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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#548780#6395. Equation Discoveringpandapythoner#AC ✓377ms32984kbC++235.2kb2024-09-05 20:49:512024-09-05 20:49:52

Judging History

你现在查看的是最新测评结果

  • [2024-09-05 20:49:52]
  • 评测
  • 测评结果:AC
  • 用时:377ms
  • 内存:32984kb
  • [2024-09-05 20:49:51]
  • 提交

answer

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

using ll = long long;
using ld = long double;

#define len(a) int((a).size())
#define all(a) begin(a), end(a)
#define rep(i, n) for (int i = 0; i < (n); i++)

enum class OPERATION {
    PLUS,
    MINUS,
    DIV,
    MUL,
    SIN,
    COS,
    X,
};

struct node {
    OPERATION op;
    array<int, 2> childs;
    int size = 0, hsh = -1;

    node() {
        op = OPERATION::X;
        childs = { -1, -1 };
    }
};

map<pair<OPERATION, pair<int, int>>, int> mp;
vector<node> tree;

int new_node() {
    tree.push_back(node());
    return len(tree) - 1;
}

ld eval(int v, ld x) {
    if (tree[v].op == OPERATION::X) {
        return x;
    } else if (tree[v].op == OPERATION::PLUS) {
        return eval(tree[v].childs[0], x) + eval(tree[v].childs[1], x);
    } else if (tree[v].op == OPERATION::MINUS) {
        return eval(tree[v].childs[0], x) - eval(tree[v].childs[1], x);
    } else if (tree[v].op == OPERATION::MUL) {
        return eval(tree[v].childs[0], x) * eval(tree[v].childs[1], x);
    } else if (tree[v].op == OPERATION::DIV) {
        auto right = eval(tree[v].childs[1], x);
        if (fabs(right) < 0.01) {
            return rand();
        }
        return eval(tree[v].childs[0], x) / right;
    } else if (tree[v].op == OPERATION::COS) {
        return cosl(eval(tree[v].childs[0], x));
    } else if (tree[v].op == OPERATION::SIN) {
        return sinl(eval(tree[v].childs[0], x));
    } else {
        assert(false);
    }
}

string build(int v) {
    if (tree[v].op == OPERATION::X) {
        return "x";
    } else if (tree[v].op == OPERATION::PLUS) {
        return "(" + build(tree[v].childs[0]) + ")+(" + build(tree[v].childs[1]) + ")";
    } else if (tree[v].op == OPERATION::MINUS) {
        return "(" + build(tree[v].childs[0]) + ")-(" + build(tree[v].childs[1]) + ")";
    } else if (tree[v].op == OPERATION::MUL) {
        return "(" + build(tree[v].childs[0]) + ")*(" + build(tree[v].childs[1]) + ")";
    } else if (tree[v].op == OPERATION::DIV) {
        return "(" + build(tree[v].childs[0]) + ")/(" + build(tree[v].childs[1]) + ")";
    } else if (tree[v].op == OPERATION::COS) {
        return "cos(" + build(tree[v].childs[0]) + ")";
    } else if (tree[v].op == OPERATION::SIN) {
        return "sin(" + build(tree[v].childs[0]) + ")";
    } else {
        assert(false);
    }
}

signed main() {
    cin.tie(nullptr)->sync_with_stdio(false);
    cout << fixed << setprecision(10);

    int root = new_node();
    for (int it = 0; it < 9; it++) {
        // cout << it << endl;

        vector<int> ord(len(tree));
        iota(all(ord), 0);
        sort(all(ord), [&](int i, int j) {
            return tree[i].size < tree[j].size;
            });

        const int N = len(tree);
        for (auto v : ord) {
            for (auto u : ord) {
                int nsize = tree[v].size + tree[u].size + 2;
                if (nsize > 9) {
                    break;
                }

                for (auto op : { OPERATION::PLUS, OPERATION::MINUS, OPERATION::DIV, OPERATION::MUL }) {
                    pair<int, int> c = { tree[v].hsh, tree[u].hsh };
                    if (op == OPERATION::PLUS || op == OPERATION::MUL) {
                        if (c.first > c.second) {
                            swap(c.first, c.second);
                        }
                    }
                    auto it = mp.find(make_pair(op, c));
                    if (it != mp.end()) {
                        continue;
                    }

