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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#177260#6395. Equation Discoveringmendicillin2TL 37ms49564kbC++173.6kb2023-09-12 19:24:052023-09-12 19:24:06

Judging History

你现在查看的是最新测评结果

  • [2023-09-12 19:24:06]
  • 评测
  • 测评结果:TL
  • 用时:37ms
  • 内存:49564kb
  • [2023-09-12 19:24:05]
  • 提交

answer

#pragma GCC optimize ("Ofast")
#include <bits/stdc++.h>
using namespace std;

template <class T> int sz(T&& a) { return int(size(forward<T>(a))); }

template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;

using ll = int64_t;
using vi = vc<int>;

template <class F>
struct ycr {
	F f;
	
	template <class T>
	explicit ycr(T&& f_) : f(forward<T>(f_)) {}

	template <class... Args>
	decltype(auto) operator()(Args&&... args) {
		return f(ref(*this), forward<Args>(args)...);
	}
};
template <class F>
decltype(auto) yc(F&& f) {
	return ycr<decay_t<F>>(forward<F>(f));
}

int main() {
	ios_base::sync_with_stdio(false), cin.tie(nullptr);
	cout << fixed << setprecision(20);

	int N; cin >> N;
	
	using D = double;
	vector<D> xs(N), ys(N);
	for (int i = 0; i < N; i++) {
		cin >> xs[i] >> ys[i];
	}

	auto check = [&](string expr, vector<D> cur) -> void {
		for (int i = 0; i < N; i++) {
			if (abs(cur[i] - ys[i]) / max<D>(1, abs(ys[i])) > 1e-3) return;
		}
		cout << expr << '\n';
		exit(0);
	};

	const int L = 10;
	vector<vector<pair<string, vector<D>>>> vals(L);
	vals[0].push_back({"x", xs});
	vector<D> t(N);
	for (int c = 1; c < L; c++) {
		// sin/cos
		for (const auto& [expr, s] : vals[c-1]) {
			{
				for (int i = 0; i < N; i++) {
					t[i] = sin(s[i]);
				}
				auto new_expr = "sin(" + expr + ")";
				check(new_expr, t);
				vals[c].push_back({new_expr, t});
			}
			{
				for (int i = 0; i < N; i++) {
					t[i] = cos(s[i]);
				}
				auto new_expr = "cos(" + expr + ")";
				check(new_expr, t);
				vals[c].push_back({new_expr, t});
			}
		}
		for (int c0 = 0; c0 <= c-1-c0; c0++) {
			int c1 = c-1-c0;
			for (const auto& [expr0, s0] : vals[c0]) {
				for (const auto& [expr1, s1] : vals[c1]) {
					for (int i = 0; i < N; i++) {
						t[i] = s0[i] + s1[i];
					}
					auto new_expr = "(" + expr0 + ")+(" + expr1 + ")";
					check(new_expr, t);
					vals[c].push_back({new_expr, t});
				}
			}
			for (const auto& [expr0, s0] : vals[c0]) {
				for (const auto& [expr1, s1] : vals[c1]) {
					for (int i = 0; i < N; i++) {
						t[i] = s0[i] - s1[i];
					}
					auto new_expr = "(" + expr0 + ")-(" + expr1 + ")";
					check(new_expr, t);
					vals[c].push_back({new_expr, t});
				}
			}
			for (const auto& [expr0, s0] : vals[c0]) {
				for (const auto& [expr1, s1] : vals[c1]) {
					for (int i = 0; i < N; i++) {
						t[i] = s1[i] - s0[i];
					}
					auto new_expr = "(" + expr1 + ")-(" + expr0 + ")";
					check(new_expr, t);
					vals[c].push_back({new_expr, t});
				}
			}
			for (const auto& [expr0, s0] : vals[c0]) {
				for (const auto& [expr1, s1] : vals[c1]) {
					for (int i = 0; i < N; i++) {
						t[i] = s0[i] * s1[i];
					}
					auto new_expr = "(" + expr0 + ")*(" + expr1 + ")";
					check(new_expr, t);
					vals[c].push_back({new_expr, t});
				}
			}
			for (const auto& [expr0, s0] : vals[c0]) {
				for (const auto& [expr1, s1] : vals[c1]) {
					bool works = true;
					for (int i = 0; i < N; i++) {
						if (abs(s1[i]) < 1e-2) {
							works = false;
							break;
						}
						t[i] = s0[i] / s1[i];
					}
					if (!works) continue;
					auto new_expr = "(" + expr0 + ")/(" + expr1 + ")";
					check(new_expr, t);
					vals[c].push_back({new_expr, t});
				}
			}
			for (const auto& [expr0, s0] : vals[c0]) {
				for (const auto& [expr1, s1] : vals[c1]) {
					bool works = true;
					for (int i = 0; i < N; i++) {
						if (abs(s0[i]) < 1e-2) {
							works = false;
							break;
						}
						t[i] = s1[i] / s0[i];
					}
					if (!works) continue;
					auto new_expr = "(" + expr1 + ")/(" + expr0 + ")";
					check(new_expr, t);
					vals[c].push_back({new_expr, t});
				}
			}
		}
	}
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 4352kb

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: 4496kb

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: 4364kb

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: 4380kb

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: 7ms
memory: 19280kb

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: 1ms
memory: 4532kb

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: 4364kb

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: 37ms
memory: 49564kb

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: 2ms
memory: 5928kb

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: 3924kb

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: 3996kb

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: 2ms
memory: 5856kb

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: 3980kb

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: 3988kb

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)+((x)-(x))

result:

ok great!!

Test #15:

score: 0
Accepted
time: 1ms
memory: 4512kb

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: -100
Time Limit Exceeded

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:


result: