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#include <bits/stdc++.h> #pragma comment(linker, "/STACK:134217728") using namespace std; long double x, y, z; string s[] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; long double a[12]; int main() { cin >> x >> y >> z; if (min(z, min(x, y)) > 1) { a[0] = z * log(y) + log(log(x)); a[1] = y * log(z) + log(log(x)); a[2] = log(y * z) + log(log(x)); a[3] = a[2]; a[4] = z * log(x) + log(log(y)); a[5] = x * log(z) + log(log(y)); a[6] = log(x * z) + log(log(y)); a[7] = a[6]; a[8] = y * log(x) + log(log(z)); a[9] = x * log(y) + log(log(z)); a[10] = log(x * y) + log(log(z)); a[11] = a[10]; } else { a[0] = pow(y, z) * log(x); a[1] = pow(z, y) * log(x); a[2] = y * z * log(x); a[3] = a[2]; a[4] = pow(x, z) * log(y); a[5] = pow(z, x) * log(y); a[6] = x * z * log(y); a[7] = a[6]; a[8] = pow(x, y) * log(z); a[9] = pow(y, x) * log(z); a[10] = x * y * log(z); a[11] = a[10]; } long double mx = *max_element(a, a + 12); for (int i = 0; i < 12; i++) { if (fabs(mx - a[i]) < 1e-17) { cout << s[i]; return 0; } } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(false); cin.tie(0); long double x, y, z; cin >> x >> y >> z; const long double eps = (long double)1e-12; auto check = [&](long double x, long double y) { return abs(x - y) < eps || abs(x - y) < eps * abs(x); }; long double logx = log(x); long double logy = log(y); long double logz = log(z); vector<long double> a(11); a[0] = logx * pow(y, z); a[1] = logx * pow(z, y); a[2] = logx * y * z; a[3] = a[2]; a[4] = logy * pow(x, z); a[5] = logy * pow(z, x); a[6] = logy * x * z; a[7] = a[6]; a[8] = logz * pow(x, y); a[9] = logz * pow(y, x); a[10] = logz * x * y; long double tmp = -1; int pos = -1; for (int i = 0; i < 11; i++) { if (!check(a[i], tmp) && a[i] > tmp) { tmp = a[i]; pos = i; } } if (pos == 0) { cout << "x^y^z" << '\n'; } else if (pos == 1) { cout << "x^z^y" << '\n'; } else if (pos == 2) { cout << "(x^y)^z" << '\n'; } else if (pos == 4) { cout << "y^x^z" << '\n'; } else if (pos == 5) { cout << "y^z^x" << '\n'; } else if (pos == 6) { cout << "(y^x)^z" << '\n'; } else if (pos == 8) { cout << "z^x^y" << '\n'; } else if (pos == 9) { cout << "z^y^x" << '\n'; } else { cout << "(z^x)^y" << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; const int mod = 1e9 + 7, maxn = 200005, ln = 17; const int shift = 30, etf = mod - 1; const double epcilon = 1e-10; const long long int inf = (long long int)1e15; const double PI = (double)3.141592653589793238; string s[] = {"x^y^z", "x^z^y", "(x^y)^z", "y^x^z", "y^z^x", "(y^x)^z", "z^x^y", "z^y^x", "(z^x)^y"}; double a[10], x, y, z; double pop(double p, double q, double r) { if (p < 1.0) return -10.0 * inf; if (p == 1.0) return -1.0 * inf; return (r * log10(q)) + log10(log10(p)); } double pom(double p, double q, double r) { if (p < 1.0) return -10.0 * inf; if (p == 1.0) return -1.0 * inf; return (log10(q) + log10(r)) + log10(log10(p)); } void solve() { int idx; double mn = inf; a[0] = pop(1.0 / x, y, z); a[1] = pop(1.0 / x, z, y); a[2] = pom(1.0 / x, y, z); a[3] = pop(1.0 / y, x, z); a[4] = pop(1.0 / y, z, x); a[5] = pom(1.0 / y, x, z); a[6] = pop(1.0 / z, x, y); a[7] = pop(1.0 / z, y, x); a[8] = pom(1.0 / z, x, y); for (int i = 0; i < 9; i++) { if (mn - a[i] > epcilon) { idx = i; mn = a[i]; } } cout << s[idx] << endl; } void solve2() { int idx; double mx = -100.0 * inf; a[0] = pop(x, y, z); a[1] = pop(x, z, y); a[2] = pom(x, y, z); a[3] = pop(y, x, z); a[4] = pop(y, z, x); a[5] = pom(y, x, z); a[6] = pop(z, x, y); a[7] = pop(z, y, x); a[8] = pom(z, x, y); for (int i = 0; i < 9; i++) { if (a[i] - mx > epcilon) { idx = i; mx = a[i]; } } cout << s[idx] << endl; } int main() { cin >> x >> y >> z; if (x < 1.0 && y < 1.0 && z < 1.0) { solve(); return 0; } solve2(); return 0; }
#include <bits/stdc++.h> using namespace std; const double EPS = 1e-8; double A[3] = {0}; int id[3] = {0}; bool cmp(int a1, int a2) { return A[a1] < A[a2]; } const char *ansstr[13] = { "", "x^y^z", "x^z^y", "(x^y)^z", "", "y^x^z", "y^z^x", "(y^x)^z", "", "z^x^y", "z^y^x", "(z^x)^y", "", }; int main() { cin >> A[0] >> A[1] >> A[2]; id[0] = 0, id[1] = 1, id[2] = 2; sort(id, id + 3, cmp); double ans = -1e200; int ansid = -1; if (A[id[2]] > 1) { for (int i = 0; i <= 2; i++) { double x = A[i]; double y = A[i == 0 ? 1 : 0]; double z = A[i == 2 ? 1 : 2]; if (A[i] > 1) { double a[5] = {0}; a[1] = log(log(x)) + log(y) * z; a[2] = log(log(x)) + log(z) * y; a[3] = log(log(x)) + log(y) + log(z); for (int j = 1; j <= 3; j++) { if (a[j] > ans + EPS) { ans = a[j]; ansid = j + i * 4; } } } } } else if (A[id[2]] == 1) { for (int i = 0; i <= 2; i++) { if (A[i] == 1) { ans = 1; ansid = 1 + i * 4; break; } } } else { for (int i = 0; i <= 2; i++) { double x = A[i]; double y = A[i == 0 ? 1 : 0]; double z = A[i == 2 ? 1 : 2]; double a[5]; a[1] = -log(-log(x)) - log(y) * z; a[2] = -log(-log(x)) - log(z) * y; a[3] = -log(-log(x)) - log(y) - log(z); for (int j = 1; j <= 3; j++) { if (a[j] > ans + EPS) { ans = a[j]; ansid = j + i * 4; } } } } cout << ansstr[ansid] << endl; return 0; }
#include <bits/stdc++.h> const int inf = 1e9 + 5; const long long linf = 5e18 + 5; const long double eps = 1e-7; const int dd = 2e5 + 7; const int maxn = 2e3 + 10; const long long mod = 1e9 + 7; using namespace std; long double fun(vector<long double> qwe, int k) { long double x = qwe[0]; long double y = qwe[1]; long double z = qwe[2]; long double ans = 0; if (k == 0) { ans = log(x) * pow(y, z); } if (k == 1) { ans = log(x) * pow(z, y); } if (k == 2) { ans = log(x) * y * z; } if (k == 3) { ans = log(x) * y * z; } if (k == 4) { ans = log(y) * pow(x, z); } if (k == 5) { ans = log(y) * pow(z, x); } if (k == 6) { ans = log(y) * x * z; } if (k == 7) { ans = log(y) * x * z; } if (k == 8) { ans = log(z) * pow(x, y); } if (k == 9) { ans = log(z) * pow(y, x); } if (k == 10) { ans = log(z) * x * y; } if (k == 11) { ans = log(z) * x * y; } return ans; } int main() { ios_base::sync_with_stdio(0); if (0) { freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); } else { if (!01) { freopen( "sufpref" ".in", "r", stdin); freopen( "sufpref" ".out", "w", stdout); } } vector<pair<long double, string> > qwe(3); cin >> qwe[0].first >> qwe[1].first >> qwe[2].first; qwe[0].second = "x"; qwe[1].second = "y"; qwe[2].second = "z"; vector<long double> zxc; zxc.push_back(qwe[0].first); zxc.push_back(qwe[1].first); zxc.push_back(qwe[2].first); long double maxx = -linf; int ind = 0; for (long long i = 0; i < 12; ++i) { if (maxx < fun(zxc, i)) maxx = fun(zxc, i), ind = i; } map<int, string> asd; asd[0] = qwe[0].second + "^" + qwe[1].second + "^" + qwe[2].second; asd[1] = qwe[0].second + "^" + qwe[2].second + "^" + qwe[1].second; asd[2] = "(" + qwe[0].second + "^" + qwe[1].second + ")" + "^" + qwe[2].second; asd[3] = "(" + qwe[0].second + "^" + qwe[2].second + ")" + "^" + qwe[1].second; asd[4] = qwe[1].second + "^" + qwe[0].second + "^" + qwe[2].second; asd[5] = qwe[1].second + "^" + qwe[2].second + "^" + qwe[0].second; asd[6] = "(" + qwe[1].second + "^" + qwe[0].second + ")" + "^" + qwe[2].second; asd[7] = "(" + qwe[1].second + "^" + qwe[2].second + ")" + "^" + qwe[0].second; asd[8] = qwe[2].second + "^" + qwe[0].second + "^" + qwe[1].second; asd[9] = qwe[2].second + "^" + qwe[1].second + "^" + qwe[0].second; asd[10] = "(" + qwe[2].second + "^" + qwe[0].second + ")" + "^" + qwe[1].second; asd[11] = "(" + qwe[2].second + "^" + qwe[1].second + ")" + "^" + qwe[0].second; cout << asd[ind]; return 0; }
#include <bits/stdc++.h> using namespace std; string v[12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; pair<long double, long double> sol[12]; const long double EPS = 1e-12; long double cmp(pair<long double, long double> a, pair<long double, long double> b) { long double res1, res2; res1 = a.second * log(a.first); res2 = b.second * log(b.first); if (abs(res1 - res2) < EPS) return 0; return res1 - res2; } int main() { int i, pos; long double x, y, z; cin >> x >> y >> z; sol[0] = {x, pow(y, z)}; sol[1] = {x, pow(z, y)}; sol[2] = {x, y * z}; sol[3] = {x, z * y}; sol[4] = {y, pow(x, z)}; sol[5] = {y, pow(z, x)}; sol[6] = {y, x * z}; sol[6] = {y, z * x}; sol[8] = {z, pow(x, y)}; sol[9] = {z, pow(y, x)}; sol[10] = {z, x * y}; sol[11] = {z, y * x}; pos = 0; for (i = 1; i < 12; ++i) { if (cmp(sol[pos], sol[i]) < 0) pos = i; } cout << v[pos]; return 0; }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(0); long double x, y, z, a[13], mx; string s[13] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int ind = 0; cin >> x >> y >> z; a[0] = pow(y, z) * log(x); mx = a[0]; a[1] = pow(z, y) * log(x); a[2] = z * y * log(x); a[3] = z * y * log(x); a[4] = pow(x, z) * log(y); a[5] = pow(z, x) * log(y); a[6] = z * x * log(y); a[7] = z * x * log(y); a[8] = pow(x, y) * log(z); a[9] = pow(y, x) * log(z); a[10] = y * x * log(z); a[11] = y * x * log(z); for (int i = 0; i < 12; i++) { if (mx + 1e-15 < a[i]) { mx = a[i]; ind = i; } } cout << s[ind] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; bool bigger(complex<long double> a, complex<long double> b) { if (imag(a) == 0 && imag(b) == 0) { return real(a) > real(b); } else if (imag(a) == 0 && imag(b) != 0) { return true; } else if (imag(a) != 0 && imag(b) == 0) { return false; } else if (imag(a) != 0 && imag(b) != 0) { return real(a) < real(b); } } int main() { long double ax, ay, az; cin >> ax >> ay >> az; complex<long double> x(ax, 0.0L); complex<long double> y(ay, 0.0L); complex<long double> z(az, 0.0L); complex<long double> cmaz(3, 3); string ans = "xd"; if (bigger(z * log(y) + log(log(x)), cmaz)) { cmaz = z * log(y) + log(log(x)); ans = "x^y^z"; } if (bigger(y * log(z) + log(log(x)), cmaz)) { cmaz = y * log(z) + log(log(x)); ans = "x^z^y"; } if (bigger(log(y * z) + log(log(x)), cmaz)) { cmaz = log(y * z) + log(log(x)); ans = "(x^y)^z"; } if (bigger(z * log(x) + log(log(y)), cmaz)) { cmaz = z * log(x) + log(log(y)); ans = "y^x^z"; } if (bigger(x * log(z) + log(log(y)), cmaz)) { cmaz = x * log(z) + log(log(y)); ans = "y^z^x"; } if (bigger(log(x * z) + log(log(y)), cmaz)) { cmaz = log(x * z) + log(log(y)); ans = "(y^x)^z"; } if (bigger(y * log(x) + log(log(z)), cmaz)) { cmaz = y * log(x) + log(log(z)); ans = "z^x^y"; } if (bigger(x * log(y) + log(log(z)), cmaz)) { cmaz = x * log(y) + log(log(z)); ans = "z^y^x"; } if (bigger(log(x * y) + log(log(z)), cmaz)) { cmaz = log(x * y) + log(log(z)); ans = "(z^x)^y"; } cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; const double inf = 100000000000000000; const int MOD = 1e9 + 7; const int maxn = 1e6 + 10; const int maxv = 1e3 + 10; const double eps = 1e-9; int ju = 0; double f22(double a, double b) { if (ju) a = 1.0 / a; if (a > 1.0 - eps) return log(log(a)) + log(b); return -inf; } double f33(double a, double b, double c) { if (ju) a = 1.0 / a; if (a > 1.0 - eps) return log(log(a)) + c * log(b); return -inf; } double f1(double a, double b, double c) { return f33(a, b, c); } double f2(double a, double b, double c) { return f33(a, c, b); } double f3(double a, double b, double c) { return f22(a, b * c); } double f4(double a, double b, double c) { return f22(a, b * c); } double f5(double a, double b, double c) { return f33(b, a, c); } double f6(double a, double b, double c) { return f33(b, c, a); } double f7(double a, double b, double c) { return f22(b, a * c); } double f8(double a, double b, double c) { return f22(b, a * c); } double f9(double a, double b, double c) { return f33(c, a, b); } double f10(double a, double b, double c) { return f33(c, b, a); } double f11(double a, double b, double c) { return f22(c, a * b); } double f12(double a, double b, double c) { return f22(c, a * b); } bool judge(double l, double r, int ju) { if (ju) return l > r + eps; return l < r - eps; } int main() { double x, y, c; while (scanf("%lf%lf%lf", &x, &y, &c) != EOF) { ju = 0; if (x < 1.0 + eps && y < 1.0 + eps && c < 1.0 + eps) { ju = 1; } double res = 0; int id = 0; res = f1(x, y, c); id = 1; if (judge(res, f2(x, y, c), ju)) { res = f2(x, y, c); id = 2; } if (judge(res, f3(x, y, c), ju)) { res = f3(x, y, c); id = 3; } if (judge(res, f4(x, y, c), ju)) { res = f4(x, y, c); id = 4; } if (judge(res, f5(x, y, c), ju)) { res = f5(x, y, c); id = 5; } if (judge(res, f6(x, y, c), ju)) { res = f6(x, y, c); id = 6; } if (judge(res, f7(x, y, c), ju)) { res = f7(x, y, c); id = 7; } if (judge(res, f8(x, y, c), ju)) { res = f8(x, y, c); id = 8; } if (judge(res, f9(x, y, c), ju)) { res = f9(x, y, c); id = 9; } if (judge(res, f10(x, y, c), ju)) { res = f10(x, y, c); id = 10; } if (judge(res, f11(x, y, c), ju)) { res = f11(x, y, c); id = 11; } if (judge(res, f12(x, y, c), ju)) { res = f12(x, y, c); id = 12; } if (id == 1) puts("x^y^z"); else if (id == 2) puts("x^z^y"); else if (id == 3) puts("(x^y)^z"); else if (id == 4) puts("(x^z)^y"); else if (id == 5) puts("y^x^z"); else if (id == 6) puts("y^z^x"); else if (id == 7) puts("(y^x)^z"); else if (id == 8) puts("(y^z)^x"); else if (id == 9) puts("z^x^y"); else if (id == 10) puts("z^y^x"); else if (id == 11) puts("(z^x)^y"); else puts("(z^y)^x"); } return 0; }
#include <bits/stdc++.h> using namespace std; bool compare(complex<long double> a, complex<long double> b) { if (imag(a) == 0 and imag(b) == 0) return real(a) > real(b); else if (imag(a) == 0 and imag(b) != 0) return true; else if (imag(a) != 0 and imag(b) == 0) return false; else if (imag(a) != 0 and imag(b) != 0) return real(a) < real(b); } complex<long double> eval(string exp, complex<long double>* inp) { if (exp.size() == 5) { complex<long double> x = inp[exp[0] - 'x'], y = inp[exp[2] - 'x'], z = inp[exp[4] - 'x']; return z * log(y) + log(log(x)); } else { complex<long double> x = inp[exp[1] - 'x'], y = inp[exp[3] - 'x'], z = inp[exp[6] - 'x']; return log(y * z) + log(log(x)); } } int main() { long double x1, y1, z1; cin >> x1 >> y1 >> z1; string exp[9] = {"x^y^z", "x^z^y", "(x^y)^z", "y^x^z", "y^z^x", "(y^x)^z", "z^x^y", "z^y^x", "(z^x)^y"}; int ans = -1; complex<long double> temp; complex<long double> inp[3] = {complex<long double>(x1, 0), complex<long double>(y1, 0), complex<long double>(z1, 0)}; for (int i = 0; i < 9; i++) { if (ans == -1) { temp = eval(exp[i], inp); ans = i; } else if (compare(eval(exp[i], inp), temp)) { temp = eval(exp[i], inp); ans = i; } } cout << exp[ans] << endl; }
#include <bits/stdc++.h> using namespace std; const int mod = 1e9 + 7; double eps = 1e-12; int idx(-1); double m(-1e18), cur; double a, b, c, xy, yz, zx, yx, zy, xz; void f1() { cur = yz + log(a); if (cur > m + eps) { m = cur; idx = 0; } cur = zy + log(a); if (cur > m + eps) { m = cur; idx = 1; } cur = c + log(xy); if (cur > m + eps) { m = cur; idx = 2; } cur = b + log(xz); if (cur > m + eps) { m = cur; idx = 3; } } void f2() { cur = xz + log(b); if (cur > m + eps) { m = cur; idx = 4; } cur = zx + log(b); if (cur > m + eps) { m = cur; idx = 5; } cur = c + log(yx); if (cur > m + eps) { m = cur; idx = 6; } cur = a + log(yz); if (cur > m + eps) { m = cur; idx = 7; } } void f3() { cur = xy + log(c); if (cur > m + eps) { m = cur; idx = 8; } cur = yx + log(c); if (cur > m + eps) { m = cur; idx = 9; } cur = b + log(zx); if (cur > m + eps) { m = cur; idx = 10; } cur = a + log(zy); if (cur > m + eps) { m = cur; idx = 11; } } int main() { string s[12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; double x, y, z; cin >> x >> y >> z; a = log(x), b = log(y), c = log(z); xy = y * log(x), yz = z * log(y), zx = x * log(z); yx = x * log(y), zy = y * log(z), xz = z * log(x); if (x > 1.05 && y > 1.05 && z > 1.05) f1(), f2(), f3(); else if (x > 1.05 && y > 1.05) f1(), f2(); else if (y > 1.05 && z > 1.05) f2(), f3(); else if (x > 1.05 && z > 1.05) f1(), f3(); else if (x > 1.05) f1(); else if (y > 1.05) f2(); else if (z > 1.05) f3(); else { cur = pow(x, pow(y, z)); if (cur > m + eps) { m = cur; idx = 0; } cur = pow(x, pow(z, y)); if (cur > m + eps) { m = cur; idx = 1; } cur = pow(pow(x, y), z); if (cur > m + eps) { m = cur; idx = 2; } cur = pow(pow(x, z), y); if (cur > m + eps) { m = cur; idx = 3; } cur = pow(y, pow(x, z)); if (cur > m + eps) { m = cur; idx = 4; } cur = pow(y, pow(z, x)); if (cur > m + eps) { m = cur; idx = 5; } cur = pow(pow(y, x), z); if (cur > m + eps) { m = cur; idx = 6; } cur = pow(pow(y, z), x); if (cur > m + eps) { m = cur; idx = 7; } cur = pow(z, pow(x, y)); if (cur > m + eps) { m = cur; idx = 8; } cur = pow(z, pow(y, x)); if (cur > m + eps) { m = cur; idx = 9; } cur = pow(pow(z, x), y); if (cur > m + eps) { m = cur; idx = 10; } cur = pow(pow(z, y), x); if (cur > m + eps) { m = cur; idx = 11; } } cout << s[idx]; return 0; }
