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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#249281#6395. Equation Discoveringreal_sigma_teamAC ✓96ms3984kbC++234.4kb2023-11-12 02:38:392023-11-12 02:38:39

Judging History

你现在查看的是最新测评结果

  • [2023-11-12 02:38:39]
  • 评测
  • 测评结果:AC
  • 用时:96ms
  • 内存:3984kb
  • [2023-11-12 02:38:39]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std;

#define all(x) x.begin(), x.end()

using ld = long double;

vector<vector<int>> g;
vector<int> type;

vector<pair<ld, ld>> eq;

mt19937 rnd(4235);

pair<ld, bool> evaluate(ld x, int u) {
    if (g[u].size() == 0) return {x, 0};
    if (g[u].size() == 1) {
        pair<ld, bool> val = evaluate(x, g[u][0]);
        if (val.second) return {0, 1};
        if (type[u] == 0) val.first = sin(val.first);
        if (type[u] == 1) val.first = cos(val.first);
        return val;
    }
    if (g[u].size() == 2) {
        pair<ld, bool> v1 = evaluate(x, g[u][0]);
        pair<ld, bool> v2 = evaluate(x, g[u][1]);
        if (v1.second || v2.second) return {0, 1};
        switch (type[u]) {
            case 0: v1.first += v2.first; return v1;
            case 1: v1.first -= v2.first; return v1;
            case 2: v1.first *= v2.first; return v1;
            case 3:
                if (abs(v2.first) <= 0.01) return {0, 1};
                v1.first /= v2.first;
                return v1;
        }
    }
}

string gen_ans(int u) {
    if (g[u].size() == 0) return "x";
    if (g[u].size() == 1) {
        if (type[u] == 0) return "sin(" + gen_ans(g[u][0]) + ")";
        if (type[u] == 1) return "cos(" + gen_ans(g[u][0]) + ")";
    }
    if (g[u].size() == 2) {
        switch (type[u]) {
            case 0: return "(" + gen_ans(g[u][0]) + ")+(" + gen_ans(g[u][1]) + ")";
            case 1: return "(" + gen_ans(g[u][0]) + ")-(" + gen_ans(g[u][1]) + ")";
            case 2: return "(" + gen_ans(g[u][0]) + ")*(" + gen_ans(g[u][1]) + ")";
            case 3: return "(" + gen_ans(g[u][0]) + ")/(" + gen_ans(g[u][1]) + ")";
        }
    }
}

void gen2(int i) {
    if (i == g.size()) {
        bool ok = 1;
        for (auto [x, y] : eq) {
            auto [val, fl] = evaluate(x, 0);
            if (fl) {
                ok = 0;
                break;
            }
            if (abs(val - y) / max((ld)1, abs(y)) <= 1e-3) {}
            else {
                ok = 0;
                break;
            }
        }
        if (ok) {
            cout << gen_ans(0);
            exit(0);
        }
        return;
    }
    if (g[i].size() == 0) {
        type[i] = 0;
        gen2(i + 1);
    } else if (g[i].size() == 1) {
        for (type[i] = 0; type[i] < 2; ++type[i]) gen2(i + 1);
    } else {
        for (type[i] = 0; type[i] < 4; ++type[i]) gen2(i + 1);
    }
}

bool ok;
int ptr;
int gen(string s) {
    if (s.empty()) return -1;
    int u = ptr++;
    int bal = 0;
    for (int i = 0; i < s.size(); ++i) {
        bal += (s[i] == '(') - (s[i] == ')');
        if (bal == 0) {
            if (i + 1 == s.size() && i != 1) {
                ok = 0;
                break;
            }
            int v;
            v = gen(string(s.begin() + 1, s.begin() + i));
            if (v != -1) g[u].push_back(v);
            v = gen(string(s.begin() + i + 1, s.end()));
            if (v != -1) g[u].push_back(v);
            break;
        }
    }
    return u;
}

string cur;
int bal;

void gen(int i) {
    if (i == cur.size()) {
        g.assign(cur.size() / 2, {});
        type.resize(cur.size() / 2);
        ptr = 0;
        ok = 1;
        gen(cur);
        if (!ok) return;
        gen2(0);
        return;
    }
    if (rnd() & 1) {
        if (bal > 0) {
            bal--;
            cur[i] = ')';
            gen(i + 1);
            bal++;
        }
        if (bal + 1 <= (cur.size() - i - 1)) {
            bal++;
            cur[i] = '(';
            gen(i + 1);
            bal--;
        }
    } else {
        if (bal + 1 <= (cur.size() - i - 1)) {
            bal++;
            cur[i] = '(';
            gen(i + 1);
            bal--;
        }
        if (bal > 0) {
            bal--;
            cur[i] = ')';
            gen(i + 1);
            bal++;
        }
    }
}

