QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#249176 | #6395. Equation Discovering | real_sigma_team | TL | 827ms | 3744kb | C++23 | 3.7kb | 2023-11-12 01:47:02 | 2023-11-12 01:47:02 |
Judging History
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;
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);
}
}
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) {
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;
}
bool ok(string s) {
int bal = 0;
bool ok = 1;
for (auto i : s) {
bal += (i == '(') - (i == ')');
ok &= bal >= 0;
}
ok &= bal == 0;
return ok;
}
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;
for (int len = 1; len <= 10; ++len) {
for (int mask = 0; mask < (1 << (len * 2)); ++mask) {
string s(2 * len, '#');
for (int i = 0; i < 2 * len; ++i) s[i] = (mask >> i & 1) ? '(' : ')';
if (ok(s)) {
g.assign(len, {});
type.resize(len);
ptr = 0;
gen(s);
gen2(0);
}
}
}
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 3584kb
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: 2ms
memory: 3552kb
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: 3564kb
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: 1ms
memory: 3548kb
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: 38ms
memory: 3580kb
input:
5 78.611917 -0.992212 -29.857271 1.011993 -75.513655 1.006611 68.512394 1.145128 7.961096 0.881661
output:
((sin(x))*(sin(x)))+(cos(x))
result:
ok great!!
Test #6:
score: 0
Accepted
time: 1ms
memory: 3580kb
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: 3552kb
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: 726ms
memory: 3740kb
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: 357ms
memory: 3628kb
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: 1ms
memory: 3556kb
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: 3676kb
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: 5ms
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:
((x)*(sin(x)))*(cos(x))
result:
ok great!!
Test #13:
score: 0
Accepted
time: 0ms
memory: 3740kb
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: 3680kb
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: 4ms
memory: 3584kb
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: 772ms
memory: 3624kb
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: 535ms
memory: 3584kb
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: 70ms
memory: 3584kb
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: 1ms
memory: 3736kb
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: 1ms
memory: 3740kb
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: 30ms
memory: 3624kb
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: 827ms
memory: 3628kb
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: 1ms
memory: 3736kb
input:
1 31.424306 31.456129
output:
(x)+(sin(x))
result:
ok great!!
Test #24:
score: 0
Accepted
time: 7ms
memory: 3588kb
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: 1ms
memory: 3648kb
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: 3580kb
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: -100
Time Limit Exceeded
input:
4 1.560797 17.311340 1.000000 0.616661 2.000000 -0.369041 3.000000 -0.166678