#include <bits/stdc++.h> using namespace std; using PII = pair<int, int>; using LD = long double; vector<string> rasp = {"x^y^z", "x^z^y", "(x^y)^z", "y^x^z", "y^z^x", "(y^x)^z", "z^x^y", "z^y^x", "(z^x)^y"}; LD answer = -2, x, y, z; string str; void ch(LD &ret1, LD &toCh, string C) { if (ret1 - toCh > 0.0001) toCh = ret1, str = C; } void solve(LD x, LD y, LD z, int code) { vector<LD> arr = {log(x) * pow(y, z), log(x) * pow(z, y), log(x) * y * z}; for (auto &cur : arr) ch(cur, answer, rasp[code + (&cur - &arr[0])]); } int main() { cin >> x >> y >> z; solve(x, y, z, 0); solve(y, x, z, 3); solve(z, x, y, 6); cout << str; }
#include <bits/stdc++.h> using namespace std; int main() { string s[12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; long double x, y, z, a[12], mx; int i, k; cin >> x >> y >> z; a[0] = pow(y, z) * log(x); a[1] = pow(z, y) * log(x); a[2] = a[3] = z * y * log(x); a[4] = pow(x, z) * log(y); a[5] = pow(z, x) * log(y); a[6] = a[7] = x * z * log(y); a[8] = pow(x, y) * log(z); a[9] = pow(y, x) * log(z); a[10] = a[11] = x * y * log(z); mx = a[0]; k = 0; for (i = 1; i < 12; i++) if (a[i] > mx) { mx = a[i]; k = i; } cout << s[k] << endl; }
#include <bits/stdc++.h> using namespace std; double x, y, z; string b[15]; void Pre() { b[1] = "x^y^z"; b[2] = "x^z^y"; b[3] = "(x^y)^z"; b[4] = "(x^z)^y"; b[5] = "y^x^z"; b[6] = "y^z^x"; b[7] = "(y^x)^z"; b[8] = "(y^z)^x"; b[9] = "z^x^y"; b[10] = "z^y^x"; b[11] = "(z^x)^y"; b[12] = "(z^y)^x"; } void solve() { vector<pair<double, int> > res; if (x < 1 && y < 1 && z < 1) { res.push_back(make_pair(pow(y, z) * log(x), 1)); res.push_back(make_pair(pow(z, y) * log(x), 2)); res.push_back(make_pair(y * z * log(x), 3)); res.push_back(make_pair(y * z * log(x), 4)); res.push_back(make_pair(pow(x, z) * log(y), 5)); res.push_back(make_pair(pow(z, x) * log(y), 6)); res.push_back(make_pair(x * z * log(y), 7)); res.push_back(make_pair(x * z * log(y), 8)); res.push_back(make_pair(pow(x, y) * log(z), 9)); res.push_back(make_pair(pow(y, x) * log(z), 10)); res.push_back(make_pair(y * x * log(z), 11)); res.push_back(make_pair(y * x * log(z), 12)); } else { if (x >= 1) res.push_back(make_pair(z * log(y) + log(log(x)), 1)); if (x >= 1) res.push_back(make_pair(y * log(z) + log(log(x)), 2)); if (x >= 1) res.push_back(make_pair(log(y) + log(z) + log(log(x)), 3)); if (x >= 1) res.push_back(make_pair(log(y) + log(z) + log(log(x)), 4)); if (y >= 1) res.push_back(make_pair(z * log(x) + log(log(y)), 5)); if (y >= 1) res.push_back(make_pair(x * log(z) + log(log(y)), 6)); if (y >= 1) res.push_back(make_pair(log(x) + log(z) + log(log(y)), 7)); if (y >= 1) res.push_back(make_pair(log(x) + log(z) + log(log(y)), 8)); if (z >= 1) res.push_back(make_pair(y * log(x) + log(log(z)), 9)); if (z >= 1) res.push_back(make_pair(x * log(y) + log(log(z)), 10)); if (z >= 1) res.push_back(make_pair(log(y) + log(x) + log(log(z)), 11)); if (z >= 1) res.push_back(make_pair(log(y) + log(x) + log(log(z)), 12)); } sort(res.begin(), res.end()); int id = res[res.size() - 1].second; double maxx = res[res.size() - 1].first; for (int i = 0; i < res.size(); i++) { if (res[i].first == maxx) { id = min(id, res[i].second); } } printf("%s\n", b[id].c_str()); } int main() { while (scanf("%lf %lf %lf", &x, &y, &z) != EOF) { Pre(); solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; const int INF = (int)(1e9); const long long INF64 = (long long)(1e18); const long double EPS = 1e-9; const long double PI = 3.1415926535897932384626433832795; int main() { double x, y, z; cin >> x >> y >> z; string arr[13]; arr[1] = "x^y^z"; arr[2] = "x^z^y"; arr[3] = "(x^y)^z"; arr[4] = "(x^z)^y"; arr[5] = "y^x^z"; arr[6] = "y^z^x"; arr[7] = "(y^x)^z"; arr[8] = "(y^z)^x"; arr[9] = "z^x^y"; arr[10] = "z^y^x"; arr[11] = "(z^x)^y"; arr[12] = "(z^y)^x"; if (x > 1 && y > 1 && z > 1) { double res[13]; res[1] = z * log(y) + log(log(x)); res[2] = y * log(z) + log(log(x)); res[3] = log(z) + log(y) + log(log(x)); res[4] = log(y) + log(z) + log(log(x)); res[5] = z * log(x) + log(log(y)); res[6] = x * log(z) + log(log(y)); res[7] = log(z) + log(x) + log(log(y)); res[8] = log(x) + log(z) + log(log(y)); res[9] = y * log(x) + log(log(z)); res[10] = x * log(y) + log(log(z)); res[11] = log(y) + log(x) + log(log(z)); res[12] = log(x) + log(y) + log(log(z)); double ans = -INF64 * 1.0; int pos; for (int i = 1; i <= 12; ++i) { if ((res[i] - ans) > EPS) { ans = res[i]; pos = i; } } cout << arr[pos] << endl; } else if (x <= 1 && y <= 1 && z <= 1) { double res[13]; res[1] = pow(x, pow(y, z)); res[2] = pow(x, pow(z, y)); res[3] = pow(pow(x, y), z); res[4] = pow(pow(x, z), y); res[5] = pow(y, pow(x, z)); res[6] = pow(y, pow(z, x)); res[7] = pow(pow(y, x), z); res[8] = pow(pow(y, z), x); res[9] = pow(z, pow(x, y)); res[10] = pow(z, pow(y, x)); res[11] = pow(pow(z, x), y); res[12] = pow(pow(z, y), x); double ans = -INF64 * 1.0; int pos; for (int i = 1; i <= 12; ++i) { if ((res[i] - ans) > EPS) { pos = i; ans = res[i]; } } cout << arr[pos] << endl; } else { double ans = -INF64; int pos; double res[13]; if (x > 1) { res[1] = z * log(y) + log(log(x)); res[2] = y * log(z) + log(log(x)); res[3] = log(z) + log(y * log(x)); res[4] = log(y) + log(z * log(x)); for (int i = 1; i <= 4; ++i) { if ((res[i] - ans) > EPS) { ans = res[i]; pos = i; } } } if (y > 1) { res[5] = z * log(x) + log(log(y)); res[6] = x * log(z) + log(log(y)); res[7] = log(z) + log(x * log(y)); res[8] = log(x) + log(z * log(y)); for (int i = 5; i <= 8; ++i) { if ((res[i] - ans) > EPS) { ans = res[i]; pos = i; } } } if (z > 1) { res[9] = y * log(x) + log(log(z)); res[10] = x * log(y) + log(log(z)); res[11] = log(y) + log(x * log(z)); res[12] = log(x) + log(y * log(z)); for (int i = 9; i <= 12; ++i) { if ((res[i] - ans) > EPS) { ans = res[i]; pos = i; } } } cout << arr[pos] << endl; } return 0; }
#include <bits/stdc++.h> char *s[9] = {"x^y^z", "x^z^y", "(x^y)^z", "y^x^z", "y^z^x", "(y^x)^z", "z^x^y", "z^y^x", "(z^x)^y"}; double sx, sy, sz; long double x, y, z; std::vector<long double> a; int main() { scanf("%lf%lf%lf", &sx, &sy, &sz); x = sx; y = sy; z = sz; a = {logl(x) * powl(y, z), logl(x) * powl(z, y), logl(x) * y * z, logl(y) * powl(x, z), logl(y) * powl(z, x), logl(y) * x * z, logl(z) * powl(x, y), logl(z) * powl(y, x), logl(z) * x * y}; printf("%s\n", s[max_element(a.begin(), a.end()) - a.begin()]); return 0; }
#include <bits/stdc++.h> int c = 1; double x, y, z, a[20]; char b[20][20]; double lg(double x) { if (x < 0) return -2e9; else return log(x); } int main() { scanf("%lf %lf %lf", &x, &y, &z); strcpy(b[1], "x^y^z"); strcpy(b[2], "x^z^y"); strcpy(b[3], "(x^y)^z"); strcpy(b[4], "(x^z)^y"); strcpy(b[5], "y^x^z"); strcpy(b[6], "y^z^x"); strcpy(b[7], "(y^x)^z"); strcpy(b[8], "(y^z)^x"); strcpy(b[9], "z^x^y"); strcpy(b[10], "z^y^x"); strcpy(b[11], "(z^x)^y"); strcpy(b[12], "(z^y)^x"); if (x <= 1 && y <= 1 && z <= 1) { a[1] = pow(x, pow(y, z)); a[2] = pow(x, pow(z, y)); a[3] = pow(x, y * z); a[4] = pow(x, z * y); a[5] = pow(y, pow(x, z)); a[6] = pow(y, pow(z, x)); a[7] = pow(y, x * z); a[8] = pow(y, z * x); a[9] = pow(z, pow(x, y)); a[10] = pow(z, pow(y, x)); a[11] = pow(z, x * y); a[12] = pow(z, y * x); } else { a[1] = z * lg(y) + lg(lg(x)); a[2] = y * lg(z) + lg(lg(x)); a[3] = lg(y * z) + lg(lg(x)); a[4] = lg(z * y) + lg(lg(x)); a[5] = z * lg(x) + lg(lg(y)); a[6] = x * lg(z) + lg(lg(y)); a[7] = lg(x * z) + lg(lg(y)); a[8] = lg(z * x) + lg(lg(y)); a[9] = y * lg(x) + lg(lg(z)); a[10] = x * lg(y) + lg(lg(z)); a[11] = lg(x * y) + lg(lg(z)); a[12] = lg(y * x) + lg(lg(z)); } for (int i = 2; i <= 12; i++) if (a[i] > a[c]) c = i; printf("%s\n", b[c]); scanf("\n"); return 0; }
#include <bits/stdc++.h> using namespace std; const long double eps = 1e-12; long double ans[15]; string Ans[] = {"", "x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int main() { ios_base::sync_with_stdio(false); cin.tie(0); int n; long double aa, bb, cc; cin >> aa >> bb >> cc; long double x = aa, y = bb, z = cc; int i; long double lx = log(x); long double ly = log(y); long double lz = log(z); if (x + eps < 1.0 || y + eps < 1.0 || z + eps < 1.0) { ans[1] = lx * pow(y, z); ans[2] = lx * pow(z, y); ans[3] = lx * y * z; ans[4] = lx * z * y; ans[5] = ly * pow(x, z); ans[6] = ly * pow(z, x); ans[7] = ly * x * z; ans[8] = ly * x * z; ans[9] = lz * pow(x, y); ans[10] = lz * pow(y, x); ans[11] = lz * x * y; ans[12] = lz * x * y; } else { ans[1] = z * log(y) + log(log(x)); ans[2] = y * log(z) + log(log(x)); ans[3] = log(z * y * log(x)); ans[4] = log(z * y * log(x)); ans[5] = z * log(x) + log(log(y)); ans[6] = x * log(z) + log(log(y)); ans[7] = log(x * z * log(y)); ans[8] = log(x * z * log(y)); ans[9] = y * log(x) + log(log(z)); ans[10] = x * log(y) + log(log(z)); ans[11] = log(x * y * log(z)); ans[12] = log(x * y * log(z)); } double k = ans[1]; int si = 1; for (i = 2; i <= 12; i++) if (ans[i] > k + eps) { k = ans[i]; si = i; } cout << Ans[si] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = 1000000007; const int MAX = 10000005; int main() { long double x, y, z, maxvalue, minindex; cin >> x >> y >> z; maxvalue = x * y * log(z); minindex = 11; if (pow(y, x) * log(z) >= maxvalue) { maxvalue = pow(y, x) * log(z); minindex = 10; } if (pow(x, y) * log(z) >= maxvalue) { maxvalue = pow(x, y) * log(z); minindex = 9; } if (x * z * log(y) >= maxvalue) { maxvalue = x * z * log(y); minindex = 7; } if (pow(z, x) * log(y) >= maxvalue) { maxvalue = pow(z, x) * log(y); minindex = 6; } if (pow(x, z) * log(y) >= maxvalue) { maxvalue = pow(x, z) * log(y); minindex = 5; } if (y * z * log(x) >= maxvalue) { maxvalue = y * z * log(x); minindex = 3; } if (pow(z, y) * log(x) >= maxvalue) { maxvalue = pow(z, y) * log(x); minindex = 2; } if (pow(y, z) * log(x) >= maxvalue) { maxvalue = pow(y, z) * log(x); minindex = 1; } if (minindex == 11) cout << "(z^x)^y"; if (minindex == 10) cout << "z^y^x"; if (minindex == 9) cout << "z^x^y"; if (minindex == 7) cout << "(y^x)^z"; if (minindex == 6) cout << "y^z^x"; if (minindex == 5) cout << "y^x^z"; if (minindex == 3) cout << "(x^y)^z"; if (minindex == 2) cout << "x^z^y"; if (minindex == 1) cout << "x^y^z"; return 0; }
#include <bits/stdc++.h> using namespace std; const int inf = 1.01e9; const long double eps = 1e-16; int main() { string best = ""; long double res = -1e300; long double x, y, z; double xx, yy, zz; scanf("%lf%lf%lf", &xx, &yy, &zz); x = xx, y = yy, z = zz; long double val; val = logl(x) * powl(y, z); if (val > res + abs(res) * eps) res = val, best = "x^y^z"; val = logl(x) * powl(z, y); if (val > res + abs(res) * eps) res = val, best = "x^z^y"; val = logl(x) * y * z; if (val > res + abs(res) * eps) res = val, best = "(x^y)^z"; val = logl(y) * powl(x, z); if (val > res + abs(res) * eps) res = val, best = "y^x^z"; val = logl(y) * powl(z, x); if (val > res + abs(res) * eps) res = val, best = "y^z^x"; val = logl(y) * x * z; if (val > res + abs(res) * eps) res = val, best = "(y^x)^z"; val = logl(z) * powl(x, y); if (val > res + abs(res) * eps) res = val, best = "z^x^y"; val = logl(z) * powl(y, x); if (val > res + abs(res) * eps) res = val, best = "z^y^x"; val = logl(z) * x * y; if (val > res + abs(res) * eps) res = val, best = "(z^x)^y"; printf("%s\n", best.data()); return 0; }
#include <bits/stdc++.h> using namespace std; bool mm[14]; long double a[14]; int main() { long double x, y, z, mx = -1e20; cin >> x >> y >> z; int ans = 0; { a[1] = z * log(y) + log(abs(log(x))); if (log(x) < 0) mm[1] = 1; } { a[2] = y * log(z) + log(abs(log(x))); if (log(x) < 0) mm[2] = 1; } { a[3] = log(y * z * abs(log(x))); if (y * z * log(x) < 0) mm[3] = 1; } { a[5] = z * log(x) + log(abs(log(y))); if (log(y) < 0) mm[5] = 1; } { a[6] = x * log(z) + log(abs(log(y))); if (log(y) < 0) mm[6] = 1; } { a[7] = log(x * z * abs(log(y))); if (x * z * log(y) < 0) mm[7] = 1; } { a[9] = y * log(x) + log(abs(log(z))); if (log(z) < 0) mm[9] = 1; } { a[10] = x * log(y) + log(abs(log(z))); if (log(z) < 0) mm[10] = 1; } { a[11] = log(x * y * abs(log(z))); if (x * y * log(z) < 0) mm[11] = 1; } for (int i = 1; i <= 12; ++i) { if (i % 4 == 0) continue; if (mm[i]) continue; if (a[i] - 1e-8 > mx) { mx = a[i]; ans = i; } } if (!ans) { mx = 1e20; for (int i = 1; i <= 12; ++i) { if (i % 4 == 0) continue; if (a[i] + 1e-8 < mx) { mx = a[i]; ans = i; } } } switch (ans) { case 1: cout << "x^y^z" << endl; break; ; case 2: cout << "x^z^y" << endl; break; ; case 3: cout << "(x^y)^z" << endl; break; ; case 5: cout << "y^x^z" << endl; break; ; case 6: cout << "y^z^x" << endl; break; ; case 7: cout << "(y^x)^z" << endl; break; ; case 9: cout << "z^x^y" << endl; break; ; case 10: cout << "z^y^x" << endl; break; ; case 11: cout << "(z^x)^y" << endl; break; ; } }
#include <bits/stdc++.h> using namespace std; const int Maxn = 100010; const long double eps = 1e-10; long double a[Maxn], b[Maxn]; long double x, y, z; const char* result[12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int main() { cin >> x >> y >> z; a[0] = z * log(y); a[1] = y * log(z); a[2] = a[3] = log(y) + log(z); a[4] = z * log(x); a[5] = x * log(z); a[6] = a[7] = log(x) + log(z); a[8] = y * log(x); a[9] = x * log(y); a[10] = a[11] = log(x) + log(y); b[0] = b[1] = b[2] = b[3] = log(x); b[4] = b[5] = b[6] = b[7] = log(y); b[8] = b[9] = b[10] = b[11] = log(z); bool flag = false; for (int i = 0; i < 12; i++) flag |= (b[i] > 0); if (flag) { int pos = 0; for (int i = 0; i < 12; i++) if (b[i] > 0) { pos = i; break; } for (int i = 0; i < 12; i++) if (b[i] > 0) { if (a[i] + log(b[i]) > a[pos] + log(b[pos]) + eps) pos = i; } printf("%s\n", result[pos]); } else { int pos = 0; for (int i = 0; i < 12; i++) b[i] *= -1.0; for (int i = 0; i < 12; i++) { if (a[i] + log(b[i]) + eps < a[pos] + log(b[pos])) pos = i; } printf("%s\n", result[pos]); } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long double x, y, z, res = -1.0; string str; cin >> x >> y >> z; if (pow(y, z) * log10(x) > res) { str = "x^y^z"; res = pow(y, z) * log10(x); } if (pow(z, y) * log10(x) > res) { str = "x^z^y"; res = pow(z, y) * log10(x); } if (pow(x, z) * log10(y) > res) { str = "y^x^z"; res = pow(x, z) * log10(y); } if (pow(z, x) * log10(y) > res) { str = "y^z^x"; res = pow(z, x) * log10(y); } if (pow(x, y) * log10(z) > res) { str = "z^x^y"; res = pow(x, y) * log10(z); } if (pow(y, x) * log10(z) > res) { str = "z^y^x"; res = pow(y, x) * log10(z); } if (y * z * log10(x) > res) { str = "(x^y)^z"; res = y * z * log10(x); } if (x * z * log10(y) > res) { str = "(y^x)^z"; res = x * z * log10(y); } if (y * x * log10(z) > res) { str = "(z^x)^y"; } cout << str << endl; return 0; }
