向量检索：选择距离、建立索引并检查召回

import java.util.*;
public class Main {
    record Point(String id,double[] v){} record Hit(String id,double distance){}
    static double distance(double[] a,double[] b){
        if(a.length==0||a.length!=b.length)throw new IllegalArgumentException("dimension");
        double r=0;for(int i=0;i<a.length;i++){
            if(!Double.isFinite(a[i])||!Double.isFinite(b[i]))throw new IllegalArgumentException("coordinate");
            double delta=a[i]-b[i];if(!Double.isFinite(delta))throw new IllegalArgumentException("difference overflow");
            r=Math.hypot(r,delta); // 逐维稳定累计欧氏长度。
        }
        if(!Double.isFinite(r))throw new IllegalArgumentException("distance overflow");return r;
    }
    static List<String> top(double[] q,List<Point> points,int k){
        if(k<0)throw new IllegalArgumentException("k");distance(q,q);
        Comparator<Hit> order=Comparator.comparingDouble(Hit::distance).thenComparing(Hit::id);
        PriorityQueue<Hit> heap=new PriorityQueue<>(order.reversed());Set<String> ids=new HashSet<>();
        for(Point p:points){
            if(p.id()==null||!ids.add(p.id()))throw new IllegalArgumentException("duplicate id");
            Hit hit=new Hit(p.id(),distance(q,p.v()));
            heap.offer(hit);if(heap.size()>k)heap.poll(); // 根是最差者，淘汰后仍保留最佳k项。
        }
        List<Hit> sorted=new ArrayList<>(heap);sorted.sort(order); // 堆迭代不是排序结果。
        return sorted.stream().map(Hit::id).toList();
    }
    static void eq(List<String> e,List<String> a){if(!e.equals(a))throw new AssertionError(a);}
    public static void main(String[] args){
        List<Point> p=List.of(new Point("a",new double[]{2}),new Point("c",new double[]{-1}),new Point("b",new double[]{1}));
        eq(List.of("b","c"),top(new double[]{0},p,2));
        eq(List.of(),top(new double[]{0},List.of(),3));
        eq(List.of(),top(new double[]{0},p,0));
        eq(List.of("b","c","a"),top(new double[]{0},p,10));
        try{top(new double[]{0},List.of(p.get(0),p.get(0)),1);throw new AssertionError();}catch(IllegalArgumentException expected){}
        try{top(new double[]{0,1},p,1);throw new AssertionError();}catch(IllegalArgumentException expected){}
        System.out.println("PASS 6 tests");
    }
}