to nearest centroid
        assign_cluster(data, centroids, labels);

        // Update centroids
        vector<vector<double>> old_centroids = centroids;
        update_centroids(data, labels, centroids);

        // Check for convergence
        bool converged = true;
        for (int i = 0; i < centroids.size(); i++) {
            if (distance(old_centroids[i], centroids[i]) > 1e-6) {
                converged = false;
                break;
            }
        }
        if (converged) {
            break;
        }
    }
}

// Print cluster labels
void print_clusters(const vector<int>& labels) {
    vector<vector<int>> clusters(labels.size());
    for (int i = 0; i < labels.size(); i++) {
        clusters[labels[i]].push_back(i + 1);
    }
    for (int i = 0; i < clusters.size(); i++) {
        cout << "cluster" << i + 1 << ":";
        for (int j = 0; j < clusters[i].size(); j++) {
            cout << clusters[i][j];
            if (j < clusters[i].size() - 1) {
                cout << ",";
            }
        }
        cout << endl;
    }
}

// Main function
int main() {
    // Read input data
    int n, m, k;
    cin >> n >> m >> k;
    vector<vector<double>> data(n, vector<double>(m));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            cin >> data[i][j];
        }
    }
    vector<int> initial_centroids(k);
    for (int i = 0; i < k; i++) {
        cin >> initial_centroids[i];
    }

    // Run K-means algorithm
    vector<int> labels;
    vector<vector<double>> centroids;
    kmeans(data, k, labels, centroids);

    // Print cluster labels
    print_clusters(labels);

    return 0;
}

该程序也读入输入数据，包括点的个数、坐标数、聚类数、所有点的坐标和初始聚类中心的编号，然后使用 K-means 算法进行聚类，输出每个聚类中的点的编号。注意，这里使用 vector 容器进行数据存储和操作，需要包含头文件 `<vector>`。