#include <bits/stdc++.h> using namespace std; void sc(int& a) { scanf("%d", &a); } void sc(long long int& a) { scanf("%lld", &a); } void sc(int& a, int& b) { sc(a); sc(b); } void sc(long long int& a, long long int& b) { sc(a); sc(b); } void sc(int& a, int& b, int& c) { sc(a, b); sc(c); } void sc(long long int& a, long long int& b, long long int& c) { sc(a, b); sc(c); } void prl(int a) { printf("%d\n", a); } void prl(long long int a) { printf("%lld\n", a); } void prl() { printf("\n"); } void prs(int a) { printf("%d ", a); } void prs(long long int a) { printf("%lld ", a); } void prl(long long int a, long long int b, long long int c = -1, long long int d = -1, long long int e = -1, long long int f = -1) { cout << a << " " << b << " " << c << " " << d << " " << e << " " << f << endl; } int mod = 1000000007; long long int modpow(long long int a, long long int b, long long int mod) { long long int res = 1; while (b > 0) { if (b & 1) res = (res * a) % mod; a = (a * a) % mod; b = b / 2; } return res % mod; } long long int pow(long long int a, long long int b) { long long int res = 1; while (b > 0) { if (b & 1) res = (res * a); a = (a * a); b = b / 2; } return res; } bool comp(pair<double, int> x, pair<double, int> y) { if (x.first != y.first) return x.first > y.first; return x.second < y.second; } map<int, string> mp; int main() { mp[1] = "x^y^z"; mp[2] = "x^z^y"; mp[3] = "(x^y)^z"; mp[4] = "(x^z)^y"; mp[5] = "y^x^z"; mp[6] = "y^z^x"; mp[7] = "(y^x)^z"; mp[8] = "(y^z)^x"; mp[9] = "z^x^y"; mp[10] = "z^y^x"; mp[11] = "(z^x)^y"; mp[12] = "(z^y)^x"; double x, y, z; cin >> x >> y >> z; int ans = 0; vector<pair<double, int> > t; if (x <= 1 and y <= 1 and z <= 1) { t.push_back(make_pair(pow(x, pow(y, z)), 1)); t.push_back(make_pair(pow(x, pow(z, y)), 2)); t.push_back(make_pair(pow(x, y * z), 3)); t.push_back(make_pair(pow(y, pow(x, z)), 5)); t.push_back(make_pair(pow(y, pow(z, x)), 6)); t.push_back(make_pair(pow(y, x * z), 7)); t.push_back(make_pair(pow(z, pow(x, y)), 9)); t.push_back(make_pair(pow(z, pow(y, x)), 10)); t.push_back(make_pair(pow(z, x * y), 11)); } else { double logx = log(x), logy = log(y), logz = log(z); if (x > 1) { t.push_back(make_pair(z * logy + log(logx), 1)); t.push_back(make_pair(y * logz + log(logx), 2)); t.push_back(make_pair(log(y * z * logx), 3)); } if (y > 1) { t.push_back(make_pair(z * logx + log(logy), 5)); t.push_back(make_pair(x * logz + log(logy), 6)); t.push_back(make_pair(log(x * z * logy), 7)); } if (z > 1) { t.push_back(make_pair(y * logx + log(logz), 9)); t.push_back(make_pair(x * logy + log(logz), 10)); t.push_back(make_pair(log(x * y * logz), 11)); } } sort(t.begin(), t.end(), comp); ans = t[0].second; cout << mp[ans] << endl; return 0; }
#include <bits/stdc++.h> #pragma comment(linker, "/STACK:66777216") using namespace std; const double eps = 1e-7; const double pi = acos(-1.0); const long long INF = (long long)2e9 + 1; const long long LINF = (long long)8e18; const long long inf = (long long)2e9 + 1; const long long linf = (long long)8e18; const long long MM = (long long)1e9 + 7; int solve(); void gen(); int main() { solve(); return 0; } string s[12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int solve() { long double x, y, z; cin >> x >> y >> z; vector<long double> a(12); a[0] = pow(y, z) * log(x); a[1] = pow(z, y) * log(x); a[2] = y * z * log(x); a[3] = a[2]; a[4] = pow(x, z) * log(y); a[5] = pow(z, x) * log(y); a[6] = z * x * log(y); a[7] = a[6]; a[8] = pow(x, y) * log(z); a[9] = pow(y, x) * log(z); a[10] = x * y * log(z); a[11] = a[10]; long double maxi = a[0]; for (int i = 0; i < 12; ++i) { if (abs(a[i] - maxi) > eps) { maxi = max(maxi, a[i]); } } int ans = 0; for (int i = 0; i < (int)12; i++) { if (abs(a[i] - maxi) < eps) { ans = i; break; } } cout << s[ans]; return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long double x, y, z; cin >> x >> y >> z; long double res = log(x) * pow(y, z); int out = 1; if (log(x) * pow(z, y) > res) out = 2, res = log(x) * pow(z, y); if (log(x) * z * y > res) out = 3, res = log(x) * z * y; if (log(y) * pow(x, z) > res) out = 5, res = log(y) * pow(x, z); if (log(y) * pow(z, x) > res) out = 6, res = log(y) * pow(z, x); if (log(y) * x * z > res) out = 7, res = log(y) * x * z; if (log(z) * pow(x, y) > res) out = 9, res = log(z) * pow(x, y); if (log(z) * pow(y, x) > res) out = 10, res = log(z) * pow(y, x); if (log(z) * x * y > res) out = 11; if (out == 1) puts("x^y^z"); if (out == 2) puts("x^z^y"); if (out == 3) puts("(x^y)^z"); if (out == 5) puts("y^x^z"); if (out == 6) puts("y^z^x"); if (out == 7) puts("(y^x)^z"); if (out == 9) puts("z^x^y"); if (out == 10) puts("z^y^x"); if (out == 11) puts("(z^x)^y"); }
#include <bits/stdc++.h> using namespace std; long double x, y, z; string ans = "x^y^z"; int main() { cin >> x >> y >> z; long double res = log(x) * pow(y, z); long double res1 = log(x) * pow(z, y); if (res1 > res) { res = res1; ans = "x^z^y"; } res1 = log(x) * y * z; if (res1 > res) { res = res1; ans = "(x^y)^z"; } res1 = log(y) * pow(x, z); if (res1 > res) { res = res1; ans = "y^x^z"; } res1 = log(y) * pow(z, x); if (res1 > res) { res = res1; ans = "y^z^x"; } res1 = log(y) * x * z; if (res1 > res) { res = res1; ans = "(y^x)^z"; } res1 = log(z) * pow(x, y); if (res1 > res) { res = res1; ans = "z^x^y"; } res1 = log(z) * pow(y, x); if (res1 > res) { res = res1; ans = "z^y^x"; } res1 = log(z) * x * y; if (res1 > res) { res = res1; ans = "(z^x)^y"; } cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; char out[12][15] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; long double a[15]; int main() { double x, y, z; scanf("%lf%lf%lf", &x, &y, &z); long double logx = log(x); long double logy = log(y); long double logz = log(z); a[0] = logx * powl(y, z); a[1] = logx * powl(z, y); a[2] = logx * y * z; a[3] = -1; a[4] = logy * powl(x, z); a[5] = logy * powl(z, x); a[6] = logy * x * z; a[7] = -1; a[8] = logz * powl(x, y); a[9] = logz * powl(y, x); a[10] = logz * x * y; a[11] = -1; long double ans = a[0]; int pos = 0; for (int i = 1; i < 12; i++) { if (!fabs(ans - a[i]) < 1e-8 && a[i] > ans) { ans = a[i]; pos = i; } } printf("%s\n", out[pos]); return 0; }
#include <bits/stdc++.h> std::string ans[12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; const double EPS = 1e-10; long double best; int id; bool better(long double val) { if (fabs(val - best) < EPS) return false; else if (best < val) { best = val; return true; } return false; } void try2(long double x, long double y, long double z, int pos) { long double val = z * y * log(x); if (better(val)) id = pos; } void try1(long double x, long double y, long double z, int pos) { long double val = powl(y, z) * log(x); if (better(val)) id = pos; } int main(void) { long double x, y, z; std::cin >> x >> y >> z; best = -1e12; id = -1; try1(x, y, z, 0); try1(x, z, y, 1); try2(x, y, z, 2); try2(x, z, y, 3); try1(y, x, z, 4); try1(y, z, x, 5); try2(y, x, z, 6); try2(y, z, x, 7); try1(z, x, y, 8); try1(z, y, x, 9); try2(z, x, y, 10); try2(z, y, x, 11); std::cout << ans[id] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; const long double EPS = 1e-9; struct LDBL { long double l; LDBL(long double ll) : l(ll){}; bool operator<(const LDBL& other) const { return l - other.l > EPS; } bool operator==(const LDBL& other) const { return abs(other.l - l) < EPS; } }; string res[] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int main() { long double x, y, z; cin >> x >> y >> z; long double x1, y1, z1; if (x > 5) x1 = 5; else x1 = x; if (y > 5) y1 = 5; else y1 = y; if (z > 5) z1 = 5; else z1 = z; if (x < 0.5) x1 = 0.5; if (y < 0.5) y1 = 0.5; if (z < 0.5) z1 = 0.5; for (int i = (0); i < (int)(100); i++) { while (x > y && !(x1 > y1)) x1 += 0.01; while (x > z && !(x1 > z1)) x1 += 0.01; while (y > x && !(y1 > x1)) y1 += 0.01; while (y > z && !(y1 > z1)) y1 += 0.01; while (z > x && !(z1 > x1)) z1 += 0.01; while (z > y && !(z1 > y1)) z1 += 0.01; } pair<LDBL, int> a[] = { {pow(x1, pow(y1, z1)), 0}, {pow(x1, pow(z1, y1)), 1}, {pow(pow(x1, y1), z1), 2}, {pow(pow(x1, z1), y1), 3}, {pow(y1, pow(x1, z1)), 4}, {pow(y1, pow(z1, x1)), 5}, {pow(pow(y1, x1), z1), 6}, {pow(pow(y1, z1), x1), 7}, {pow(z1, pow(x1, y1)), 8}, {pow(z1, pow(y1, x1)), 9}, {pow(pow(z1, x1), y1), 10}, {pow(pow(z1, y1), x1), 11}}; sort(a, a + 12); cout << res[a[0].second] << endl; }
#include <bits/stdc++.h> using namespace std; pair<int, long double> loglog(long double x) { if (x >= 1) return {1, log(log(x))}; else return {0, log(abs(log(x)))}; } int main() { long double x, y, z; cin >> x >> y >> z; vector<tuple<int, long double, int, string>> vec; vec.emplace_back(x >= 1, log(abs(log(x))) + log(y) * z, 8, "x^y^z"); vec.emplace_back(x >= 1, log(abs(log(x))) + log(z) * y, 7, "x^z^y"); vec.emplace_back(x >= 1, log(abs(log(x))) + log(y) + log(z), 6, "(x^y)^z"); vec.emplace_back(y >= 1, log(abs(log(y))) + log(x) * z, 5, "y^x^z"); vec.emplace_back(y >= 1, log(abs(log(y))) + log(z) * x, 4, "y^z^x"); vec.emplace_back(y >= 1, log(abs(log(y))) + log(x) + log(z), 3, "(y^x)^z"); vec.emplace_back(z >= 1, log(abs(log(z))) + log(x) * y, 2, "z^x^y"); vec.emplace_back(z >= 1, log(abs(log(z))) + log(y) * x, 1, "z^y^x"); vec.emplace_back(z >= 1, log(abs(log(z))) + log(x) + log(y), 0, "(z^x)^y"); for (auto &p : vec) if (get<0>(p) == 0) get<1>(p) *= -1; sort((vec).begin(), (vec).end()); cout << get<3>(vec.back()) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const double pi = acos(-1.0); const double eps = 1e-12; inline int sgn(long double u) { if (u > eps) return 1; else if (u < -eps) return -1; else return 0; } long double x, y, z; long double a[12]; string ans[12]; pair<long double, int> u[12]; int main() { while (cin >> x >> y >> z) { ans[0] = "x^y^z"; ans[1] = "x^z^y"; ans[2] = "(x^y)^z"; ans[3] = "(x^z)^y"; ans[4] = "y^x^z"; ans[5] = "y^z^x"; ans[6] = "(y^x)^z"; ans[7] = "(y^z)^x"; ans[8] = "z^x^y"; ans[9] = "z^y^x"; ans[10] = "(z^x)^y"; ans[11] = "(z^y)^x"; a[0] = exp(z * log(y)) * log(x); a[1] = exp(y * log(z)) * log(x); a[2] = y * z * log(x); a[3] = y * z * log(x); a[4] = exp(z * log(x)) * log(y); a[5] = exp(x * log(z)) * log(y); a[6] = x * z * log(y); a[7] = x * z * log(y); a[8] = exp(y * log(x)) * log(z); a[9] = exp(x * log(y)) * log(z); a[10] = x * y * log(z); a[11] = x * y * log(z); for (int i = 0; i < 12; i++) { u[i].first = -a[i]; u[i].second = i; } sort(u, u + 12); cout << ans[u[0].second] << endl; } return 0; }
#include <bits/stdc++.h> inline int cmp(double x, double y = 0, double tol = 1e-7) { return (x <= y + tol) ? (x + tol < y) ? -1 : 0 : 1; } using namespace std; inline long long gcd(long long a, long long b) { return (b ? gcd(b, a % b) : a); } inline long long lcm(long long a, long long b) { return (a / gcd(a, b)) * b; } const int MAXN = 300005; long double a(long double x, long double y, long double z) { long double aux = 1; for (int i = 0; i < (int)z; i++) { aux *= y; } aux *= (pow(y, z - (int)z)); return aux * ((long double)log(x)); } long double b(long double x, long double y, long double z) { return y * z * log(x); } string ans[12]; long double v[12]; int main() { long double maior = -10000007, r; double x, y, z; cin >> x >> y >> z; if (true) { ans[0] = "x^y^z"; ans[1] = "x^z^y"; ans[2] = "y^x^z"; ans[3] = "y^z^x"; ans[4] = "z^x^y"; ans[5] = "z^y^x"; ans[6] = "(x^y)^z"; ans[7] = "(x^z)^y"; ans[8] = "(y^x)^z"; ans[9] = "(y^z)^x"; ans[10] = "(z^x)^y"; ans[11] = "(z^y)^x"; maior = max(maior, v[0] = a(x, y, z)); maior = max(maior, v[1] = a(x, z, y)); maior = max(maior, v[2] = a(y, x, z)); maior = max(maior, v[3] = a(y, z, x)); maior = max(maior, v[4] = a(z, x, y)); maior = max(maior, v[5] = a(z, y, x)); maior = max(maior, v[6] = b(x, y, z)); maior = max(maior, v[7] = b(x, z, y)); maior = max(maior, v[8] = b(y, x, z)); maior = max(maior, v[9] = b(y, z, x)); maior = max(maior, v[10] = b(z, x, y)); maior = max(maior, v[11] = b(z, y, x)); for (int i = 0; i < 12; i++) { } for (int i = 0; i < 12; i++) { if (v[i] == maior) { cout << ans[i] << endl; break; } } return 0; } }
#include <bits/stdc++.h> using namespace std; const long double eps = 0.00000001; struct Number { long double x, y, z; Number() {} Number(long double x, long double y, long double z) { this->x = x; this->y = y; this->z = z; } }; bool cmp(Number A, Number B) { if (A.x == 1) { if (B.x < 1) return true; return false; } if (B.x == 1) { if (A.x < 1) return false; return true; } if (A.x < 3 && A.y < 3 && A.z < 3) { return (pow(A.x, pow(A.y, A.z)) - eps > pow(B.x, pow(B.y, B.z))); } A.x = log(A.x); B.x = log(B.x); if (A.x > eps && B.x < -eps) return true; if (A.x < -eps && B.x > eps) return false; bool inv = false; if (A.x < -eps && B.x < -eps) A.x *= -1, B.x *= -1, inv = true; if (A.x > -eps && A.x < eps) A.x = eps / 100; if (B.x > -eps && B.x < eps) B.x = eps / 100; long double a = log(A.x) + log(A.y) * A.z; long double b = log(B.x) + log(B.y) * B.z; if (abs(a - b) < eps) return false; return ((a > b) ^ inv); } Number a[12]; string ans[12]; void init(long double x, long double y, long double z) { a[0] = Number(x, y, z); ans[0] = "x^y^z"; a[1] = Number(x, z, y); ans[1] = "x^z^y"; a[2] = Number(x, y * z, 1); ans[2] = "(x^y)^z"; a[4] = Number(y, x, z); ans[4] = "y^x^z"; a[5] = Number(y, z, x); ans[5] = "y^z^x"; a[6] = Number(y, x * z, 1); ans[6] = "(y^x)^z"; a[8] = Number(z, x, y); ans[8] = "z^x^y"; a[9] = Number(z, y, x); ans[9] = "z^y^x"; a[10] = Number(z, x * y, 1); ans[10] = "(z^x)^y"; } int main() { long double x, y, z; cin >> x >> y >> z; init(x, y, z); int bestInd = 0; for (int i = 1; i < 12; i++) { if (i == 3 || i == 7 || i == 11) continue; if (a[i].x == 1 && a[bestInd].x > 1) continue; if (cmp(a[i], a[bestInd]) == true) bestInd = i; } cout << ans[bestInd] << '\n'; }
#include <bits/stdc++.h> using namespace std; char print[13][10] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; long double a[20]; int main() { long double x, y, z; while (cin >> x >> y >> z) { long double x1 = log(x); long double y1 = log(y); long double z1 = log(z); a[0] = x1 * pow(y, z); a[1] = x1 * pow(z, y); a[2] = a[3] = x1 * y * z; a[4] = y1 * pow(x, z); a[5] = y1 * pow(z, x); a[6] = a[7] = y1 * x * z; a[8] = z1 * pow(x, y); a[9] = z1 * pow(y, x); a[10] = a[11] = z1 * x * y; long double Max = -1; int flag; for (int i = 0; i < 12; i++) { if (a[i] > Max) { Max = a[i]; flag = i; } } printf("%s\n", print[flag]); } }