signed main() {
    cin.tie(0)->sync_with_stdio(0);

    int n;
    cin >> n;
    eq.resize(n);
    for (int i = 0; i < n; ++i) cin >> eq[i].first >> eq[i].second;
    vector<int> lenn;
    for (int len = 2; len <= 20; len += 2) {
        lenn.push_back(len);
        cur = string(len, '#');
        gen(0);
    }
    shuffle(lenn.begin(), lenn.end(), rnd);
    for (auto len : lenn) {
        cur = string(len, '#');
        gen(0);
    }
}

详细

Test #1:

score: 100
Accepted
time: 0ms
memory: 3720kb

input:

3
1.000000 1.000000
2.000000 4.000000
3.000000 9.000000

output:

(x)*(x)

result:

ok great!!

Test #2:

score: 0
Accepted
time: 1ms
memory: 3740kb

input:

3
0.618000 1.517072
0.314000 3.132637
1.414000 0.494016

output:

(sin(x))/((x)*(x))

result:

ok great!!

Test #3:

score: 0
Accepted
time: 0ms
memory: 3944kb

input:

5
77.685777 233.057331
-66.445083 -199.335249
79.966717 239.900151
84.982130 254.946390
-31.528900 -94.586700

output:

((x)+(x))+(x)

result:

ok great!!

Test #4:

score: 0
Accepted
time: 0ms
memory: 3752kb

input:

5
25.032427 -0.100652
38.727324 1.658518
27.684334 -0.669555
64.282391 8.275303
52.640700 -0.962660

output:

(sin(x))/(cos(x))

result:

ok great!!

Test #5:

score: 0
Accepted
time: 2ms
memory: 3692kb

input:

5
78.611917 -0.992212
-29.857271 1.011993
-75.513655 1.006611
68.512394 1.145128
7.961096 0.881661

output:

(cos(x))+((sin(x))*(sin(x)))

result:

ok great!!

Test #6:

score: 0
Accepted
time: 0ms
memory: 3808kb

input:

5
-78.733375 0.503570
-20.187183 0.735779
-38.984992 0.730890
47.859232 0.622831
-19.657164 0.641512

output:

sin(sin(cos(cos(x))))

result:

ok great!!

Test #7:

score: 0
Accepted
time: 0ms
memory: 3748kb

input:

5
3.241091 -32.628130
-83.514144 86.463432
33.586619 40.691607
41.123543 -147.352644
26.896326 27.404018

output:

(x)/(sin(x))

result:

ok great!!

Test #8:

score: 0
Accepted
time: 96ms
memory: 3948kb

input:

20
-4.908422 -0.693287
3.569189 0.328182
1.946572 -0.667466
6.515336 -0.829948
-1.394076 0.752980
6.722989 0.831881
1.241795 0.835231
-2.443177 -0.143098
-4.180762 -0.803482
1.511247 0.589509
0.627755 0.554244
-1.865604 -0.470029
-4.756347 -0.656984
1.850611 -0.426016
6.580133 -0.474416
6.861815 -0....

output:

sin(sin((x)/(sin(((x)/(x))/(x)))))

result:

ok great!!

Test #9:

score: 0
Accepted
time: 16ms
memory: 3740kb

input:

20
76.797930 0.000002
-76.263778 -0.000002
55.449039 0.000006
10.462093 0.000873
-78.051671 -0.000002
-52.781249 -0.000007
47.053973 0.000010
96.629212 0.000001
-40.697847 -0.000015
31.141805 0.000033
-87.087384 -0.000002
-54.709885 -0.000006
-65.741847 -0.000004
-87.430820 -0.000001
9.420126 0.0011...

output:

(x)/(((x)*((x)*(x)))*(x))

result:

ok great!!

Test #10:

score: 0
Accepted
time: 0ms
memory: 3744kb

input:

20
24.490647 23.891773
17.327799 16.329001
21.204241 21.912414
83.489542 84.461510
-55.546573 -54.703972
-7.608368 -8.578356
-3.286697 -3.142101
-66.606831 -66.014954
-44.896454 -45.688502
97.541741 97.389961
-59.986043 -59.694554
57.723989 58.646803
-99.857351 -99.233536
29.134673 28.376609
-98.668...

output:

(x)+(sin(x))

result:

ok great!!

