IOI 2010 Languages — More than 102 points?

#	User	Rating
1	tourist	4009
2	jiangly	3823
3	Benq	3738
4	Radewoosh	3633
5	jqdai0815	3620
6	orzdevinwang	3529
7	ecnerwala	3446
8	Um_nik	3396
9	ksun48	3390
10	gamegame	3386

#	User	Contrib.
1	cry	167
2	Um_nik	163
3	maomao90	162
3	atcoder_official	162
5	adamant	159
6	-is-this-fft-	158
7	awoo	157
8	TheScrasse	154
9	Dominater069	153
9	nor	153

I think IOI 2010 Languages is a very interesting (but also slightly annoying) problem — not only is it one of the few IOI problems that use machine learning, but the maximum score is 110 points instead of the usual 100.

Because of how unusual the problem is, there are relatively few people who try to solve it and far fewer with more than 100 points.

I've recently been trying to push the limits on how many points I can score. So far, I've managed to score 102 points on Yandex — the highest score I'm aware of.

My code for 102 points

#include <bits/stdc++.h>
#define FOR(i, x, y) for (int i = x; i < y; i++)
typedef long long ll;

#include "grader.h"

const int SZ = 100, LANGS = 56, MOD = 539653;

ll si[SZ], bi[SZ], tr[SZ], qu[SZ];
double cnt[LANGS];
int freq[LANGS][MOD];

inline double hyperb(int x) { return x / (x + 1.1); }

void excerpt(int *E) {
    FOR(i, 0, SZ - 3) {
        si[i] = E[i];
        bi[i] = ((si[i] << 16) + E[i + 1]) % MOD;
        tr[i] = ((bi[i] << 16) + E[i + 2]) % MOD;
        qu[i] = ((tr[i] << 16) + E[i + 3]) % MOD;
    }

    int best = 0;
    double best_sim = 0;
    FOR(i, 0, LANGS) {
        double sim = 0;
        FOR(j, 0, SZ - 3) {
            sim += hyperb(freq[i][qu[j]]) * 6;
            sim += hyperb(freq[i][tr[j]]);
            sim += hyperb(freq[i][bi[j]]) * 4;
            sim += hyperb(freq[i][si[j]]);
        }
        sim /= log(cnt[i] + 2);

        if (sim > best_sim) best = i, best_sim = sim;
    }

    int ans = language(best);
    cnt[ans]++;
    FOR(i, 0, SZ - 3) {
        freq[ans][qu[i]]++;
        freq[ans][tr[i]]++;
        freq[ans][bi[i]]++;
        freq[ans][si[i]]++;
    }
}

I found the correct weights by trial and error, so there's obviously a lot of room for improvement.

Here's my question: how high can we (realistically) go? A score of 103 points requires at least 93.6% accuracy, but my code only has an accuracy of 92.8%

dolphingarlic's blog