#include <bits/stdc++.h> using namespace std; const long double ESP = 1E-8; long double cal(long double x, long double y, long double z) { return log(x) * pow(y, z); } long double ca(long double x, long double y, long double z) { return y * z * log(x); } int main() { const char* result[12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; long double a[20]; long double x, y, z; cin >> x >> y >> z; a[0] = cal(x, y, z); a[1] = cal(x, z, y); a[2] = ca(x, y, z); a[3] = ca(x, z, y); a[4] = cal(y, x, z); a[5] = cal(y, z, x); a[6] = ca(y, x, z); a[7] = ca(y, z, x); a[8] = cal(z, x, y); a[9] = cal(z, y, x); a[10] = ca(z, x, y); a[11] = ca(z, y, x); long double maxn = a[0]; int res = 0; for (int i = 1; i < 12; ++i) { if (maxn < a[i] - ESP) { maxn = a[i]; res = i; } } printf("%s", result[res]); return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-9; const int inf = 0x3f3f3f3f; const long long INF = (long long)1e18; int sign(long double x) { return x < -eps ? -1 : x > eps; } bool bigger(const complex<long double> &a, const complex<long double> &b) { if (sign(imag(a)) == 0 && sign(imag(b)) == 0) return sign(real(a) - real(b)) > 0; if (sign(imag(a)) == 1 && sign(imag(b)) == 1) return sign(real(a) - real(b)) < 0; return sign(imag(a) - imag(b)) < 0; } complex<long double> x, y, z, maxn; string s = "x^y^z"; int main() { cin >> x >> y >> z; maxn = z * log(y) + log(log(x)); if (bigger(y * log(z) + log(log(x)), maxn)) { maxn = y * log(z) + log(log(x)); s = "x^z^y"; } if (bigger(log(y * z) + log(log(x)), maxn)) { maxn = log(y * z) + log(log(x)); s = "(x^y)^z"; } if (bigger(z * log(x) + log(log(y)), maxn)) { maxn = z * log(x) + log(log(y)); s = "y^x^z"; } if (bigger(x * log(z) + log(log(y)), maxn)) { maxn = x * log(z) + log(log(y)); s = "y^z^x"; } if (bigger(log(x * z) + log(log(y)), maxn)) { maxn = log(x * z) + log(log(y)); s = "(y^x)^z"; } if (bigger(y * log(x) + log(log(z)), maxn)) { maxn = y * log(x) + log(log(z)); s = "z^x^y"; } if (bigger(x * log(y) + log(log(z)), maxn)) { maxn = x * log(y) + log(log(z)); s = "z^y^x"; } if (bigger(log(x * y) + log(log(z)), maxn)) { maxn = log(x * y) + log(log(z)); s = "(z^x)^y"; } cout << s << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long mInv[41]; long long fact[41]; long long factInv[41]; map<long, long> mymap; set<string> dictionary; set<string>::iterator it; pair<set<string>::iterator, bool> ret; long long getmoduloInv(long long n) { if (n == 1) return 1; if (mInv[n] > 0) return mInv[n]; long long m = (-1 * 1000000007) / n; m += 1000000007; m *= getmoduloInv(1000000007 % n); mInv[n] = (m % 1000000007); return mInv[n]; } double getDist(double x1, double y1, double x2, double y2, double x3, double y3) { double dist1 = ((x1 - x3) * (x1 - x3)) + ((y1 - y3) * (y1 - y3)); double dist2 = ((x2 - x3) * (x2 - x3)) + ((y2 - y3) * (y2 - y3)); double dist3 = ((x1 - x2) * (x1 - x2)) + ((y1 - y2) * (y1 - y2)); if (dist3 < 0.00000002) return (dist1 + dist2) / 2; if (dist1 < dist2) return getDist(x1, y1, (x1 + x2) / 2, (y1 + y2) / 2, x3, y3); return getDist(x2, y2, (x1 + x2) / 2, (y1 + y2) / 2, x3, y3); } long long C[100005], N, L, M, D; long long cumCost[100005]; long findPos(long val) { long long pos = 0, total = 0; while (cumCost[pos] <= val) { pos++; } return pos; } long long x[2020], y[2020]; typedef pair<long long, long long> flower; vector<flower> flowers; void printVal(long long v) { if (v < 1) return; long long temp = 1, val = 0; while (temp <= v) { val++; temp = temp << 1; } cout << val << " "; if (temp > v) printVal(v - (temp / 2)); } double vals[13]; void fillVals(double b, double p1, double p2, long startPoint) { if (b < 1.0) vals[startPoint] = vals[startPoint + 1] = vals[startPoint + 2] = 0.0; else { vals[startPoint] = log(log(b)) + p2 * log(p1); vals[startPoint + 1] = log(log(b)) + p1 * log(p2); vals[startPoint + 2] = log(log(b)) + log(p1) + log(p2); } } int main(void) { long long test_cases = 1; cout << setprecision(15) << fixed; long long n; bool found = false; double x, y, z; cin >> x >> y >> z; if (x < 4 && y < 4 && z < 4) { vals[0] = pow(x, (pow(y, z))); vals[1] = pow(x, (pow(z, y))); vals[2] = pow(x, (y * z)); vals[3] = pow(y, (pow(x, z))); vals[4] = pow(y, (pow(z, x))); vals[5] = pow(y, (x * z)); vals[6] = pow(z, (pow(x, y))); vals[7] = pow(z, (pow(y, x))); vals[8] = pow(z, (x * y)); } else { fillVals(x, y, z, 0); fillVals(y, x, z, 3); fillVals(z, x, y, 6); } long minPos = 0; for (long i = 1; i < 9; i++) { if (vals[i] > vals[minPos] + 0.00000002) minPos = i; } if (minPos == 0) cout << "x^y^z" << endl; else if (minPos == 1) cout << "x^z^y" << endl; else if (minPos == 2) cout << "(x^y)^z" << endl; if (minPos == 3) cout << "y^x^z" << endl; else if (minPos == 4) cout << "y^z^x" << endl; else if (minPos == 5) cout << "(y^x)^z" << endl; if (minPos == 6) cout << "z^x^y" << endl; else if (minPos == 7) cout << "z^y^x" << endl; else if (minPos == 8) cout << "(z^x)^y" << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long double EPS = 0.000000001; map<int, long double> fazc; long double calc1(vector<int> &a) { long double retorno = pow(fazc[a[1]], fazc[a[2]]); retorno *= log(fazc[a[0]]); return retorno; } long double calc2(vector<int> &a) { long double retorno = fazc[a[2]] * fazc[a[1]]; retorno *= log(fazc[a[0]]); return retorno; } int main() { long double x, y, z; cin >> x >> y >> z; vector<int> a(3, 0); vector<int> trad(3, 0); a[1] = 1; a[2] = 2; trad[1] = 1; trad[2] = 2; map<int, char> m; m[0] = 'x'; m[1] = 'y'; m[2] = 'z'; fazc[0] = x; fazc[1] = y; fazc[2] = z; bool primeiro = true; long double max1 = calc1(a); for (int i = 0; i < 6; i++) { long double auxi = calc1(a); if (auxi > max1 + EPS) { max1 = auxi; primeiro = true; for (int j = 0; j < 3; j++) trad[j] = a[j]; } next_permutation(a.begin(), a.begin() + 3); } sort(a.begin(), a.end()); long double max2 = calc2(a); vector<int> trad2(3, 0); trad2[1] = 1; trad2[2] = 2; for (int i = 0; i < 6; i++) { long double auxi = calc2(a); auxi = calc2(a); if (auxi > max2 + EPS) { max2 = auxi; primeiro = false; for (int j = 0; j < 3; j++) trad2[j] = a[j]; } next_permutation(a.begin(), a.begin() + 3); } if (abs(max1 - max2) < EPS) { cout << m[trad[0]] << "^" << m[trad[1]] << "^" << m[trad[2]] << endl; return 0; } if (max1 > max2) { cout << m[trad[0]] << "^" << m[trad[1]] << "^" << m[trad[2]] << endl; return 0; } cout << "(" << m[trad2[0]] << "^" << m[trad2[1]] << ")^" << m[trad2[2]] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const long double eps = FLT_MIN, inf = 1e60; long double x, y, z; long double f(int idx) { if (idx == 1) return (x <= 1.) ? -inf : z * log(y) + log(log(x)); if (idx == 2) return (x <= 1.) ? -inf : y * log(z) + log(log(x)); if (idx == 3 || idx == 4) return (x <= 1.) ? -inf : log(z) + log(y) + log(log(x)); if (idx == 5) return (y <= 1.) ? -inf : z * log(x) + log(log(y)); if (idx == 6) return (y <= 1.) ? -inf : x * log(z) + log(log(y)); if (idx == 7 || idx == 8) return (y <= 1.) ? -inf : log(z) + log(x) + log(log(y)); if (idx == 9) return (z <= 1.) ? -inf : y * log(x) + log(log(z)); if (idx == 10) return (z <= 1.) ? -inf : x * log(y) + log(log(z)); if (idx == 11 || idx == 12) return (z <= 1.) ? -inf : log(x) + log(y) + log(log(z)); } long double g(int idx) { if (idx == 1) return pow(x, pow(y, z)); if (idx == 2) return pow(x, pow(z, y)); if (idx == 3 || idx == 4) return pow(x, y * z); if (idx == 5) return pow(y, pow(x, z)); if (idx == 6) return pow(y, pow(z, x)); if (idx == 7 || idx == 8) return pow(y, x * z); if (idx == 9) return pow(z, pow(x, y)); if (idx == 10) return pow(z, pow(y, x)); if (idx == 11 || idx == 12) return pow(z, y * x); } long double t(int idx) { return (x <= 1 && y <= 1 && z <= 1) ? g(idx) : f(idx); } int main() { map<int, string> ans; ans[1] = "x^y^z"; ans[2] = "x^z^y"; ans[3] = "(x^y)^z"; ans[4] = "(x^z)^y"; ans[5] = "y^x^z"; ans[6] = "y^z^x"; ans[7] = "(y^x)^z"; ans[8] = "(y^z)^x"; ans[9] = "z^x^y"; ans[10] = "z^y^x"; ans[11] = "(z^x)^y"; ans[12] = "(z^y)^x"; cin >> x >> y >> z; long double maxi; int idx = -1; for (int i = 1; i <= 12; i++) { fprintf(stderr, "t(%d) = %.10Lf\n", i, t(i)); if (idx == -1 || (t(i) - maxi > eps)) maxi = t(i), idx = i; } cout << ans[idx] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const long double eps = 1e-12; inline bool eq(const long double &x, const long double &y) { return abs(x - y) < eps || abs(x - y) < eps * abs(x); } int main() { ios::sync_with_stdio(false); cin.tie(NULL), cout.tie(NULL); long double x, y, z; cin >> x >> y >> z; long double logx = log(x); long double logy = log(y); long double logz = log(z); long double A[] = {logx * pow(y, z), logx * pow(z, y), logx * y * z, logx * y * z, logy * pow(x, z), logy * pow(z, x), logy * x * z, logy * x * z, logz * pow(x, y), logz * pow(y, x), logz * x * y, logz * x * y}; int ans = 0; long double mx = -1; for (int i = 0; i < 12; i++) { if (!eq(A[i], mx) && A[i] > mx) { mx = A[i]; ans = i; } } string B[] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; cout << B[ans] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; using ull = unsigned long long; using pii = pair<int, int>; using pll = pair<ll, ll>; template <class T> inline bool Min(T &a, T b) { return a > b ? (a = b, true) : false; } template <class T> inline bool Max(T &a, T b) { return a < b ? (a = b, true) : false; } inline int ni() { int a; scanf("%d", &a); return a; } inline ll nl() { ll a; scanf("%lld", &a); return a; } inline double nd() { double a; scanf("%lf", &a); return a; } inline void pi(int a) { printf("%d ", a); } inline void pl(ll a) { printf("%lld ", a); } inline void pd(double a) { printf("%.12lf ", a); } const int N = 1e5 + 10; using ld = long double; void solve() { ld x, y, z; cin >> x >> y >> z; ld ans[10]; ans[1] = log(x) * pow(y, z); ans[2] = log(x) * pow(z, y); ans[3] = log(x) * y * z; ans[4] = log(y) * pow(x, z); ans[5] = log(y) * pow(z, x); ans[6] = log(y) * x * z; ans[7] = log(z) * pow(x, y); ans[8] = log(z) * pow(y, x); ans[9] = log(z) * x * y; ans[0] = ans[1]; int t = 1; for (int i = 1; i <= 9; i++) if (Max(ans[0], ans[i])) t = i; if (t == 1) puts("x^y^z"); if (t == 2) puts("x^z^y"); if (t == 3) puts("(x^y)^z"); if (t == 4) puts("y^x^z"); if (t == 5) puts("y^z^x"); if (t == 6) puts("(y^x)^z"); if (t == 7) puts("z^x^y"); if (t == 8) puts("z^y^x"); if (t == 9) puts("(z^x)^y"); } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const double EPS = 1e-15; double x, y, z, arr[12]; int main() { ios::sync_with_stdio(0); cin >> x >> y >> z; int cnt = (x < 1) + (y < 1) + (z < 1); if (cnt != 3) { if (x > 1) { arr[1] = log(y) * z + log(log(x)); arr[2] = log(z) * y + log(log(x)); arr[3] = log(y) + log(z) + log(log(x)); } else if (x < 1) arr[1] = arr[2] = arr[3] = -1e18; else arr[1] = arr[2] = arr[3] = -1e17; if (y > 1) { arr[4] = log(x) * z + log(log(y)); arr[5] = log(z) * x + log(log(y)); arr[6] = log(x) + log(z) + log(log(y)); } else if (y < 1) arr[4] = arr[5] = arr[6] = -1e18; else arr[4] = arr[5] = arr[6] = -1e17; if (z > 1) { arr[7] = log(x) * y + log(log(z)); arr[8] = log(y) * x + log(log(z)); arr[9] = log(x) + log(y) + log(log(z)); } else if (z < 1) arr[7] = arr[8] = arr[9] = -1e18; else arr[7] = arr[8] = arr[9] = -1e17; } else { arr[1] = -(log(y) * z + log(log(1 / x))); arr[2] = -(log(z) * y + log(log(1 / x))); arr[3] = -(log(y) + log(z) + log(log(1 / x))); arr[4] = -(log(x) * z + log(log(1 / y))); arr[5] = -(log(z) * x + log(log(1 / y))); arr[6] = -(log(x) + log(z) + log(log(1 / y))); arr[7] = -(log(x) * y + log(log(1 / z))); arr[8] = -(log(y) * x + log(log(1 / z))); arr[9] = -(log(x) + log(y) + log(log(1 / z))); } int mx = 1; for (int i = 2; i < 10; ++i) if (arr[i] > arr[mx]) mx = i; if (mx == 1) cout << "x^y^z"; if (mx == 2) cout << "x^z^y"; if (mx == 3) cout << "(x^y)^z"; if (mx == 4) cout << "y^x^z"; if (mx == 5) cout << "y^z^x"; if (mx == 6) cout << "(y^x)^z"; if (mx == 7) cout << "z^x^y"; if (mx == 8) cout << "z^y^x"; if (mx == 9) cout << "(z^x)^y"; return 0; }
#include <bits/stdc++.h> using namespace std; long long gcd(long long x, long long y) { return (y ? gcd(y, x % y) : x); } long long lcm(long long x, long long y) { return x * (y / gcd(x, y)); } long double one(long double x, long double y, long double z) { return pow(y, z) * log(x); } long double two(long double x, long double y, long double z) { return z * y * log(x); } int main() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); vector<long double> x(3); for (int i = 0; i < 3; i++) { int p, d; char aux; cin >> p >> aux >> d; x[i] = (double)(p * 10.0 + d) / 10.0; } int cnt = 0; int ans = -1; long double mx = -1e9; bool f = false; vector<string> a = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; vector<long double> as(12); for (int i = 0; i < 3; i++) { if (i) cnt += 2; for (int j = 0; j < 3; j++) { for (int k = 0; k < 3; k++) { if (i != j && i != k && k != j) { long double o = one(x[i], x[j], x[k]); if (o > mx) mx = o; as[cnt] = o; long double t = two(x[i], x[j], x[k]); if (t > mx) mx = t; as[cnt + 2] = t; cnt++; } } } } for (int i = 0; i < 12; i++) { if (as[i] == mx) { cout << a[i] << endl; return 0; } } return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 10 + 10; const double EPS = 1e-8; long double a[MAXN]; string s[MAXN] = {"", "x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int main() { long double x, y, z; while (cin >> x >> y >> z) { a[1] = pow(y, z) * log(x); a[2] = pow(z, y) * log(x); a[3] = z * y * log(x); a[4] = y * z * log(x); a[5] = pow(x, z) * log(y); a[6] = pow(z, x) * log(y); a[7] = z * x * log(y); a[8] = x * z * log(y); a[9] = pow(x, y) * log(z); a[10] = pow(y, x) * log(z); a[11] = y * x * log(z); a[12] = x * y * log(z); int MaxID = 1; for (int i = 1; i <= 12; ++i) { if (a[i] - a[MaxID] > EPS) MaxID = i; } cout << s[MaxID] << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; long double a[3]; char ch[3] = {'x', 'y', 'z'}; const long double eps = 1e-15; struct Node { int form; int ord[3]; long double x, y, z; Node(int o0, int o1, int o2, int _form) { ord[0] = o0; ord[1] = o1; ord[2] = o2; x = a[o0]; y = a[o1]; z = a[o2]; form = _form; } bool operator<(Node& o) { if (fabs(x - 1) < eps && fabs(o.x - 1) < eps) { return false; } long double logx1 = log(x), logx2 = log(o.x); if (fabs(logx1) < eps) { return logx2 > 0; } if (fabs(logx2) < eps) { return logx1 < 0; } if (logx1 > 0 && logx2 < 0) { return false; } if (logx1 < 0 && logx2 > 0) { return true; } long double k1 = Gao(y, z, form) + log(abs(logx1)), k2 = Gao(o.y, o.z, o.form) + log(abs(logx2)); return logx1 < 0 ? k1 > k2 : k1 < k2; } long double Gao(long double y, long double z, int form) { if (form == 0) { return z * log(y); } else { return log(y) + log(z); } } void Output() { if (form == 0) { cout << ch[ord[0]] << "^" << ch[ord[1]] << "^" << ch[ord[2]] << endl; } else { cout << "(" << ch[ord[0]] << "^" << ch[ord[1]] << ")^" << ch[ord[2]] << endl; } } }; void Update(Node& x, Node y) { if (x < y) { x = y; } } int main() { long double x, y, z; while (cin >> x >> y >> z) { a[0] = x; a[1] = y; a[2] = z; Node maxv = Node(0, 1, 2, 0); Update(maxv, Node(0, 2, 1, 0)); Update(maxv, Node(0, 1, 2, 1)); Update(maxv, Node(1, 0, 2, 0)); Update(maxv, Node(1, 2, 0, 0)); Update(maxv, Node(1, 0, 2, 1)); Update(maxv, Node(2, 0, 1, 0)); Update(maxv, Node(2, 1, 0, 0)); Update(maxv, Node(2, 0, 1, 1)); maxv.Output(); } return 0; }
#include <bits/stdc++.h> using namespace std; vector<string> ve = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; long double x, y, z; void get(char c, long double &a) { if (c == 'x') a = x; if (c == 'y') a = y; if (c == 'z') a = z; } long double calc(string s) { long double a, b, c; get(s.back(), c); s.pop_back(); s.pop_back(); if (s.back() == ')') { s.pop_back(); get(s.back(), b); s.pop_back(); s.pop_back(); get(s.back(), a); return b * c * log(a); } else { get(s.back(), b); s.pop_back(); s.pop_back(); get(s.back(), a); return pow(b, c) * log(a); } } int main() { ios::sync_with_stdio(false), cin.tie(0), cout.tie(0); cin >> x >> y >> z; long double ans = -1; int id = -1; for (int i = 0; i < 12; i++) { long double t = calc(ve[i]); if (t > ans) { ans = t; id = i; } } cout << ve[id] << endl; return 0; }
#include <bits/stdc++.h> const double pi = (double)(2.0 * acos(0.0)); const int inf = 1 << 30; const double eps = 1E-9; const double e = exp(1.0); const int sz = 100000 + 5; const int mod = 1000000000 + 7; using namespace std; int main() { double x, y, z, res, v; string st = ""; scanf("%lf %lf %lf", &x, &y, &z); if (x < 1.0 + eps && y < 1.0 + eps && z < 1.0 + eps) { res = 1e18; v = z * log(y) + log(log(1.0 / x)); if (res > v + eps) res = v, st = "x^y^z"; v = y * log(z) + log(log(1.0 / x)); if (res > v + eps) res = v, st = "x^z^y"; v = log(y) + log(z) + log(log(1.0 / x)); if (res > v + eps) res = v, st = "(x^y)^z"; v = z * log(x) + log(log(1.0 / y)); if (res > v + eps) res = v, st = "y^x^z"; v = x * log(z) + log(log(1.0 / y)); if (res > v + eps) res = v, st = "y^z^x"; v = log(x) + log(z) + log(log(1.0 / y)); if (res > v + eps) res = v, st = "(y^x)^z"; v = y * log(x) + log(log(1.0 / z)); if (res > v + eps) res = v, st = "z^x^y"; v = x * log(y) + log(log(1.0 / z)); if (res > v + eps) res = v, st = "z^y^x"; v = log(x) + log(y) + log(log(1.0 / z)); if (res > v + eps) res = v, st = "(z^x)^y"; cout << st << endl; } else { res = -1e18; if (x > 1.0 + eps) { v = z * log(y) + log(log(x)); if (res + eps < v) res = v, st = "x^y^z"; v = y * log(z) + log(log(x)); if (res + eps < v) res = v, st = "x^z^y"; v = log(y) + log(z) + log(log(x)); if (res + eps < v) res = v, st = "(x^y)^z"; } if (y > 1.0 + eps) { v = z * log(x) + log(log(y)); if (res + eps < v) res = v, st = "y^x^z"; v = x * log(z) + log(log(y)); if (res + eps < v) res = v, st = "y^z^x"; v = log(x) + log(z) + log(log(y)); if (res + eps < v) res = v, st = "(y^x)^z"; } if (z > 1.0 + eps) { v = y * log(x) + log(log(z)); if (res + eps < v) res = v, st = "z^x^y"; v = x * log(y) + log(log(z)); if (res + eps < v) res = v, st = "z^y^x"; v = log(x) + log(y) + log(log(z)); if (res + eps < v) res = v, st = "(z^x)^y"; } cout << st << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int dx[5] = {0, 1, -1, 0, 0}; const int dy[5] = {0, 0, 0, -1, 1}; const double pi = acos(-1.0); long double x, y, z; long double ans[15]; void input_LL(long long &r) { r = 0; char t = getchar(); while (!isdigit(t)) t = getchar(); long long sign = 1; if (t == '-') sign = -1; while (!isdigit(t)) t = getchar(); while (isdigit(t)) r = r * 10 + t - '0', t = getchar(); r = r * sign; } void input_int(int &r) { r = 0; char t = getchar(); while (!isdigit(t)) t = getchar(); int sign = 1; if (t == '-') sign = -1; while (!isdigit(t)) t = getchar(); while (isdigit(t)) r = r * 10 + t - '0', t = getchar(); r = r * sign; } int main() { cin >> x >> y >> z; ans[1] = pow(y, z) * log(x); ans[2] = pow(z, y) * log(x); ans[3] = z * y * log(x); ans[4] = ans[3]; ans[5] = pow(x, z) * log(y); ans[6] = pow(z, x) * log(y); ans[7] = x * z * log(y); ans[8] = ans[7]; ans[9] = pow(x, y) * log(z); ans[10] = pow(y, x) * log(z); ans[11] = x * y * log(z); ans[12] = ans[11]; int j = 1; for (int i = 2; i <= 12; i++) if (ans[j] < ans[i]) j = i; switch (j) { case 1: puts("x^y^z"); break; case 2: puts("x^z^y"); break; case 3: puts("(x^y)^z"); break; case 4: puts("(x^z)^y"); break; case 5: puts("y^x^z"); break; case 6: puts("y^z^x"); break; case 7: puts("(y^x)^z"); break; case 8: puts("(y^z)^x"); break; case 9: puts("z^x^y"); break; case 10: puts("z^y^x"); break; case 11: puts("(z^x)^y"); break; case 12: puts("(z^y)^x"); break; } return 0; }