Test #11:

score: 0
Accepted
time: 0ms
memory: 3984kb

input:

20
89.594917 88.596688
-45.187625 -44.253669
97.451471 97.513530
35.078537 35.576300
82.504351 81.771201
-49.755211 -50.243625
-23.019693 -23.876242
-45.247155 -44.293590
75.324114 75.398156
78.533049 78.526282
99.112156 100.100628
31.983437 31.445903
71.251578 70.407388
-44.178279 -43.983549
-25.28...

output:

(x)-(sin(x))

result:

ok great!!

Test #12:

score: 0
Accepted
time: 1ms
memory: 3744kb

input:

20
16.664144 7.850741
44.708237 22.196248
-10.852343 1.533223
-42.713221 -12.119419
-27.815914 -11.038511
31.908696 13.299065
-82.394044 40.761558
-37.317157 -12.907073
-35.369997 17.659068
93.569121 -45.722539
-30.589159 -15.242258
16.180069 6.553209
56.572831 1.366451
99.591187 -47.440823
12.73229...

output:

(sin(x))*((x)*(cos(x)))

result:

ok great!!

Test #13:

score: 0
Accepted
time: 0ms
memory: 3692kb

input:

20
-583.519562 0.000000
-169.653469 0.000000
372.798856 0.000000
180.084282 0.000000
139.388742 0.000000
-648.300263 0.000000
-859.523046 0.000000
-267.278551 0.000000
635.554372 0.000000
299.925737 0.000000
-628.299469 0.000000
169.393099 0.000000
556.144161 0.000000
-881.876627 0.000000
328.692044...

output:

(x)-(x)

result:

ok great!!

Test #14:

score: 0
Accepted
time: 0ms
memory: 3808kb

input:

20
746.491049 746.491049
414.031997 414.031997
-975.051138 -975.051138
45.313068 45.313068
-181.090458 -181.090458
119.607074 119.607074
245.794647 245.794647
-794.156219 -794.156219
461.647608 461.647608
-392.604379 -392.604379
384.522118 384.522118
-461.749513 -461.749513
766.462890 766.462890
244...

output:

x

result:

ok great!!

Test #15:

score: 0
Accepted
time: 1ms
memory: 3816kb

input:

20
4.278335 0.092599
3.559350 0.559919
-2.517239 0.403581
-0.955317 0.182475
3.048015 0.888213
-0.638367 0.393205
-2.188885 0.183959
-0.367275 0.597938
1.106453 0.948186
0.339096 0.971773
-0.678258 0.364003
4.364111 0.060002
-0.671364 0.369012
-2.777257 0.600136
1.617698 0.909755
-3.400784 0.950952
...

output:

sin(((x)/(x))+(sin(x)))

result:

ok great!!

Test #16:

score: 0
Accepted
time: 36ms
memory: 3812kb

input:

20
3.692126 -0.260752
0.663419 1.200876
1.167172 0.874743
4.852602 0.631308
3.373109 -0.334749
4.749943 0.529545
-2.549440 -0.245748
-1.158832 0.881804
4.115764 -0.040747
-3.401216 -0.330886
-4.320685 0.119451
-0.070540 1.332133
-4.666465 0.446117
-4.720184 0.499803
-1.731319 0.332854
4.232513 0.046...

output:

(sin(sin(cos((x)/(x)))))+(sin(cos(x)))

result:

ok great!!

Test #17:

score: 0
Accepted
time: 91ms
memory: 3776kb

input:

20
1.462467 0.804429
-2.922001 0.192241
4.580542 -0.620639
-0.475001 -0.799291
-1.988595 -0.234001
1.262913 0.840075
-3.176510 -0.034797
2.030387 0.180297
-3.244547 -0.099928
-3.321420 -0.164361
-0.538138 -0.818609
2.485817 -0.209990
-0.282936 -0.652106
0.964792 0.840607
-1.300754 -0.837872
4.323400...

output:

sin(sin((sin(x))+(sin(sin((x)+(x))))))

result:

ok great!!

Test #18:

score: 0
Accepted
time: 3ms
memory: 3804kb

input:

20
-1.290592 0.818752
0.639318 0.516086
-4.576452 0.791075
2.349231 0.829843
3.053369 0.646833
-4.276424 0.836563
-4.295090 0.835111
1.704429 0.790551
1.694925 0.788364
0.763954 0.527671
-0.477936 0.769603
0.395468 0.525360
0.686854 0.519231
-1.940048 0.637497
2.188388 0.840879
1.028990 0.584344
3.9...

output:

sin(cos(sin((cos((x)-(x)))+(x))))

result:

ok great!!