                    int cur_hash = len(mp);
                    mp[make_pair(op, c)] = cur_hash;
                    int w = new_node();
                    tree[w].op = op;
                    tree[w].childs = { v, u };
                    tree[w].hsh = cur_hash;
                    tree[w].size = nsize;
                }
            }

            for (auto op : { OPERATION::COS, OPERATION::SIN }) {
                int nsize = tree[v].size + 1;
                if (nsize > 9) {
                    continue;
                }

                auto it = mp.find(make_pair(op, pair<int, int>{tree[v].hsh, -1}));
                if (it != mp.end()) {
                    continue;
                }

                int cur_hash = len(mp);
                mp[make_pair(op, pair<int, int>{tree[v].hsh, -1})] = cur_hash;
                int w = new_node();
                tree[w].op = op;
                tree[w].childs = { v, -1 };
                tree[w].hsh = cur_hash;
                tree[w].size = nsize;
            }
        }
        // cout << len(tree) << endl;
    }

    int n;
    cin >> n;
    vector<ld> x(n), y(n);
    for (int i = 0; i < n; i++) {
        cin >> x[i] >> y[i];
    }

    for (int v = 0; v < len(tree); v++) {
        bool fail = false;
        for (int i = 0; i < n; i++) {
            if (fabs(eval(v, x[i]) - y[i]) > 1e-6) {
                fail = true;
                break;
            }
        }

        if (fail) {
            continue;
        }
        cout << build(v) << '\n';
        return 0;
    }
    assert(false);
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 223ms
memory: 32264kb

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: 223ms
memory: 31920kb

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: 217ms
memory: 31136kb

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: 225ms
memory: 32320kb

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: 224ms
memory: 31920kb

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: 235ms
memory: 32212kb

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: 223ms
memory: 31504kb

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: 335ms
memory: 32888kb

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: 241ms
memory: 31040kb

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: 231ms
memory: 31208kb

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: 212ms
memory: 32764kb

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: 220ms
memory: 31564kb

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:

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

result:

ok great!!

Test #13:

score: 0
Accepted
time: 221ms
memory: 32316kb

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: 231ms
memory: 31576kb

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: 218ms
memory: 31436kb

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

result:

ok great!!

Test #16:

score: 0
Accepted
time: 268ms
memory: 31200kb

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

result:

ok great!!

Test #17:

score: 0
Accepted
time: 330ms
memory: 32388kb

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: 334ms
memory: 32096kb

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

result:

ok great!!

Test #19:

score: 0
Accepted
time: 234ms
memory: 32144kb

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: 228ms
memory: 30868kb

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:

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

result:

ok great!!

Test #21:

score: 0
Accepted
time: 242ms
memory: 31920kb

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: 261ms
memory: 32700kb

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: 223ms
memory: 32420kb

input:

1
31.424306 31.456129

output:

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

result:

ok great!!

Test #24:

score: 0
Accepted
time: 228ms
memory: 31020kb

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: 242ms
memory: 30912kb

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: 208ms
memory: 31292kb

input:

4
0.009999 1.000000
1.000000 1.000000
2.000000 1.000000
3.000000 1.000000

output:

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

result:

ok great!!

Test #27:

score: 0
Accepted
time: 242ms
memory: 31760kb

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: 292ms
memory: 31604kb

input:

4
0.020000 0.712709
1.000000 0.577284
2.000000 0.964383
3.000000 0.786224

output:

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

result:

ok great!!

Test #29:

score: 0
Accepted
time: 219ms
memory: 32696kb

input:

1
10.000000 9.990000

output:

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

result:

ok great!!

Test #30:

score: 0
Accepted
time: 234ms
memory: 31728kb

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: 365ms
memory: 32932kb

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: 377ms
memory: 31116kb

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: 232ms
memory: 32852kb

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: 209ms
memory: 32920kb

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: 240ms
memory: 31612kb

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: 228ms
memory: 31656kb

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: 236ms
memory: 32984kb

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!!