#include <bits/stdc++.h> double res[10]; int ans = 0; void calc(double x, double y, double z, double &res1, double &res2, double &res3) { if (x <= 1.0) { res1 = res2 = res3 = -2000.0; return; } res1 = z * log(y) + log(log(x)); res2 = y * log(z) + log(log(x)); res3 = log(y) + log(z) + log(log(x)); } void printf_Result() { switch (ans) { case 0: puts("x^y^z"); break; case 1: puts("x^z^y"); break; case 2: puts("(x^y)^z"); break; case 3: puts("y^x^z"); break; case 4: puts("y^z^x"); break; case 5: puts("(y^x)^z"); break; case 6: puts("z^x^y"); break; case 7: puts("z^y^x"); break; case 8: puts("(z^x)^y"); break; } } int main() { double x, y, z; scanf("%lf %lf %lf", &x, &y, &z); if (x <= 1 && y <= 1 && z <= 1) { res[0] = pow(y, z) * log(x); res[1] = pow(z, y) * log(x); res[2] = y * z * log(x); res[3] = pow(z, x) * log(y); res[4] = pow(x, z) * log(y); res[5] = z * x * log(y); res[6] = pow(y, x) * log(z); res[7] = pow(x, y) * log(z); res[8] = x * y * log(z); for (int i = 1; i <= 8; ++i) if (res[i] > res[ans]) ans = i; printf_Result(); return 0; } calc(x, y, z, res[0], res[1], res[2]); calc(y, x, z, res[3], res[4], res[5]); calc(z, x, y, res[6], res[7], res[8]); for (int i = 1; i <= 8; ++i) if (res[i] > res[ans]) ans = i; printf_Result(); return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-9; const int mod = (int)1e+9 + 7; const double pi = acos(-1.); bool compare(complex<long double> a, complex<long double> b) { if (imag(a) == 0 && imag(b) == 0) { return real(a) > real(b); } else if (imag(a) == 0 && imag(b) != 0) { return true; } else if (imag(a) != 0 && imag(b) == 0) { return false; } else if (imag(a) != 0 && imag(b) != 0) { return real(a) < real(b); } return (true); } int main() { { srand(time(0)); const string file = ""; if (!file.empty()) { freopen((file + ".in").c_str(), "r", stdin); freopen((file + ".out").c_str(), "w", stdout); } } long double ax, ay, az; cin >> ax >> ay >> az; complex<long double> x(ax, 0.0L); complex<long double> y(ay, 0.0L); complex<long double> z(az, 0.0L); complex<long double> ansc(3, 3); string ans = "..."; if (compare(z * log(y) + log(log(x)), ansc)) { ansc = z * log(y) + log(log(x)); ans = "x^y^z"; } if (compare(y * log(z) + log(log(x)), ansc)) { ansc = y * log(z) + log(log(x)); ans = "x^z^y"; } if (compare(log(y * z) + log(log(x)), ansc)) { ansc = log(y * z) + log(log(x)); ans = "(x^y)^z"; } if (compare(z * log(x) + log(log(y)), ansc)) { ansc = z * log(x) + log(log(y)); ans = "y^x^z"; } if (compare(x * log(z) + log(log(y)), ansc)) { ansc = x * log(z) + log(log(y)); ans = "y^z^x"; } if (compare(log(x * z) + log(log(y)), ansc)) { ansc = log(x * z) + log(log(y)); ans = "(y^x)^z"; } if (compare(y * log(x) + log(log(z)), ansc)) { ansc = y * log(x) + log(log(z)); ans = "z^x^y"; } if (compare(x * log(y) + log(log(z)), ansc)) { ansc = x * log(y) + log(log(z)); ans = "z^y^x"; } if (compare(log(x * y) + log(log(z)), ansc)) { ansc = log(x * y) + log(log(z)); ans = "(z^x)^y"; } cout << ans; return (0); }
#include <bits/stdc++.h> using namespace std; char str[12][10] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; bool cmp(complex<long double> x, complex<long double> y) { if (imag(x) == 0 && imag(y) == 0) { return real(x) > real(y); } else if (imag(x) == 0 && imag(y) != 0) { return true; } else if (imag(x) != 0 && imag(y) == 0) { return false; } else { return real(x) < real(y); } } complex<long double> arr[12]; int main() { long double a, b, c; cin >> a >> b >> c; complex<long double> x(a, 0.0L); complex<long double> y(b, 0.0L); complex<long double> z(c, 0.0L); arr[0] = z * log(y) + log(log(x)); arr[1] = y * log(z) + log(log(x)); arr[2] = log(y * z) + log(log(x)); arr[3] = arr[2]; arr[4] = z * log(x) + log(log(y)); arr[5] = x * log(z) + log(log(y)); arr[6] = log(x * z) + log(log(y)); arr[7] = arr[6]; arr[8] = y * log(x) + log(log(z)); arr[9] = x * log(y) + log(log(z)); arr[10] = log(x * y) + log(log(z)); arr[11] = arr[10]; int idx = 0; for (int i = 1; i < 12; i++) { if (cmp(arr[i], arr[idx])) { idx = i; } } printf("%s\n", str[idx]); return 0; }
#include <bits/stdc++.h> double x, y, z; int ans; double num[15]; int main() { int i; for (i = 1; i <= 12; i++) num[i] = -1e100; scanf("%lf%lf%lf", &x, &y, &z); if (x <= 1 && y <= 1 && z <= 1) { num[1] = pow(x, pow(y, z)); num[2] = pow(x, pow(z, y)); num[3] = pow(pow(x, y), z); num[5] = pow(y, pow(x, z)); num[6] = pow(y, pow(z, z)); num[7] = pow(pow(y, x), z); num[9] = pow(z, pow(x, y)); num[10] = pow(z, pow(y, x)); num[11] = pow(pow(z, x), y); } else { if (x > 1) { num[1] = z * log(y) + log(log(x)); num[2] = y * log(z) + log(log(x)); num[3] = log(y) + log(z) + log(log(x)); } if (y > 1) { num[5] = z * log(x) + log(log(y)); num[6] = x * log(z) + log(log(y)); num[7] = log(x) + log(z) + log(log(y)); } if (z > 1) { num[9] = y * log(x) + log(log(z)); num[10] = x * log(y) + log(log(z)); num[11] = log(x) + log(y) + log(log(z)); } } for (ans = 1, i = 2; i <= 12; i++) if (num[i] > num[ans] + 1e-6) ans = i; if (ans == 1) printf("x^y^z"); else if (ans == 2) printf("x^z^y"); else if (ans == 3) printf("(x^y)^z"); else if (ans == 5) printf("y^x^z"); else if (ans == 6) printf("y^z^x"); else if (ans == 7) printf("(y^x)^z"); else if (ans == 9) printf("z^x^y"); else if (ans == 10) printf("z^y^x"); else printf("(z^x)^y"); return 0; }
#include <bits/stdc++.h> using namespace std; template <typename Arg1> void __f(const char* name, Arg1&& arg1) { cerr << name << " : " << arg1 << std::endl; } template <typename Arg1, typename... Args> void __f(const char* names, Arg1&& arg1, Args&&... args) { const char* comma = strchr(names + 1, ','); cerr.write(names, comma - names) << " : " << arg1 << " | "; __f(comma + 1, args...); } int main() { long double x, y, z; cin >> x >> y >> z; string s[12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; long double ans = 0.0, res[12]; int index; res[0] = pow(y, z) * log(x); res[1] = pow(z, y) * log(x); res[2] = y * z * log(x); res[3] = z * y * log(x); res[4] = pow(x, z) * log(y); res[5] = pow(z, x) * log(y); res[6] = x * z * log(y); res[7] = z * x * log(y); res[8] = pow(x, y) * log(z); res[9] = pow(y, x) * log(z); res[10] = x * y * log(z); res[11] = y * x * log(z); ans = res[0]; index = 0; for (int i = 0; i < 12; i++) if (res[i] > ans) ans = res[i], index = i; cout << s[index] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; namespace mainns { class Solver621D { public: void run(); }; void Solver621D::run() { vector<string> formulas = {"x^y^z", "x^z^y", "(x^y)^z", "y^x^z", "y^z^x", "(y^x)^z", "z^x^y", "z^y^x", "(z^x)^y"}; vector<function<complex<double>(complex<double>, complex<double>, complex<double>)>> functors = { [](complex<double> x, complex<double> y, complex<double> z) { return log(log(x)) + z * log(y); }, [](complex<double> x, complex<double> y, complex<double> z) { return log(log(x)) + y * log(z); }, [](complex<double> x, complex<double> y, complex<double> z) { return log(log(x)) + log(y) + log(z); }, [](complex<double> x, complex<double> y, complex<double> z) { return log(log(y)) + z * log(x); }, [](complex<double> x, complex<double> y, complex<double> z) { return log(log(y)) + x * log(z); }, [](complex<double> x, complex<double> y, complex<double> z) { return log(log(y)) + log(x) + log(z); }, [](complex<double> x, complex<double> y, complex<double> z) { return log(log(z)) + y * log(x); }, [](complex<double> x, complex<double> y, complex<double> z) { return log(log(z)) + x * log(y); }, [](complex<double> x, complex<double> y, complex<double> z) { return log(log(z)) + log(x) + log(y); }, }; double xr, yr, zr; cin >> xr >> yr >> zr; complex<double> x = {xr, 0.0}, y = {yr, 0.0}, z = {zr, 0.0}; vector<complex<double>> results; for (auto f : functors) results.push_back(f(x, y, z)); auto compareExponentsOf = [](complex<double> a, complex<double> b) -> bool { double aSign = abs(a.imag()) > 0.001 ? -1.0 : 1.0; double bSign = abs(b.imag()) > 0.001 ? -1.0 : 1.0; if (aSign == bSign) return (a.real() * aSign < b.real() * bSign); else return aSign < bSign; }; auto maxIndex = max_element(begin(results), end(results), compareExponentsOf) - begin(results); cout << formulas[maxIndex]; } } // namespace mainns using CurrentSolver = mainns::Solver621D; int main() { ios::sync_with_stdio(false); CurrentSolver().run(); return 0; }
#include <bits/stdc++.h> using namespace std; const int64_t INF = 0x7FFFFFFF; const int MAX = 3; const double eps = 1e-9; struct Variable { char key; double value; bool operator<(const Variable& var) const { return key < var.key || (key == var.key && value < var.value); } }; Variable var[MAX]; char ans[100]; double f1() { double x, y, z; x = var[0].value; y = var[1].value; z = var[2].value; return z * log(y) + log(log(x)); } double f2() { double x, y, z; x = var[0].value; y = var[1].value; z = var[2].value; return log(log(x)) + log(y) + log(z); } double f3() { double x, y, z; x = var[0].value; y = var[1].value; z = var[2].value; return pow(x, pow(y, z)); } double f4() { double x, y, z; x = var[0].value; y = var[1].value; z = var[2].value; return pow(pow(x, y), z); } int main(int argc, char* args[]) { double x, y, z; double maxs1 = -INF; cin >> x >> y >> z; var[0].key = 'x'; var[0].value = x; var[1].key = 'y'; var[1].value = y; var[2].key = 'z'; var[2].value = z; sort(var, var + 3); ans[0] = '\0'; if (x > 16 || y > 16 || z > 16) { do { double val1 = f1(); double val2 = f2(); if (!isnan(val1) && (val1 - maxs1) > eps) { maxs1 = val1; sprintf(ans, "%c^%c^%c", var[0].key, var[1].key, var[2].key); } next_permutation(var, var + 3); val1 = f1(); if (!isnan(val1) && (val1 - maxs1) > eps) { maxs1 = val1; sprintf(ans, "%c^%c^%c", var[0].key, var[1].key, var[2].key); } prev_permutation(var, var + 3); if (!isnan(val2) && (val2 - maxs1) > eps) { maxs1 = val2; sprintf(ans, "(%c^%c)^%c", var[0].key, var[1].key, var[2].key); } next_permutation(var, var + 3); val2 = f2(); if (!isnan(val2) && (val2 - maxs1) > eps) { maxs1 = val2; sprintf(ans, "(%c^%c)^%c", var[0].key, var[1].key, var[2].key); } } while (next_permutation(var, var + 3)); } else if (x <= 16 && y <= 16 && z <= 16) { do { double val1 = f3(); double val2 = f4(); if (!isnan(val1) && (val1 - maxs1) > eps) { maxs1 = val1; sprintf(ans, "%c^%c^%c", var[0].key, var[1].key, var[2].key); } next_permutation(var, var + 3); val1 = f3(); if (!isnan(val1) && (val1 - maxs1) > eps) { maxs1 = val1; sprintf(ans, "%c^%c^%c", var[0].key, var[1].key, var[2].key); } prev_permutation(var, var + 3); if (!isnan(val2) && (val2 - maxs1) > eps) { maxs1 = val2; sprintf(ans, "(%c^%c)^%c", var[0].key, var[1].key, var[2].key); } next_permutation(var, var + 3); val2 = f4(); if (!isnan(val2) && (val2 - maxs1) > eps) { maxs1 = val2; sprintf(ans, "(%c^%c)^%c", var[0].key, var[1].key, var[2].key); } } while (next_permutation(var, var + 3)); } puts(ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int INF = (int)1e9 + 7; const int MAXN = (int)2e6 + 7; long double eps = 1e-11; long double a[33]; int p[33]; void reconstruct(int id) { vector<int> v; if (id == 1) v = {0, 1, 2}; if (id == 2) v = {0, 2, 1}; if (id == 3) v = {0, 1, 2}; if (id == 4) v = {0, 2, 1}; if (id == 5) v = {1, 0, 2}; if (id == 6) v = {1, 2, 0}; if (id == 7) v = {1, 0, 2}; if (id == 8) v = {1, 2, 0}; if (id == 9) v = {2, 0, 1}; if (id == 10) v = {2, 1, 0}; if (id == 11) v = {2, 0, 1}; if (id == 12) v = {2, 1, 0}; for (int i = 0; i < 3; i++) p[i] = v[i]; } string get(int id) { string x = "x"; string y = "y"; string z = "z"; id--; if (id / 4 == 1) { x = "y"; y = "x"; z = "z"; } if (id / 4 == 2) { x = "z"; y = "x"; z = "y"; } id %= 4; if (id == 0) return x + "^" + y + "^" + z; if (id == 1) return x + "^" + z + "^" + y; if (id == 2) return "(" + x + "^" + y + ")" + "^" + z; if (id == 3) return "(" + x + "^" + z + ")" + "^" + y; while (true) { } } int main() { for (int i = 0; i < 3; i++) cin >> a[i]; for (int i = 0; i < 3; i++) p[i] = i; pair<long double, int> ans; for (int id = 1; id <= 12; id++) { int block = (id - 1) / 2; reconstruct(id); long double x = a[p[0]]; long double y = a[p[1]]; long double z = a[p[2]]; long double first; if (block % 2 == 1) first = log(x) * y * z; else first = log(x) * pow(y, z); if (id == 1) ans = make_pair(first, id); else { if (abs(first - ans.first) < eps) continue; if (first > ans.first) { ans = make_pair(first, id); } } } cout << get(ans.second); return 0; }
#include <bits/stdc++.h> using namespace std; const double PI = acos(-1.0); const long double eps = 1e-6; const int mod = 1000000000 + 7; const int INF = 1000000000; const int maxn = 100; int T, n, m; double hehe, haha, ohoh; long double x, y, z; long double a[maxn]; bool eq(long double &x, long double &y) { return abs(x - y) < eps || abs(x - y) < eps * abs(x); } int main() { while (~scanf("%lf%lf%lf", &hehe, &haha, &ohoh)) { x = hehe; y = haha; z = ohoh; long double logx = log(x); long double logy = log(y); long double logz = log(z); a[1] = logx * pow(y, z); a[2] = logx * pow(z, y); a[3] = logx * y * z; a[4] = logx * z * y; a[5] = logy * pow(x, z); a[6] = logy * pow(z, x); a[7] = logy * x * z; a[8] = logy * z * x; a[9] = logz * pow(x, y); a[10] = logz * pow(y, x); a[11] = logz * x * y; a[12] = logz * y * x; long double ans = a[1]; int id = 1; for (int i = 2; i <= 12; i++) { if (a[i] > ans && !eq(a[i], ans)) { ans = a[i]; id = i; } } if (id == 1) printf("x^y^z\n"); else if (id == 2) printf("x^z^y\n"); else if (id == 3) printf("(x^y)^z\n"); else if (id == 5) printf("y^x^z\n"); else if (id == 6) printf("y^z^x\n"); else if (id == 7) printf("(y^x)^z\n"); else if (id == 9) printf("z^x^y\n"); else if (id == 10) printf("z^y^x\n"); else if (id == 11) printf("(z^x)^y\n"); } return 0; }
#include <bits/stdc++.h> using namespace std; int i, p; long double x, y, z, Logx, Logy, Logz; long double a[13]; string s[13]; int main() { cin >> x >> y >> z; Logx = log(x), Logy = log(y), Logz = log(z); a[1] = Logx * pow(y, z), s[1] = "x^y^z"; a[2] = Logx * pow(z, y), s[2] = "x^z^y"; a[3] = Logx * y * z, s[3] = "(x^y)^z"; a[4] = Logx * z * y, s[4] = "(x^z)^y"; a[5] = Logy * pow(x, z), s[5] = "y^x^z"; a[6] = Logy * pow(z, x), s[6] = "y^z^x"; a[7] = Logy * x * z, s[7] = "(y^x)^z"; a[8] = Logy * z * x, s[8] = "(y^z)^x"; a[9] = Logz * pow(x, y), s[9] = "z^x^y"; a[10] = Logz * pow(y, x), s[10] = "z^y^x"; a[11] = Logz * x * y, s[11] = "(z^x)^y"; a[12] = Logz * y * x, s[12] = "(z^y)^x"; p = 1; for (int i = 2; i <= 12; i++) if (a[i] > a[p] + (long double)(1e-9)) p = i; cout << s[p]; return 0; }