Test #19:

score: 0
Accepted
time: 0ms
memory: 3804kb

input:

20
-0.425664 0.425664
5.789130 -5.789130
-3.787451 3.787451
0.301151 -0.301151
-8.592688 8.592688
2.669073 -2.669073
5.308311 -5.308311
-0.139985 0.139985
-5.857648 5.857648
-4.992568 4.992568
6.105319 -6.105319
-3.765244 3.765244
5.912188 -5.912188
-6.224392 6.224392
-0.543340 0.543340
3.434037 -3....

output:

((x)-(x))-(x)

result:

ok great!!

Test #20:

score: 0
Accepted
time: 0ms
memory: 3800kb

input:

20
466.316736 -0.978078
-899.828376 0.971830
493.698428 0.451443
543.034476 -0.444891
547.435563 -0.716269
-477.216617 -0.300738
397.144177 -0.964489
-215.994986 0.699650
-125.191685 -0.454687
-278.649888 0.814495
958.350526 0.164022
-505.445050 0.344182
-930.587439 0.625688
397.543136 -0.991345
-25...

output:

sin((x)-((x)+(x)))

result:

ok great!!

Test #21:

score: 0
Accepted
time: 4ms
memory: 3816kb

input:

20
999.999999 0.987127
-999.999999 0.987127
100.000001 -0.333949
-100.000001 -0.333949
999.999998 -0.829877
-999.999998 -0.829877
512.000001 -0.871928
-512.000001 -0.871928
511.999999 -0.985382
-511.999999 -0.985382
0.000000 0.000000
0.000001 0.000000
-0.000001 0.000000
0.180000 0.001050
-0.180000 0...

output:

sin((x)*(((x)*(x))*(x)))

result:

ok great!!

Test #22:

score: 0
Accepted
time: 88ms
memory: 3948kb

input:

20
0.009999 0.914653
0.009999 0.914653
0.009999 0.914653
0.009999 0.914653
0.009999 0.914653
0.009999 0.914653
0.009999 0.914653
1.000000 0.914653
1.000000 0.914653
2.005000 0.914653
2.005000 0.914653
3.000000 0.914653
3.000000 0.914653
0.009999 0.914653
0.009999 0.914653
0.009999 0.914653
0.009999 ...

output:

cos(cos(((cos(x))+(cos(x)))/(cos(x))))

result:

ok great!!

Test #23:

score: 0
Accepted
time: 0ms
memory: 3816kb

input:

1
31.424306 31.456129

output:

(x)+(sin(x))

result:

ok great!!

Test #24:

score: 0
Accepted
time: 0ms
memory: 3720kb

input:

20
-29.440025 807.835022
19.414601 415.755934
11.492851 155.071326
18.966989 397.680650
3.027310 15.219226
-4.525550 11.429503
-7.906286 46.696786
-21.105731 403.240419
16.717653 312.915228
25.349563 693.299470
28.071737 844.165892
28.141608 848.233317
-26.371446 642.710272
-13.802857 162.913147
-23...

output:

(x)+((x)+((x)*(x)))

result:

ok great!!

Test #25:

score: 0
Accepted
time: 0ms
memory: 3744kb

input:

20
458.594270 0.909297
236.772098 0.909297
679.844094 0.909297
-113.768271 0.909297
-919.765157 0.909297
450.713950 0.909297
-560.756795 0.909297
35.253093 0.909297
-530.329136 0.909297
-846.165765 0.909297
-294.618124 0.909297
595.795664 0.909297
441.685140 0.909297
220.854674 0.909297
-649.606144 ...

output:

sin(((x)+(x))/(x))

result:

ok great!!

Test #26:

score: 0
Accepted
time: 0ms
memory: 3744kb

input:

4
0.009999 1.000000
1.000000 1.000000
2.000000 1.000000
3.000000 1.000000

output:

cos((x)-(x))

result:

ok great!!

Test #27:

score: 0
Accepted
time: 36ms
memory: 3744kb

input:

4
1.560797 17.311340
1.000000 0.616661
2.000000 -0.369041
3.000000 -0.166678

output:

(cos(sin(x)))/((cos(x))*((x)+(x)))

result:

ok great!!

Test #28:

score: 0
Accepted
time: 92ms
memory: 3748kb

input:

4
0.020000 0.712709
1.000000 0.577284
2.000000 0.964383
3.000000 0.786224

output:

cos(sin((cos(sin(cos((x)/(x)))))+(x)))

result:

ok great!!

