设计评分规则并公平比较两个版本

BigInteger coefficient = BigInteger.ONE;
coefficient = coefficient.multiply(BigInteger.valueOf(n - i + 1))
    .divide(BigInteger.valueOf(i)); // 组合数递推保证本步可整除。
BigInteger outcomes = BigInteger.ONE.shiftLeft(n); // 精确构造二的n次方。
BigInteger numerator = tail.shiftLeft(1).min(outcomes); // 双侧尾概率不超过一。

import java.math.BigInteger;
public class Main {
    record Result(int n,int wins,BigInteger numerator,BigInteger denominator){}
    static Result compare(int[] base,int[] candidate){
        if(base.length!=candidate.length||base.length>10000)throw new IllegalArgumentException("size");
        int wins=0,losses=0;
        for(int i=0;i<base.length;i++){if(candidate[i]>base[i])wins++;else if(candidate[i]<base[i])losses++;} // 比较不做减法，避免溢出。
        int n=wins+losses;if(n==0)return new Result(0,0,BigInteger.ONE,BigInteger.ONE);
        int k=Math.min(wins,losses);BigInteger c=BigInteger.ONE,tail=c;
        for(int i=1;i<=k;i++){c=c.multiply(BigInteger.valueOf(n-i+1)).divide(BigInteger.valueOf(i));tail=tail.add(c);} // 组合数逐项精确累加。
        BigInteger denominator=BigInteger.ONE.shiftLeft(n);
        return new Result(n,wins,tail.shiftLeft(1).min(denominator),denominator); // 双侧概率封顶为一。
    }
    static void check(int n,int wins,int a,int b,Result r){
        if(r.n()!=n||r.wins()!=wins||!r.numerator().multiply(BigInteger.valueOf(b)).equals(r.denominator().multiply(BigInteger.valueOf(a))))throw new AssertionError(r);
    }
    public static void main(String[] args){
        check(3,3,1,4,compare(new int[]{0,0,0},new int[]{1,1,1}));
        check(4,4,1,8,compare(new int[4],new int[]{1,1,1,1}));
        check(4,2,1,1,compare(new int[4],new int[]{1,1,-1,-1}));
        check(0,0,1,1,compare(new int[]{7},new int[]{7}));
        check(0,0,1,1,compare(new int[]{},new int[]{}));
        check(1,1,1,1,compare(new int[]{Integer.MIN_VALUE},new int[]{Integer.MAX_VALUE}));
        try{compare(new int[1],new int[0]);throw new AssertionError();}catch(IllegalArgumentException expected){}
        System.out.println("PASS 7 tests");
    }
}