#include <bits/stdc++.h> using namespace std; long double x, y, z, r[15]; int main() { std ::cin >> x >> y >> z; int id = 1; r[1] = pow(y, z) * log(x); if (r[1] > r[id]) id = 1; r[2] = pow(z, y) * log(x); if (r[2] > r[id]) id = 2; r[3] = y * z * log(x); if (r[3] > r[id]) id = 3; r[4] = y * z * log(x); if (r[4] > r[id]) id = 4; r[5] = pow(x, z) * log(y); if (r[5] > r[id]) id = 5; r[6] = pow(z, x) * log(y); if (r[6] > r[id]) id = 6; r[7] = x * z * log(y); if (r[7] > r[id]) id = 7; r[8] = x * z * log(y); if (r[8] > r[id]) id = 8; r[9] = pow(x, y) * log(z); if (r[9] > r[id]) id = 9; r[10] = pow(y, x) * log(z); if (r[10] > r[id]) id = 10; r[11] = x * y * log(z); if (r[11] > r[id]) id = 11; r[12] = x * y * log(z); if (r[12] > r[id]) id = 12; if (id == 1) puts("x^y^z"); if (id == 2) puts("x^z^y"); if (id == 3) puts("(x^y)^z"); if (id == 4) puts("(x^z)^y"); if (id == 5) puts("y^x^z"); if (id == 6) puts("y^z^x"); if (id == 7) puts("(y^x)^z"); if (id == 8) puts("(y^z)^x"); if (id == 9) puts("z^x^y"); if (id == 10) puts("z^y^x"); if (id == 11) puts("(z^x)^y"); if (id == 12) puts("(z^y)^x"); return 0; }
#include <bits/stdc++.h> using namespace std; double a[20]; double cal1(double x, double y, double z) { double ans; ans = z * log(y) + log(log(x)); return ans; } double cal2(double x, double y, double z) { double ans; ans = log(y) + log(z) + log(log(x)); return ans; } int solve(double x, double y, double z) { for (int i = 1; i <= 12; i++) a[i] = -(1000000007); if (x <= 1 && y <= 1 && z <= 1) { double xx = 1.0 / x, yy = 1.0 / y, zz = 1.0 / z; if (xx != 1) { a[1] = cal1(xx, y, z); a[2] = cal1(xx, z, y); a[3] = cal2(xx, y, z); a[4] = cal2(xx, z, y); } if (yy != 1) { a[5] = cal1(yy, x, z); a[6] = cal1(yy, z, x); a[7] = cal2(yy, x, z); a[8] = cal2(yy, z, x); } if (zz != 1) { a[9] = cal1(zz, x, y); a[10] = cal1(zz, y, x); a[11] = cal2(zz, x, y); a[12] = cal2(zz, y, x); } int re = 1; double mmax = a[1]; for (int i = 1; i <= 12; i++) { if (a[i] < mmax) mmax = a[i], re = i; } return re; } else { if (x > 1) { a[1] = cal1(x, y, z); a[2] = cal1(x, z, y); a[3] = cal2(x, y, z); a[4] = cal2(x, z, y); } if (y > 1) { a[5] = cal1(y, x, z); a[6] = cal1(y, z, x); a[7] = cal2(y, x, z); a[8] = cal2(y, z, x); } if (z > 1) { a[9] = cal1(z, x, y); a[10] = cal1(z, y, x); a[11] = cal2(z, x, y); a[12] = cal2(z, y, x); } } int re = 1; double mmax = a[1]; for (int i = 1; i <= 12; i++) { if (a[i] > mmax) mmax = a[i], re = i; } return re; } int out[5]; void print(int mark) { if (mark == 1) printf("x^y^z\n"); if (mark == 2) printf("x^z^y\n"); if (mark == 3) printf("(x^y)^z\n"); if (mark == 4) printf("(x^z)^y\n"); if (mark == 5) printf("y^x^z\n"); if (mark == 6) printf("y^z^x\n"); if (mark == 7) printf("(y^x)^z\n"); if (mark == 8) printf("(y^z)^x\n"); if (mark == 9) printf("z^x^y\n"); if (mark == 10) printf("z^y^x\n"); if (mark == 11) printf("(z^x)^y\n"); if (mark == 12) printf("(z^y)^x\n"); } int main() { double x, y, z; while (cin >> x >> y >> z) { int mark = solve(x, y, z); print(mark); } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long double x, y, z; cin >> x >> y >> z; long double a[13]; a[1] = log(x) * pow(y, z); a[2] = log(x) * pow(z, y); a[3] = y * z * log(x); a[4] = log(y) * pow(x, z); a[5] = log(y) * pow(z, x); a[6] = x * z * log(y); a[7] = log(z) * pow(x, y); a[8] = log(z) * pow(y, x); a[9] = x * y * log(z); long double ans = a[1]; int m = 1; for (int i = 2; i < 10; ++i) { if (a[i] > ans) { ans = a[i]; m = i; } } if (m == 1) { cout << "x^y^z\n"; } if (m == 2) { cout << "x^z^y\n"; } if (m == 3) { cout << "(x^y)^z\n"; } if (m == 4) { cout << "y^x^z\n"; } if (m == 5) { cout << "y^z^x\n"; } if (m == 6) { cout << "(y^x)^z\n"; } if (m == 7) { cout << "z^x^y\n"; } if (m == 8) { cout << "z^y^x\n"; } if (m == 9) { cout << "(z^x)^y\n"; } return 0; }
#include <bits/stdc++.h> typedef long double (*fnt)(long double x, long double y, long double z); using namespace std; long double f1(long double x, long double y, long double z) { return log(x) * pow(y, z); } long double f2(long double x, long double y, long double z) { return log(x) * pow(z, y); } long double f3(long double x, long double y, long double z) { return log(pow(x, y)) * z; } long double f4(long double x, long double y, long double z) { return log(pow(x, z)) * y; } long double f5(long double x, long double y, long double z) { return log(y) * pow(x, z); } long double f6(long double x, long double y, long double z) { return log(y) * pow(z, x); } long double f7(long double x, long double y, long double z) { return log(pow(y, x)) * z; } long double f8(long double x, long double y, long double z) { return log(pow(y, z)) * x; } long double f9(long double x, long double y, long double z) { return log(z) * pow(x, y); } long double f10(long double x, long double y, long double z) { return log(z) * pow(y, x); } long double f11(long double x, long double y, long double z) { return log(pow(z, x)) * y; } long double f12(long double x, long double y, long double z) { return log(pow(z, y)) * x; } string str[15]; fnt A[15] = {f1, f1, f2, f3, f4, f5, f6, f7, f8, f9, f10, f11, f12}; int main(int argc, char const *argv[]) { str[1] = "x^y^z"; str[2] = "x^z^y"; str[3] = "(x^y)^z"; str[4] = "(x^z)^y"; str[5] = "y^x^z"; str[6] = "y^z^x"; str[7] = "(y^x)^z"; str[8] = "(y^z)^x"; str[9] = "z^x^y"; str[10] = "z^y^x"; str[11] = "(z^x)^y"; str[12] = "(z^y)^x"; long double x, y, z; cin >> x >> y >> z; int c = 1; for (int i = 2; i < 13; i++) { if (A[i](x, y, z) - 1e-9 > A[c](x, y, z)) { c = i; } } cout << str[c] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const double PI = acos(-1.0); const long long INF = 1e9 + 47; const long long LINF = INF * INF; mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); int get(string s) { int res = 0; for (auto i : s) if (i != '.') res = res * 10 + i - '0'; return res; } const long double EPS = 1e-6; int cmp(long double x, long double y) { if (abs(x - y) < EPS) return 0; if (x < y) return 1; else return -1; } pair<long double, int> get(long double x, long double y, long double z) { if (abs(x - 1) < EPS) return {1.0, 1}; if (x > 1) { long double pw = z * log(y); int id = 1; if (cmp(pw, y * log(z)) == 1) pw = y * log(z), id = 2; if (cmp(pw, log(y) + log(z)) == 1) pw = log(y) + log(z), id = 3; return {pw, id}; } else { long double pw = z * log(y); int id = 1; if (cmp(pw, y * log(z)) == -1) pw = y * log(z), id = 2; if (cmp(pw, log(y) + log(z)) == -1) pw = log(y) + log(z), id = 3; return {pw, id}; } } int cmp(pair<long double, long double> x, pair<long double, long double> y) { long double valx = log(x.first) * exp(x.second); long double valy = log(y.first) * exp(y.second); if (abs(valx - valy) < EPS) return 1; return valx > valy; } void solve(int x) { string s; if (x == 1) s = "x^y^z"; if (x == 2) s = "x^z^y"; if (x == 3) s = "(x^y)^z"; if (x == 5) s = "y^x^z"; if (x == 6) s = "y^z^x"; if (x == 7) s = "(y^x)^z"; if (x == 9) s = "z^x^y"; if (x == 10) s = "z^y^x"; if (x == 11) s = "(z^x)^y"; cout << s << endl; } int main() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); string first, second, Z; cin >> first >> second >> Z; long double x = get(first) / 10.0; long double y = get(second) / 10.0; long double z = get(Z) / 10.0; auto mxx = get(x, y, z); auto mxy = get(y, x, z); auto mxz = get(z, x, y); if (cmp({x, mxx.first}, {y, mxy.first})) { if (cmp({x, mxx.first}, {z, mxz.first})) solve(mxx.second); else solve(mxz.second + 8); } else { if (cmp({y, mxy.first}, {z, mxz.first})) solve(mxy.second + 4); else solve(mxz.second + 8); } cerr << "Time elapsed: " << clock() / (long double)CLOCKS_PER_SEC << endl; return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("Ofast") using namespace std; long double s[9]; string ans[9] = {"x^y^z", "x^z^y", "(x^y)^z", "y^x^z", "y^z^x", "(y^x)^z", "z^x^y", "z^y^x", "(z^x)^y"}; int main() { ios::sync_with_stdio(0); cin.tie(0); long double x, y, z; cin >> x >> y >> z; long double tx, ty, tz; tx = log(x); ty = log(y); tz = log(z); s[0] = pow(y, z) * tx; s[1] = pow(z, y) * tx; s[2] = y * z * tx; s[3] = pow(x, z) * ty; s[4] = pow(z, x) * ty; s[5] = x * z * ty; s[6] = pow(x, y) * tz; s[7] = pow(y, x) * tz; s[8] = x * y * tz; int maxi = 0; for (int i = 1; i <= 8; i++) { if (s[i] > s[maxi]) { maxi = i; } } cout << ans[maxi]; return 0; }
#include <bits/stdc++.h> using namespace std; long double X, Y, Z; string S[13] = { "", "x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x", }; void solve() { int i, j, k, l, r, x, y; string s; cin >> X >> Y >> Z; pair<long double, int> P[9]; P[0] = {-log(X) * pow(Y, Z), 1}; P[1] = {-log(X) * pow(Z, Y), 2}; P[2] = {-log(X) * (Y * Z), 3}; P[3] = {-log(Y) * pow(X, Z), 5}; P[4] = {-log(Y) * pow(Z, X), 6}; P[5] = {-log(Y) * (X * Z), 7}; P[6] = {-log(Z) * pow(X, Y), 9}; P[7] = {-log(Z) * pow(Y, X), 10}; P[8] = {-log(Z) * (X * Y), 11}; sort(P, P + 9); cout << S[P[0].second] << endl; } int main(int argc, char** argv) { string s; int i; if (argc == 1) ios::sync_with_stdio(false); for (i = 0; i < (argc - 1); i++) s += argv[i + 1], s += '\n'; for (i = 0; i < (s.size()); i++) ungetc(s[s.size() - 1 - i], stdin); solve(); return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long double x, y, z; cin >> x >> y >> z; long double best = -1000000; int bestnum = 13; if (x > 1 + 0.00001) { if (z * log(y) + log(log(x)) - best > .000001) { best = z * log(y) + log(log(x)); bestnum = 1; } if (y * log(z) + log(log(x)) - best > .000001) { best = y * log(z) + log(log(x)); bestnum = 2; } if (log(y) + log(z) + log(log(x)) - best > .00001) { best = log(y) + log(z) + log(log(x)); bestnum = 3; } } if (y > 1 + .00001) { if (z * log(x) + log(log(y)) - best > .000001) { best = z * log(x) + log(log(y)); bestnum = 5; } if (x * log(z) + log(log(y)) - best > .000001) { best = x * log(z) + log(log(y)); bestnum = 6; } if (log(x) + log(z) + log(log(y)) - best > .000001) { best = log(x) + log(z) + log(log(y)); bestnum = 7; } } if (z > 1 + .00001) { if (y * log(x) + log(log(z)) - best > .000001) { best = y * log(x) + log(log(z)); bestnum = 9; } if (x * log(y) + log(log(z)) - best > .000001) { best = x * log(y) + log(log(z)); bestnum = 10; } if (log(x) + log(y) + log(log(z)) - best > .000001) { best = log(x) + log(y) + log(log(z)); bestnum = 11; } } if (bestnum == 13) { if (pow(x, pow(y, z)) - best > .000001) { bestnum = 1; best = pow(x, pow(y, z)); } if (pow(x, pow(z, y)) - best > .000001) { bestnum = 2; best = pow(x, pow(z, y)); } if (pow(x, y * z) - best > .000001) { bestnum = 3; best = pow(x, y * z); } if (pow(y, pow(x, z)) - best > .000001) { bestnum = 5; best = pow(y, pow(x, z)); } if (pow(y, pow(z, x)) - best > .000001) { bestnum = 6; best = pow(y, pow(z, x)); } if (pow(y, x * z) - best > .000001) { bestnum = 7; best = pow(y, x * z); } if (pow(z, pow(x, y)) - best > .000001) { bestnum = 9; best = pow(z, pow(x, y)); } if (pow(z, pow(y, x)) - best > .000001) { bestnum = 10; best = pow(z, pow(y, x)); } if (pow(z, x * y) - best > .000001) { bestnum = 11; best = pow(z, x * y); } } if (bestnum == 1) cout << "x^y^z" << endl; if (bestnum == 2) cout << "x^z^y" << endl; if (bestnum == 3) cout << "(x^y)^z" << endl; if (bestnum == 5) cout << "y^x^z" << endl; if (bestnum == 6) cout << "y^z^x" << endl; if (bestnum == 7) cout << "(y^x)^z" << endl; if (bestnum == 9) cout << "z^x^y" << endl; if (bestnum == 10) cout << "z^y^x" << endl; if (bestnum == 11) cout << "(z^x)^y" << endl; }
#include <bits/stdc++.h> using namespace std; const int INF = 1 << 30; const double eps = 1e-8; const double PI = acos(-1.0); const int maxn = 1e5 + 10; long double a[20]; string s[] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int main() { long double x, y, z; while (cin >> x >> y >> z) { a[0] = pow(y, z) * log(x); a[1] = pow(z, y) * log(x); a[2] = z * y * log(x); a[3] = y * z * log(x); a[4] = pow(x, z) * log(y); a[5] = pow(z, x) * log(y); a[6] = x * z * log(y); a[7] = x * z * log(y); a[8] = pow(x, y) * log(z); a[9] = pow(y, x) * log(z); a[10] = y * x * log(z); a[11] = x * y * log(z); int index = 0; for (int i = 1; i < 12; ++i) { if (a[i] > a[index]) { index = i; } } cout << s[index] << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; char* r[] = {"x^y^z", "x^z^y", "(x^y)^z", "y^x^z", "y^z^x", "(y^x)^z", "z^x^y", "z^y^x", "(z^x)^y"}; int main(int argc, char* argv[]) { long double co[3]; cin >> co[0] >> co[1] >> co[2]; long double mxx = -1e200; unsigned int ix = 0; bool found = false; for (unsigned int i = 0; i < 3; ++i) { if (co[0] >= 1.) { found = true; long double cl = (fabs(1. - co[0]) <= 1E-11) ? -1e100 : logl(logl(co[0])), lg[2]; lg[0] = logl(co[1]); lg[1] = logl(co[2]); long double fc[3]; fc[0] = co[2] * lg[0]; fc[1] = co[1] * lg[1]; fc[2] = lg[0] + lg[1]; long double mx = max(fc[0], max(fc[1], fc[2])); unsigned int cx = 0; if (mx == fc[0]) cx = 0; else if (mx == fc[1]) cx = 1; else cx = 2; long double cr = fc[cx] + cl; if (cr > mxx) { mxx = cr; ix = (3 * i) + cx; } } if (i == 0) swap(co[0], co[1]); else if (i == 1) swap(co[0], co[2]); } if (!found) { swap(co[0], co[1]); swap(co[1], co[2]); for (unsigned int i = 0; i < 3; ++i) { long double fc[3]; fc[0] = powl(co[0], powl(co[1], co[2])); fc[1] = powl(co[0], powl(co[2], co[1])); fc[2] = powl(co[0], co[1] * co[2]); long double mx = max(fc[0], max(fc[1], fc[2])); unsigned int cx = 0; if (mx == fc[0]) cx = 0; else if (mx == fc[1]) cx = 1; else cx = 2; if (fc[cx] > mxx) { mxx = fc[cx]; ix = (3 * i) + cx; } if (i == 0) swap(co[0], co[1]); else if (i == 1) swap(co[0], co[2]); } } cout << r[ix] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int oo = 0x3f3f3f3f; const int Mod = 1e9 + 7; const int maxn = 100000; const long double eps = 1e-12; long double x, y, z; inline bool eq(const long double &x, const long double &y) { return abs(x - y) < eps || abs(x - y) < eps * abs(x); } int main() { { double a, b, c; scanf("%lf%lf%lf", &a, &b, &c); x = a, y = b, z = c; } long double logx = log(x); long double logy = log(y); long double logz = log(z); long double a[11]; a[0] = logx * pow(y, z); a[1] = logx * pow(z, y); a[2] = logx * y * z; a[3] = a[2]; a[4] = logy * pow(x, z); a[5] = logy * pow(z, x); a[6] = logy * x * z; a[7] = a[6]; a[8] = logz * pow(x, y); a[9] = logz * pow(y, x); a[10] = logz * x * y; long double tmp = -1; int ansp = -1; for (int i = 0; i <= 11; i++) if (!eq(a[i], tmp) && a[i] > tmp) { tmp = a[i]; ansp = i; } if (ansp == 0) printf("x^y^z\n"); if (ansp == 1) printf("x^z^y\n"); if (ansp == 2) printf("(x^y)^z\n"); if (ansp == 4) printf("y^x^z\n"); if (ansp == 5) printf("y^z^x\n"); if (ansp == 6) printf("(y^x)^z\n"); if (ansp == 8) printf("z^x^y\n"); if (ansp == 9) printf("z^y^x\n"); if (ansp == 10) printf("(z^x)^y\n"); return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 1.0e-12; string s[12] = { "x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x", }; struct data { int type; long double real; long double imag; bool operator<(const data& rhs) const { if (type == 1 && rhs.type == 1) { return real + eps < rhs.real; } return imag + eps < rhs.imag; } } a[12]; int main() { long double x, y, z; cin >> x >> y >> z; for (int i = 0; i < 12; i++) { a[i].type = 0; } a[0].imag = powl(y, z) * logl(x); a[1].imag = powl(z, y) * logl(x); a[2].imag = y * z * logl(x); a[3].imag = z * y * logl(x); a[4].imag = powl(x, z) * logl(y); a[5].imag = powl(z, x) * logl(y); a[6].imag = x * z * logl(y); a[7].imag = z * x * logl(y); a[8].imag = powl(x, y) * logl(z); a[9].imag = powl(y, x) * logl(z); a[10].imag = y * x * logl(z); a[11].imag = x * y * logl(z); if (logl(x) > 0) { for (int i = 0; i < 4; i++) { a[i].type = 1; } a[0].real = z * logl(y) + logl(logl(x)); a[1].real = y * logl(z) + logl(logl(x)); a[2].real = logl(y * z) + logl(logl(x)); a[3].real = logl(z * y) + logl(logl(x)); } if (logl(y) > 0) { for (int i = 4; i < 8; i++) { a[i].type = 1; } a[4].real = z * logl(x) + logl(logl(y)); a[5].real = x * logl(z) + logl(logl(y)); a[6].real = logl(x * z) + logl(logl(y)); a[7].real = logl(z * x) + logl(logl(y)); } if (logl(z) > 0) { for (int i = 8; i < 12; i++) { a[i].type = 1; } a[8].real = y * logl(x) + logl(logl(z)); a[9].real = x * logl(y) + logl(logl(z)); a[10].real = logl(y * x) + logl(logl(z)); a[11].real = logl(x * y) + logl(logl(z)); } int pos = max_element(a, a + 12) - a; puts(s[pos].c_str()); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAX = 13; long double x, y, z, a[MAX], b[MAX]; int main() { cin >> x >> y >> z; a[1] = x, b[1] = pow(y, z); a[2] = x, b[2] = pow(z, y); a[3] = x, b[3] = y * z; a[4] = x, b[4] = z * y; a[5] = y, b[5] = pow(x, z); a[6] = y, b[6] = pow(z, x); a[7] = y, b[7] = x * z; a[8] = y, b[8] = z * x; a[9] = z, b[9] = pow(x, y); a[10] = z, b[10] = pow(y, x); a[11] = z, b[11] = x * y; a[12] = z, b[12] = y * x; int ind = 1; for (int i = 1; i <= 12; i++) if (log(a[i]) * b[i] > log(a[ind]) * b[ind]) ind = i; if (ind == 1) cout << "x^y^z"; if (ind == 2) cout << "x^z^y"; if (ind == 3) cout << "(x^y)^z"; if (ind == 4) cout << "(x^z)^y"; if (ind == 5) cout << "y^x^z"; if (ind == 6) cout << "y^z^x"; if (ind == 7) cout << "(y^x)^z"; if (ind == 8) cout << "(y^z)^x"; if (ind == 9) cout << "z^x^y"; if (ind == 10) cout << "z^y^x"; if (ind == 11) cout << "(z^x)^y"; if (ind == 12) cout << "(z^y)^x"; }
