QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#113054#6395. Equation Discoveringhos_lyricAC ✓242ms170968kbC++144.0kb2023-06-16 08:30:212023-06-16 08:30:24

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-06-16 08:30:24]
  • 评测
  • 测评结果:AC
  • 用时:242ms
  • 内存:170968kb
  • [2023-06-16 08:30:21]
  • 提交

answer

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }


using Double = long double;

constexpr int COST = 9;
constexpr Double EPS = 0.9e-3;
constexpr Double DIV = 0.011;

int N;
vector<Double> X, Y;

int main() {
  for (; ~scanf("%d", &N); ) {
    X.resize(N);
    Y.resize(N);
    for (int i = 0; i < N; ++i) {
      scanf("%Lf%Lf", &X[i], &Y[i]);
    }
    
    using S = pair<string, vector<Double>>;
    vector<S> dp[COST + 1];
    {
      S ini;
      ini.first = "x";
      ini.second = X;
      dp[0].push_back(ini);
    }
    for (int j = 1; j <= COST; ++j) {
      // binary
      for (int k = 0; k <= j - 2 - k; ++k) {
        for (const S &f : dp[k]) for (const S &g : dp[j - 2 - k]) {
          for (int op = 0; op < 6; ++op) {
            [&]() -> void {
              S h;
              if (op < 4) {
                h.first = "(" + f.first + "+-*/"[op] + g.first + ")";
              } else {
                h.first = "(" + g.first + "-/"[op - 4] + f.first + ")";
              }
              h.second.resize(N);
              for (int i = 0; i < N; ++i) {
                if (op == 3 && abs(g.second[i]) < DIV) return;
                if (op == 5 && abs(f.second[i]) < DIV) return;
                switch (op) {
                  case 0: h.second[i] = f.second[i] + g.second[i]; break;
                  case 1: h.second[i] = f.second[i] - g.second[i]; break;
                  case 2: h.second[i] = f.second[i] * g.second[i]; break;
                  case 3: h.second[i] = f.second[i] / g.second[i]; break;
                  case 4: h.second[i] = g.second[i] - f.second[i]; break;
                  case 5: h.second[i] = g.second[i] / f.second[i]; break;
                  default: assert(false);
                }
              }
              dp[j].push_back(h);
            }();
          }
        }
      }
      // unary
      for (const S &f : dp[j - 1]) {
        for (int op = 0; op < 2; ++op) {
          S g;
          g.first = string() + "(" + ((op == 0) ? "sin" : "cos") + "(" + f.first + ")" + ")";
          g.second.resize(N);
          for (int i = 0; i < N; ++i) {
            switch (op) {
              case 0: g.second[i] = sin(f.second[i]); break;
              case 1: g.second[i] = cos(f.second[i]); break;
              default: assert(false);
            }
          }
          dp[j].push_back(g);
        }
      }
cerr<<"|dp["<<j<<"]| = "<<dp[j].size()<<endl;
    }
    
    for (int j = 0; j <= COST; ++j) {
      for (const S &f : dp[j]) {
        bool ok = true;
        for (int i = 0; i < N; ++i) {
          ok = ok && (abs(f.second[i] - Y[i]) / max(1.0L, abs(Y[i])) <= EPS);
        }
        if (ok) {
          puts(f.first.c_str());
          goto found;
        }
      }
    }
    // puts("HELP");
    assert(false);
   found:{}
  }
  return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 87ms
memory: 75776kb

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: 83ms
memory: 77288kb

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: 100ms
memory: 87924kb

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: 99ms
memory: 87376kb

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: 80ms
memory: 86644kb

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: 103ms
memory: 87180kb

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: 87ms
memory: 86548kb

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: 218ms
memory: 170568kb

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: 210ms
memory: 164664kb

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: 209ms
memory: 169532kb

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: 168ms
memory: 139568kb

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: 211ms
memory: 168740kb

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

result:

ok great!!

Test #13:

score: 0
Accepted
time: 218ms
memory: 165188kb

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: 221ms
memory: 170324kb

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: 242ms
memory: 168816kb

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: 214ms
memory: 165180kb

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: 221ms
memory: 169556kb

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: 120ms
memory: 92104kb

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: 225ms
memory: 169304kb

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: 213ms
memory: 170320kb

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: 120ms
memory: 92124kb

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: 133ms
memory: 93908kb

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: 75ms
memory: 66128kb

input:

1
31.424306 31.456129

output:

(x+(sin(x)))

result:

ok great!!

Test #24:

score: 0
Accepted
time: 193ms
memory: 164252kb

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: 220ms
memory: 168688kb

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: 61ms
memory: 44568kb

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: 92ms
memory: 80416kb

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: 109ms
memory: 81952kb

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: 68ms
memory: 66524kb

input:

1
10.000000 9.990000

output:

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

result:

ok great!!

Test #30:

score: 0
Accepted
time: 82ms
memory: 70228kb

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: 210ms
memory: 164992kb

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: 212ms
memory: 170012kb

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: 218ms
memory: 169972kb

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:

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

result:

ok great!!

Test #34:

score: 0
Accepted
time: 211ms
memory: 165368kb

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: 176ms
memory: 170512kb

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:

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

result:

ok great!!

Test #36:

score: 0
Accepted
time: 224ms
memory: 170968kb

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: 127ms
memory: 92980kb

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!!