Test #29:

score: 0
Accepted
time: 1ms
memory: 3744kb

input:

1
10.000000 9.990000

output:

(cos((sin(x))/(x)))*(x)

result:

ok great!!

Test #30:

score: 0
Accepted
time: 15ms
memory: 3908kb

input:

2
0.026592 0.026593
4.000000 260.000000

output:

(x)+(((x)*((x)*(x)))*(x))

result:

ok great!!

Test #31:

score: 0
Accepted
time: 84ms
memory: 3744kb

input:

20
-816.944077 0.750063
364.252903 0.749797
377.702803 0.739860
-64.648254 0.723984
960.420578 0.734135
876.304536 0.749578
-718.016803 0.722938
-720.680010 0.725173
669.591341 0.746462
-835.716345 0.750360
611.456898 0.727346
-401.888640 0.749253
-59.913119 0.749372
-421.048989 0.750298
495.542911 ...

output:

cos(cos(cos(cos(cos(cos(cos(cos(cos(x)))))))))

result:

ok great!!

Test #32:

score: 0
Accepted
time: 84ms
memory: 3744kb

input:

20
-966.243761 0.499984
-775.541582 -0.343886
665.144672 -0.467363
-440.569467 -0.446768
-15.642683 -0.064867
-891.727356 0.368493
-428.695562 -0.501273
-944.141182 -0.501731
265.202915 0.498506
-979.532068 0.423344
-678.301273 0.253567
125.728556 0.064444
-465.052762 -0.095704
-183.526425 -0.498649...

output:

sin(sin(sin(sin(sin(sin(sin(sin(sin(x)))))))))

result:

ok great!!

Test #33:

score: 0
Accepted
time: 45ms
memory: 3816kb

input:

20
167.504612 669.176868
-132.494106 -530.496735
223.716049 894.248735
-14.542026 -59.087262
83.792869 336.028843
46.267758 185.826345
90.986202 364.064505
243.671799 973.706807
176.221425 705.173795
-140.883003 -564.001461
-25.914422 -104.362161
83.745358 335.862277
-92.043462 -367.367900
16.845939...

output:

(sin(x))+((x)+((x)+((x)+(x))))

result:

ok great!!

Test #34:

score: 0
Accepted
time: 45ms
memory: 3748kb

input:

20
5.820261 -23.727611
89.024912 -355.227137
78.465702 -313.788761
189.581597 -757.441601
-26.277637 104.199881
-58.876286 234.778122
180.037331 -720.972254
57.254054 -228.367888
-180.418016 722.647178
61.635602 -247.473082
126.339101 -504.731198
-192.871864 772.431509
-69.108582 276.440784
20.47183...

output:

(sin(x))-((x)+((x)+((x)+(x))))

result:

ok great!!

Test #35:

score: 0
Accepted
time: 45ms
memory: 3804kb

input:

20
-4.724302 498.103725
-3.940617 172.814337
-2.254073 -20.019734
2.417435 22.626021
4.576524 -434.632501
-3.789730 124.524863
-0.923911 -0.581439
-2.730462 -22.213656
-1.227515 -2.137958
-2.004088 -14.640510
-1.374969 -3.505828
-4.749463 508.486587
-0.919612 -0.568834
-1.895851 -12.242133
2.276076 ...

output:

(sin(x))*((x)*((x)*((x)*(x))))

result:

ok great!!

Test #36:

score: 0
Accepted
time: 46ms
memory: 3740kb

input:

20
-1.862076 -0.079675
4.978934 -0.001570
-1.706248 -0.116906
3.159038 -0.000175
-2.164361 -0.037776
4.298608 -0.002682
3.437089 -0.002087
0.898312 1.201300
-0.915297 -1.129496
4.614390 -0.002195
0.547090 5.806825
-1.238625 -0.401631
-3.916926 0.002974
-0.651893 -3.359412
-0.913229 -1.137947
-3.8357...

output:

(sin(x))/((x)*((x)*((x)*(x))))

result:

ok great!!

Test #37:

score: 0
Accepted
time: 4ms
memory: 3740kb

input:

20
999.999999 0.987127
-999.999999 0.987127
100.000001 -0.333949
-100.000001 -0.333949
999.999998 -0.829877
-999.999998 -0.829877
512.000001 -0.871928
-512.000001 -0.871928
511.999999 -0.985382
-511.999999 -0.985382
754.901184 0.143249
0.000001 0.000000
-0.000001 0.000000
0.180000 0.001050
-0.180000...

output:

sin((x)*(((x)*(x))*(x)))

result:

ok great!!