#include <bits/stdc++.h> using namespace std; const long double eps = 1e-9; int main() { long double x, y, z, a[20]; string s[20]; long double maxx; int pos = 0; s[1] = "x^y^z"; s[2] = "x^z^y"; s[3] = "(x^y)^z"; s[4] = "(x^z)^y"; s[5] = "y^x^z"; s[6] = "y^z^x"; s[7] = "(y^x)^z"; s[8] = "(y^z)^x"; s[9] = "z^x^y"; s[10] = "z^y^x"; s[11] = "(z^x)^y"; s[12] = "(z^y)^x"; cin >> x >> y >> z; a[1] = log(x) * pow(y, z); a[2] = log(x) * pow(z, y); a[3] = log(x) * y * z; a[4] = a[3]; a[5] = log(y) * pow(x, z); a[6] = log(y) * pow(z, x); a[7] = log(y) * x * z; a[8] = a[7]; a[9] = log(z) * pow(x, y); a[10] = log(z) * pow(y, x); a[11] = log(z) * x * y; a[12] = a[11]; maxx = a[1]; pos = 1; for (int i = 2; i <= 12; i++) { if (a[i] > maxx + eps) { pos = i; maxx = a[i]; } } cout << s[pos] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; double a, b, c; long double ans[9]; void print(int x) { if (x == 0) { printf("x^y^z\n"); return; } if (x == 1) { printf("x^z^y\n"); return; } if (x == 2) { printf("(x^y)^z\n"); return; } if (x == 3) { printf("y^x^z\n"); return; } if (x == 4) { printf("y^z^x\n"); return; } if (x == 5) { printf("(y^x)^z\n"); return; } if (x == 6) { printf("z^x^y\n"); return; } if (x == 7) { printf("z^y^x\n"); return; } if (x == 8) { printf("(z^x)^y\n"); return; } } int main() { scanf("%lf%lf%lf", &a, &b, &c); long double mx = -0x3f3f3f3f; if (a <= 1 && b <= 1 && c <= 1) { ans[0] = pow(a, pow(b, c)); ans[1] = pow(a, pow(c, b)); ans[2] = pow(pow(a, c), b); ans[3] = pow(b, pow(a, c)); ans[4] = pow(b, pow(c, a)); ans[5] = pow(pow(b, a), c); ans[6] = pow(c, pow(a, b)); ans[7] = pow(c, pow(b, a)); ans[8] = pow(pow(c, b), a); } else { ans[0] = c * log(b) + log(log(a)); ans[1] = b * log(c) + log(log(a)); ans[2] = log(b * c) + log(log(a)); ans[3] = c * log(a) + log(log(b)); ans[4] = a * log(c) + log(log(b)); ans[5] = log(a * c) + log(log(b)); ans[6] = b * log(a) + log(log(c)); ans[7] = a * log(b) + log(log(c)); ans[8] = log(a * b) + log(log(c)); } int k = 0; for (int i = 0; i < 9; i++) { if (mx < ans[i] - 1e-10) { mx = ans[i]; k = i; } } print(k); return 0; }
#include <bits/stdc++.h> using namespace std; long double Ans = -1 * 1e300, x, y, z, A[14]; int p; int main() { cin >> x >> y >> z; A[1] = pow(y, z) * log(x); A[2] = pow(z, y) * log(x); A[3] = A[4] = z * y * log(x); A[5] = pow(x, z) * log(y); A[6] = pow(z, x) * log(y); A[7] = A[8] = x * z * log(y); A[9] = pow(x, y) * log(z); A[10] = pow(y, x) * log(z); A[11] = A[12] = x * y * log(z); for (int i = 1; i <= 12; i++) { if (A[i] > Ans) { Ans = A[i]; p = i; } } if (p == 1) cout << "x^y^z"; if (p == 2) cout << "x^z^y"; if (p == 3) cout << "(x^y)^z"; if (p == 4) cout << "(x^z)^y"; if (p == 5) cout << "y^x^z"; if (p == 6) cout << "y^z^x"; if (p == 7) cout << "(y^x)^z"; if (p == 8) cout << "(y^z)^x"; if (p == 9) cout << "z^x^y"; if (p == 10) cout << "z^y^x"; if (p == 11) cout << "(z^x)^y"; if (p == 12) cout << "(z^y)^x"; return 0; }
#include <bits/stdc++.h> using namespace std; static const int MOD = 1000000007; static const long long MODL = 1000000000000000003LL; static const double eps = 1e-8; template <class T> inline T MIN(const T x, const T y) { return (x < y) ? x : y; } template <class T> inline T MAX(const T x, const T y) { return (x > y) ? x : y; } template <class T> inline void UPDMIN(T &x, const T y) { if (x > y) x = y; } template <class T> inline void UPDMAX(T &x, const T y) { if (x < y) x = y; } template <class T> inline int SIZE(const T &x) { return (int)x.size(); } template <class T> inline int LENGTH(const T &x) { return (int)x.length(); } template <class T1, class T2> inline pair<T1, T2> MP(const T1 &x, const T2 &y) { return make_pair(x, y); } inline int BINT(const int x) { return 1 << x; } inline long long BLLD(const int x) { return 1LL << x; } inline int BINT_TEST(const int s, const int x) { return (s & BINT(x)) != 0; } inline int BLLD_TEST(const long long s, const int x) { return (s & BLLD(x)) != 0LL; } template <class T> inline T LOWBIT(const T x) { return (x ^ (x - 1)) & x; } template <class T> inline int BITCOUNT(const T x) { return (!x) ? x : (1 + BITCOUNT(x & (x - 1))); } const double PI = acos(-1.0); const double EPS = 1e-5; template <class T> inline T SQR(const T x) { return x * x; } template <class T1, class T2> inline T1 POW(const T1 x, const T2 y) { if (!y) return 1; else if ((y & 1) == 0) { return SQR(POW(x, y >> 1)); } else return POW(x, y ^ 1) * x; } template <class T> inline T GCD(const T x, const T y) { if (x < 0) return GCD(-x, y); if (y < 0) return GCD(x, -y); return (!y) ? x : GCD(y, x % y); } template <class T> inline T LCM(const T x, const T y) { if (x < 0) return LCM(-x, y); if (y < 0) return LCM(x, -y); return x * (y / GCD(x, y)); } template <class T> inline T EEA(const T a, const T b, T &x, T &y) { if (a < 0) { T d = EEA(-a, b, x, y); x = -x; return d; } if (b < 0) { T d = EEA(a, -b, x, y); y = -y; return d; } if (!b) { x = 1; y = 0; return a; } else { T d = EEA(b, a % b, x, y); T t = x; x = y; y = t - (a / b) * y; return d; } } template <class T> inline vector<pair<T, int> > FACTORIZE(T x) { vector<pair<T, int> > ret; if (x < 0) x = -x; for (T i = 2; x > 1;) { if (x % i == 0) { int count = 0; for (; x % i == 0; x /= i) count++; ret.push_back(MP(i, count)); } i++; if (i > x / i) i = x; } return ret; } template <class T> inline int ISPRIME(const T x) { if (x <= 1) return 0; for (T i = 2; SQR(i) <= x; i++) if (x % i == 0) return 0; return 1; } template <class T> inline T EULARFUNCTION(T x) { vector<pair<T, int> > f = FACTORIZE(x); for (typename vector<pair<T, int> >::iterator it = f.begin(); it != f.end(); it++) { x = x / it->first * (it->first - 1); } return x; } template <class T> inline T INVERSEE(const T a, const T b = MOD) { T x, y; EEA(a, b, x, y); return x ? x : 1; } template <class T> inline T MOD_STD(const T x, const T m = MOD) { return (x % m + m) % m; } template <class T> inline void MOD_STD(T *x, const T m = MOD) { *x = (*x % m + m) % m; } template <class T> inline T MOD_ADD(const T x, const T y, const T m = MOD) { return (x + y) % m; } template <class T> inline void MOD_ADD(T *x, const T y, const T m = MOD) { *x = (*x + y) % m; } template <class T> inline T MOD_MUL(const T x, const T y, const T m = MOD) { return (T)((1LL * x * y) % m); } template <class T> inline void MOD_MUL(T *x, const T y, const T m = MOD) { *x = (T)((1LL * (*x) * y) % m); } template <class T1, class T2> inline T1 MOD_POW(const T1 x, const T2 y, const T1 m = MOD) { if (y == 0) return 1 % m; else if ((y & 1) == 0) { T1 z = MOD_POW(x, y >> 1, m); return MOD_MUL(z, z, m); } else return MOD_MUL(MOD_POW(x, y ^ 1, m), x, m); } inline long long MODL_MUL(long long x, long long y, const long long m = MOD) { if (x < y) swap(x, y); long long z = 0LL; while (y > 0) { if (y & 1) { MOD_ADD(&z, x, m); } MOD_ADD(&x, x, m); y >>= 1; } return z; } inline long long MODL_POW(const long long x, const long long y, const long long m = MOD) { if (y == 0LL) return 1LL % m; else if ((y & 1) == 0LL) { long long z = MODL_POW(x, y >> 1, m); return MODL_MUL(z, z, m); } else return MODL_MUL(MODL_POW(x, y ^ 1, m), x, m); } template <class T> class MATX { private: unsigned long hig, wid; T *data; void __init() { this->data = (T *)malloc(sizeof(T) * this->hig * this->wid); memset(this->data, 0, sizeof(T) * this->hig * this->wid); } public: MATX() { this->hig = this->wid = 1; __init(); } MATX(const unsigned long _len) { this->hig = this->wid = _len; __init(); } MATX(const unsigned long _hig, const unsigned long _wid) { this->hig = _hig; this->wid = _wid; __init(); } MATX(const MATX &rhs) { this->hig = rhs.hig; this->wid = rhs.wid; this->data = (T *)malloc(sizeof(T) * this->hig * this->wid); for (unsigned long x = 0; x < this->hig; x++) for (unsigned long y = 0; y < this->wid; y++) this->data[x * this->wid + y] = rhs.at(x, y); } ~MATX() { free(this->data); } T &operator()(const unsigned long x, const unsigned long y) { if (x >= this->hig || y >= this->wid) return (*(T *)NULL); return this->data[x * wid + y]; } MATX &operator=(const MATX &rhs) { if (this->hig != rhs.hig || this->wid != rhs.wid) { free(this->data); this->hig = rhs.hig; this->wid = rhs.wid; this->data = (T *)malloc(sizeof(T) * this->hig * this->wid); } for (unsigned long x = 0; x < this->hig; x++) for (unsigned long y = 0; y < this->wid; y++) this->data[x * this->wid + y] = rhs.at(x, y); return *this; } const MATX operator+(const MATX &opn) const { MATX ret(*this); for (unsigned long x = 0; x < ret.hig; x++) for (unsigned long y = 0; y < ret.wid; y++) ret.data[x * ret.wid + y] += opn.at(x, y); return ret; } const MATX operator-(const MATX &opn) const { MATX ret(*this); for (unsigned long x = 0; x < ret.hig; x++) for (unsigned long y = 0; y < ret.wid; y++) ret.data[x * ret.wid + y] -= opn.at(x, y); return ret; } const MATX operator*(const MATX &opn) const { MATX ret(this->hig, opn.wid); const unsigned long len = MIN(this->wid, opn.hig); for (unsigned long x = 0; x < ret.hig; x++) for (unsigned long y = 0; y < ret.wid; y++) for (unsigned long z = 0; z < len; z++) ret.data[x * ret.wid + y] += this->at(x, z) * opn.at(z, y); return ret; } const MATX mul(const MATX &opn) const { return *this * opn; } template <class T2> const MATX mul(const MATX &opn, const T2 m) const { MATX ret(this->hig, opn.wid); const unsigned long len = MIN(this->wid, opn.wid); for (unsigned long x = 0; x < ret.hig; x++) for (unsigned long y = 0; y < ret.wid; y++) for (unsigned long z = 0; z < len; z++) MOD_ADD(&ret.data[x * ret.wid + y], MOD_MUL(this->at(x, z), opn.at(z, y), m), m); return ret; } MATX &operator+=(const MATX &rhs) { *this = *this + rhs; return *this; } MATX &operator-=(const MATX &rhs) { *this = *this - rhs; return *this; } MATX &operator*=(const MATX &rhs) { *this = *this * rhs; return *this; } const MATX pow(const unsigned long p) const { MATX buff(*this), ret(this->hig, this->wid); ret.set_one(); if (p > 0) for (unsigned long i = 1;; i <<= 1) { if (p & i) ret *= buff; buff *= buff; if (i > (p >> 1)) break; } return ret; } template <class T2> const MATX pow(const unsigned long p, const T2 m) const { MATX buff(*this), ret(this->hig, this->wid); ret.set_one(); if (p > 0) for (unsigned long i = 1;; i <<= 1) { if (p & i) ret = ret.mul(buff, m); buff = buff.mul(buff, m); if (i > (p >> 1)) break; } return ret; } const T at(const unsigned long x, const unsigned long y) const { if (x >= this->hig || y >= this->wid) return 0; return this->data[x * wid + y]; } void show() const { for (unsigned long x = 0; x < this->hig; x++) { for (unsigned long y = 0; y < this->wid; y++) cout << this->at(x, y) << " "; cout << endl; } } void set_one() { for (unsigned long x = 0; x < this->hig; x++) for (unsigned long y = 0; y < this->wid; y++) this->data[x * this->wid + y] = (x == y) ? 1 : 0; } }; template <class T> class Complex { public: T r, i; Complex(T x = 0.0, T y = 0.0) { this->r = x; this->i = y; } Complex operator+(const Complex &opn) const { return Complex(this->r + opn.r, this->i + opn.i); } Complex operator-(const Complex &opn) const { return Complex(this->r - opn.r, this->i - opn.i); } Complex operator*(const Complex &opn) const { return Complex(this->r * opn.r - this->i * opn.i, this->r * opn.i + this->i * opn.r); } }; class MILLERRABIN { private: static const int prime_table[12]; int witness(long long a, long long d, long long s, long long n) { long long r = MODL_POW(a, d, n); if (r == 1 || r == n - 1) return 0; for (int i = 0; i < s - 1; i++) { r = MODL_MUL(r, r, n); if (r == 1) return 1; if (r == n - 1) return 0; } return 1; } public: int test(const long long n) { if (n <= 2LL) return 0; long long p = n - 1LL, s = 0LL; while (!(p & 1)) { p >>= 1; s++; } for (int i = 0; i < 12 && this->prime_table[i] < n; i++) { if (witness(this->prime_table[i], p, s, n)) return 0; } return 1; } }; const int MILLERRABIN::prime_table[12] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}; template <class T> inline int fsign(const T x) { if (x > -eps && x < eps) return 0; return (x < 0.0) ? -1 : 1; } template <class T> class point_t { public: T x, y; point_t() { this->x = 0.0; this->y = 0.0; } point_t(const T _x, const T _y) { this->x = _x; this->y = _y; } point_t operator-(const point_t &rhs) const { return point_t(this->x - rhs.x, this->y - rhs.y); } T operator^(const point_t &rhs) const { return this->x * rhs.y - this->y * rhs.x; } T operator*(const point_t &rhs) const { return this->x * rhs.x + this->y * rhs.y; } T cross(const point_t &p, const point_t &q) const { return (p - *this) ^ (q - *this); } void rotate(double radian) { T x0 = x, y0 = y; T sinr = sin(radian); T cosr = cos(radian); x = x0 * cosr - y0 * sinr; y = x0 * sinr + y0 * cosr; } T dist2(const point_t &lhs, const point_t &rhs) const { return (lhs - rhs) * (lhs - rhs); } T dist2(const point_t &rhs) const { return (*this - rhs) * (*this - rhs); } T dist(const point_t &lhs, const point_t &rhs) const { return sqrt((lhs - rhs) * (lhs - rhs)); } T dist(const point_t &rhs) const { return sqrt((*this - rhs) * (*this - rhs)); } }; template <class T> class segment_t { public: point_t<T> p, q; segment_t() { this->p.x = this->p.y = 0.0; this->q.x = this->q.y = 0.0; } template <class T2> segment_t(const point_t<T2> &_p, const point_t<T2> &_q) { this->p.x = _p.x; this->p.y = _p.y; this->q.x = _q.x; this->q.y = _q.y; } segment_t(const T px, const T py, const T qx, const T qy) { this->p.x = px; this->p.y = py; this->q.x = qx; this->q.y = qy; } T length() const { return this->p.dist(this->q); } T length2() const { return this->p.dist2(this->q); } int contain(const point_t<T> &pnt, const int ignore_endpoint = 0) const { if (ignore_endpoint) { return fsign((this->p - pnt) ^ (this->q - pnt)) == 0 && fsign((pnt.x - this->p.x) * (pnt.x - this->q.x)) < 0 && fsign((pnt.y - this->p.y) * (pnt.y - this->q.y)) < 0; } else { return fsign((this->p - pnt) ^ (this->q - pnt)) == 0 && fsign((pnt.x - this->p.x) * (pnt.x - this->q.x)) <= 0 && fsign((pnt.y - this->p.y) * (pnt.y - this->q.y)) <= 0; } } int intersection(const segment_t &sa, const segment_t &sb, const int ignore_endpoint = 0) const { if (!ignore_endpoint) { if (sa.contain(sb.p) || sa.contain(sb.q) || sb.contain(sa.p) || sb.contain(sa.q)) return 1; } return fsign(sa.p.cross(sa.q, sb.p)) * fsign(sa.p.cross(sa.q, sb.q)) < 