QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#249160#6395. Equation Discoveringreal_sigma_teamWA 746ms3976kbC++233.3kb2023-11-12 01:36:382023-11-12 01:36:39

Judging History

你现在查看的是最新测评结果

  • [2023-11-12 01:36:39]
  • 评测
  • 测评结果:WA
  • 用时:746ms
  • 内存:3976kb
  • [2023-11-12 01:36:38]
  • 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;

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

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 = evaluate(x, 0);
            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: 0ms
memory: 3712kb

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: 0ms
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: 1ms
memory: 3796kb

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: 3740kb

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: 36ms
memory: 3768kb

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: 0ms
memory: 3736kb

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: 1ms
memory: 3796kb

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: 691ms
memory: 3688kb

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: 345ms
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: 3800kb

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: 3804kb

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: 3732kb

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: 3976kb

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: 3740kb

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: 3ms
memory: 3740kb

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: 746ms
memory: 3932kb

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: 519ms
memory: 3740kb

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: -100
Wrong Answer
time: 12ms
memory: 3968kb

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

result:

wrong answer div a small number