0 && fsign(sb.p.cross(sb.q, sa.p)) * fsign(sb.p.cross(sb.q, sa.q)) < 0; } int intersection(const segment_t &rhs, const int ignore_endpoint = 0) const { return this->intersection(*this, rhs, ignore_endpoint); } }; static const int pos0[6] = {0, 1, 4, 5, 8, 9}; static const int pos1[6] = {2, 3, 6, 7, 10, 11}; static const char res[12][12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; double a[3], bst_val; int c[3], bst_pos; inline double type0(const double x, const double y, const double z) { return log(y) * z + log(log(x)); } inline double type1(const double x, const double y, const double z) { return log(y * z) + log(log(x)); } void mainasu_entry() { for (int i = 0; i < 3; i++) c[i] = i; int cnt = 0; bst_val = 1e23; do { double buf; if (a[c[0]] < 1.0 - eps) { buf = type0(1.0 / a[c[0]], a[c[1]], a[c[2]]); if (buf < bst_val - eps || (!fsign(buf - bst_val) && pos0[cnt] < bst_pos)) { bst_val = buf; bst_pos = pos0[cnt]; } buf = type1(1.0 / a[c[0]], a[c[1]], a[c[2]]); if (buf < bst_val - eps || (!fsign(buf - bst_val) && pos1[cnt] < bst_pos)) { bst_val = buf; bst_pos = pos1[cnt]; } } else if (bst_val > -1e23 + eps) { bst_val = -1e23 + eps; bst_pos = pos0[cnt]; } cnt++; } while (next_permutation(c, c + 3)); } void tsuika_entry() { for (int i = 0; i < 3; i++) c[i] = i; int cnt = 0; bst_val = -1e23; bst_pos = -1; do { double buf; if (a[c[0]] > 1.0 + eps) { buf = type0(a[c[0]], a[c[1]], a[c[2]]); if (buf > bst_val + eps || (!fsign(buf - bst_val) && pos0[cnt] < bst_pos)) { bst_val = buf; bst_pos = pos0[cnt]; } buf = type1(a[c[0]], a[c[1]], a[c[2]]); if (buf > bst_val + eps || (!fsign(buf - bst_val) && pos1[cnt] < bst_pos)) { bst_val = buf; bst_pos = pos1[cnt]; } } cnt++; } while (next_permutation(c, c + 3)); } int main() { ios::sync_with_stdio(false); while (cin >> a[0] >> a[1] >> a[2]) { if (a[0] < 1.0 + eps && a[1] < 1.0 + eps && a[2] < 1.0 + eps) { mainasu_entry(); } else { tsuika_entry(); } cout << res[bst_pos] << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int idx, use_pow = 0; double m; double results[12]; double x, y, z; double chain(double a, double b, double c) { if (use_pow) return pow(a, (double)pow(b, c)); if (a <= (double)1.0) return -1000000000; return log10(log10(a)) + c * log10(b); } double parenthesis(double a, double b, double c) { if (use_pow) return pow((double)pow(a, b), c); if (a <= (double)1.0) return -1000000000; return log10(log10(a)) + log10(b) + log10(c); } void output(int idx) { switch (idx) { case 1: { cout << "x^y^z" << endl; break; } case 2: { cout << "x^z^y" << endl; break; } case 3: { cout << "(x^y)^z" << endl; break; } case 4: { cout << "(x^z)^y" << endl; break; } case 5: { cout << "y^x^z" << endl; break; } case 6: { cout << "y^z^x" << endl; break; } case 7: { cout << "(y^x)^z" << endl; break; } case 8: { cout << "(y^z)^x" << endl; break; } case 9: { cout << "z^x^y" << endl; break; } case 10: { cout << "z^y^x" << endl; break; } case 11: { cout << "(z^x)^y" << endl; break; } case 12: { cout << "(z^y)^x" << endl; break; } } } void solve() { results[0] = chain(x, y, z); results[1] = chain(x, z, y); results[2] = parenthesis(x, y, z); results[3] = parenthesis(x, z, y); results[4] = chain(y, x, z); results[5] = chain(y, z, x); results[6] = parenthesis(y, x, z); results[7] = parenthesis(y, z, x); results[8] = chain(z, x, y); results[9] = chain(z, y, x); results[10] = parenthesis(z, x, y); results[11] = parenthesis(z, y, x); m = results[0]; idx = 1; for (int i = 0; i < 12; i++) { if (results[i] - m > 1e-15) { m = results[i]; idx = i + 1; } } output(idx); } int main() { cin >> x >> y >> z; if (x <= 1 && y <= 1 && z <= 1) use_pow = 1; solve(); return 0; }
#include <bits/stdc++.h> using namespace std; double a1(double x, double y, double z) { return pow(y, z) * log(x); } double b1(double x, double y, double z) { return z * log(y) + log(log(x)); } double a2(double x, double z, double y) { return pow(y, z) * log(x); } double b2(double x, double z, double y) { return z * log(y) + log(log(x)); } double a5(double y, double x, double z) { return pow(y, z) * log(x); } double b5(double y, double x, double z) { return z * log(y) + log(log(x)); } double a6(double z, double x, double y) { return pow(y, z) * log(x); } double b6(double z, double x, double y) { return z * log(y) + log(log(x)); } double a9(double y, double z, double x) { return pow(y, z) * log(x); } double b9(double y, double z, double x) { return z * log(y) + log(log(x)); } double a10(double z, double y, double x) { return pow(y, z) * log(x); } double b10(double z, double y, double x) { return z * log(y) + log(log(x)); } double a3(double x, double y, double z) { return z * y * log(x); } double b3(double x, double y, double z) { return log(z * y * log(x)); } double a4(double x, double z, double y) { return z * y * log(x); } double b4(double x, double z, double y) { return log(z * y * log(x)); } double a7(double y, double x, double z) { return z * y * log(x); } double b7(double y, double x, double z) { return log(z * y * log(x)); } double a8(double z, double x, double y) { return z * y * log(x); } double b8(double z, double x, double y) { return log(z * y * log(x)); } double a11(double y, double z, double x) { return z * y * log(x); } double b11(double y, double z, double x) { return log(z * y * log(x)); } double a12(double z, double y, double x) { return z * y * log(x); } double b12(double z, double y, double x) { return log(z * y * log(x)); } double (*fa[])(double, double, double) = {a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12}; double (*fb[])(double, double, double) = {b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11, b12}; const char *s[] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; const double eps = 1e-7; int main() { double x, y, z; scanf("%lf%lf%lf", &x, &y, &z); double (**f)(double, double, double); if (min(x, min(y, z)) > 1) f = fb; else f = fa; double a = -DBL_MAX, b; int ans; for (int i = 0; i < 12; i++) if ((b = f[i](x, y, z)) - a > eps) a = b, ans = i; puts(s[ans]); return 0; }
#include <bits/stdc++.h> using namespace std; void get_a() {} void output() {} int main() { long double x, y, z; long double a[22]; cin >> x >> y >> z; a[1] = log(x) * pow(y, z); a[2] = log(x) * pow(z, y); a[3] = y * z * log(x); a[4] = log(y) * pow(x, z); a[5] = log(y) * pow(z, x); a[6] = x * z * log(y); a[7] = log(z) * pow(x, y); a[8] = log(z) * pow(y, x); a[9] = x * y * log(z); string str[] = {"", "x^y^z\n", "x^z^y\n", "(x^y)^z\n", "y^x^z\n", "y^z^x\n", "(y^x)^z\n", "z^x^y\n", "z^y^x\n", "(z^x)^y\n"}; long double ans = a[1]; int m = 1; for (int i = 2; i < 10; i++) { if (a[i] > ans) { ans = a[i]; m = i; } } cout << str[m]; return 0; }
#include <bits/stdc++.h> const int SZ = 1e5 + 5; using namespace std; int main() { long double x, y, z; cin >> x >> y >> z; string s[12]; vector<long double> v; v.push_back(pow(y, z) * log(x)); s[0] = "x^y^z"; v.push_back(pow(z, y) * log(x)); s[1] = "x^z^y"; v.push_back(z * log(pow(x, y))); s[2] = "(x^y)^z"; v.push_back(y * log(pow(x, z))); s[3] = "(x^z)^y"; v.push_back(pow(x, z) * log(y)); s[4] = "y^x^z"; v.push_back(pow(z, x) * log(y)); s[5] = "y^z^x"; v.push_back(z * log(pow(y, x))); s[6] = "(y^x)^z"; v.push_back(x * log(pow(y, z))); s[7] = "(y^z)^x"; v.push_back(pow(x, y) * log(z)); s[8] = "z^x^y"; v.push_back(pow(y, x) * log(z)); s[9] = "z^y^x"; v.push_back(y * log(pow(z, x))); s[10] = "(z^x)^y"; v.push_back(x * log(pow(z, y))); s[11] = "(z^y)^x"; int idx = 0; for (int i = 1; i < 12; i++) if (v[i] - v[idx] > 1e-9) idx = i; cout << s[idx]; }
#include <bits/stdc++.h> using namespace std; char str[12][10] = { "x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x", }; long double x, y, z; long double mx, t; int pos; void judge(int x) { if (fabs(mx - t) <= 1e-6) return; else if (mx < t) { pos = x; mx = t; } } int main() { cin >> x >> y >> z; pos = 0; mx = pow(y, z) * log(x); t = pow(z, y) * log(x); judge(1); t = z * log(pow(x, y)); judge(2); t = y * log(pow(x, z)); judge(3); t = pow(x, z) * log(y); judge(4); t = pow(z, x) * log(y); judge(5); t = z * log(pow(y, x)); judge(6); t = x * log(pow(y, z)); judge(7); t = pow(x, y) * log(z); judge(8); t = pow(y, x) * log(z); judge(9); t = y * log(pow(z, x)); judge(10); t = x * log(pow(z, y)); judge(11); printf("%s\n", str[pos]); }
#include <bits/stdc++.h> using namespace std; string S[] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int ans; long double Max; void cmp1(long double x, long double y, long double z, int l) { long double tmp = logl(x) * pow(y, z); if (tmp > Max) { Max = tmp; ans = l; } } void cmp2(long double x, long double y, long double z, int l) { long double tmp = logl(x) * y * z; if (tmp > Max) { Max = tmp; ans = l; } } int main() { long double x, y, z; cin >> x >> y >> z; Max = logl(x) * pow(y, z); cmp1(x, z, y, 1); cmp2(x, y, z, 2); cmp1(y, x, z, 4); cmp1(y, z, x, 5); cmp2(y, x, z, 6); cmp1(z, x, y, 8); cmp1(z, y, x, 9); cmp2(z, x, y, 10); cout << S[ans] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long double x, y, z; long double arr[9]; string s[9] = {"x^y^z", "x^z^y", "(x^y)^z", "y^x^z", "y^z^x", "(y^x)^z", "z^x^y", "z^y^x", "(z^x)^y"}; int main(void) { cin >> x >> y >> z; arr[0] = pow(y, z) * log(x); arr[1] = pow(z, y) * log(x); arr[2] = y * z * log(x); arr[3] = pow(x, z) * log(y); arr[4] = pow(z, x) * log(y); arr[5] = x * z * log(y); arr[6] = pow(x, y) * log(z); arr[7] = pow(y, x) * log(z); arr[8] = x * y * log(z); int ind = 0; for (int i = 0; i < 9; i++) { if (arr[i] > arr[ind]) ind = i; } cout << s[ind] << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; int32_t main() { long double x, y, z, s = -10; cin >> x >> y >> z; vector<pair<long double, string>> a(12); a[0].first = pow(y, z) * log(x); a[1].first = pow(z, y) * log(x); a[2].first = a[3].first = (y * z) * log(x); a[4].first = pow(x, z) * log(y); a[5].first = pow(z, x) * log(y); a[6].first = (x * z) * log(y); a[7].first = (x * z) * log(y); a[8].first = pow(x, y) * log(z); a[9].first = pow(y, x) * log(z); a[11].first = a[10].first = (y * x) * log(z); a[0].second = "x^y^z"; a[1].second = "x^z^y"; a[2].second = "(x^y)^z"; a[3].second = "(x^z)^y"; a[4].second = "y^x^z"; a[5].second = "y^z^x"; a[6].second = "(y^x)^z"; a[7].second = "(y^z)^x"; a[8].second = "z^x^y"; a[9].second = "z^y^x"; a[10].second = "(z^x)^y"; a[11].second = "(z^y)^x"; int id = 0; for (int i = 0; i < 12; i++) if (s < a[i].first) { s = a[i].first; id = i; } cout << a[id].second; }
#include <bits/stdc++.h> using namespace std; const int oo = 0x3f3f3f3f; const int Mod = 1e9 + 7; const int maxn = 100000; const long double eps = 1e-12; long double x, y, z; inline bool eq(const long double &x, const long double &y) { return abs(x - y) < eps || abs(x - y) < eps * abs(x); } int main() { { double a, b, c; scanf("%lf%lf%lf", &a, &b, &c); x = a, y = b, z = c; } long double logx = log(x); long double logy = log(y); long double logz = log(z); long double a[11]; a[0] = logx * pow(y, z); a[1] = logx * pow(z, y); a[2] = logx * y * z; a[3] = a[2]; a[4] = logy * pow(x, z); a[5] = logy * pow(z, x); a[6] = logy * x * z; a[7] = a[6]; a[8] = logz * pow(x, y); a[9] = logz * pow(y, x); a[10] = logz * x * y; long double tmp = -1; int ansp = -1; for (int i = 0; i <= 11; i++) if (!eq(a[i], tmp) && a[i] > tmp) { tmp = a[i]; ansp = i; } if (ansp == 0) printf("x^y^z\n"); if (ansp == 1) printf("x^z^y\n"); if (ansp == 2) printf("(x^y)^z\n"); if (ansp == 4) printf("y^x^z\n"); if (ansp == 5) printf("y^z^x\n"); if (ansp == 6) printf("(y^x)^z\n"); if (ansp == 8) printf("z^x^y\n"); if (ansp == 9) printf("z^y^x\n"); if (ansp == 10) printf("(z^x)^y\n"); return 0; }
#include <bits/stdc++.h> int setBit(int N, int pos) { return N = N | (1 << pos); } int resetBit(int N, int pos) { return N = N & ~(1 << pos); } bool checkBit(int N, int pos) { return (bool)(N & (1 << pos)); } using namespace std; long double x, y, z; int main() { string ans = "x^y^z"; while (cin >> x >> y >> z) { long double mx = powl(y, z) * log(x) - 1e-12 - 1e-12; if (powl(y, z) * log(x) > mx + 1e-12) { ans = "x^y^z"; mx = powl(y, z) * log(x); } if (powl(z, y) * log(x) > mx + 1e-12) { ans = "x^z^y"; mx = powl(z, y) * log(x); } if (y * z * log(x) > mx + 1e-12) { ans = "(x^y)^z"; mx = y * z * log(x); } if (powl(x, z) * log(y) > mx + 1e-12) { ans = "y^x^z"; mx = powl(x, z) * log(y); } if (powl(z, x) * log(y) > mx + 1e-12) { ans = "y^z^x"; mx = powl(z, x) * log(y); } if (x * z * log(y) > mx + 1e-12) { ans = "(y^x)^z"; mx = x * z * log(y); } if (powl(x, y) * log(z) > mx + 1e-12) { ans = "z^x^y"; mx = powl(x, y) * log(z); } if (powl(y, x) * log(z) > mx + 1e-12) { ans = "z^y^x"; mx = powl(y, x) * log(z); } if (x * y * log(z) > mx + 1e-12) { ans = "(z^x)^y"; mx = x * y * log(z); } puts(ans.c_str()); } return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = 1000000007; struct Sync_stdio { Sync_stdio() { cin.tie(NULL); ios_base::sync_with_stdio(false); } } _sync_stdio; double EPS = 1e-7; vector<string> v = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; long double solve1(long double a, long double b, long double c) { return pow(b, c) * log(a); } long double solve2(long double a, long double b, long double c) { return c * b * log(a); } void naive(long double a, long double b, long double c) { int idx = 0; long double best = -1e19; for (int i = (0); i < (3); ++i) { if (i == 1) { swap(a, b); } else if (i == 2) { swap(a, c); } if (solve1(a, b, c) > best + EPS) { idx = 0 + i * 4; best = solve1(a, b, c); } if (solve1(a, c, b) > best + EPS) { idx = 1 + i * 4; best = solve1(a, c, b); } if (solve2(a, b, c) > best + EPS) { idx = 2 + i * 4; best = solve2(a, b, c); } if (solve2(a, c, b) > best + EPS) { idx = 3 + i * 4; best = solve2(a, c, b); } } cout << v[idx]; exit(0); } int main() { double a, b, c; cin >> a >> b >> c; naive(a, b, c); }
#include <bits/stdc++.h> using namespace std; const long double eps = 1e-12; inline bool eq(const long double &x, const long double &y) { return abs(x - y) < eps || abs(x - y) < eps * abs(x); } int main() { long double x, y, z; { double a, b, c; scanf("%lf%lf%lf", &a, &b, &c); x = a, y = b, z = c; } long double logx = log(x); long double logy = log(y); long double logz = log(z); long double a[11]; a[0] = logx * pow(y, z); a[1] = logx * pow(z, y); a[2] = logx * y * z; a[3] = a[2]; a[4] = logy * pow(x, z); a[5] = logy * pow(z, x); a[6] = logy * x * z; a[7] = a[6]; a[8] = logz * pow(x, y); a[9] = logz * pow(y, x); a[10] = logz * x * y; long double tmp = -1; int ansp = -1; for (int _n(11), i(0); i < _n; i++) if (!eq(a[i], tmp) && a[i] > tmp) { tmp = a[i]; ansp = i; } if (ansp == 0) printf("x^y^z\n"); if (ansp == 1) printf("x^z^y\n"); if (ansp == 2) printf("(x^y)^z\n"); if (ansp == 4) printf("y^x^z\n"); if (ansp == 5) printf("y^z^x\n"); if (ansp == 6) printf("(y^x)^z\n"); if (ansp == 8) printf("z^x^y\n"); if (ansp == 9) printf("z^y^x\n"); if (ansp == 10) printf("(z^x)^y\n"); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 100005; int INF = 0x3f3f3f3f; long long mod = 1e9 + 7; int main() { string s[13] = { "", "x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x", }; int ans = 1; double x, y, z; double mx = -10000, t; double eps = 1e-9; cin >> x >> y >> z; if (x <= 1 && y <= 1 && z <= 1) { ans = 1; mx = pow(x, pow(y, z)); t = pow(x, pow(z, y)); if (t > mx + eps) { mx = t; ans = 2; } t = pow(pow(x, y), z); if (t > mx + eps) { mx = t; ans = 3; } t = pow(y, pow(x, z)); if (t > mx + eps) { mx = t; ans = 5; } t = pow(y, pow(z, x)); if (t > mx + eps) { mx = t; ans = 6; } t = pow(pow(y, x), z); if (t > mx + eps) { mx = t; ans = 7; } t = pow(z, pow(x, y)); if (t > mx + eps) { mx = t; ans = 9; } t = pow(z, pow(y, x)); if (t > mx + eps) { mx = t; ans = 10; } t = pow(pow(z, x), y); if (t > mx + eps) { mx = t; ans = 11; } } else { if (x > 1) { t = z * log(y) + log(log(x)); if (t > mx + eps) { mx = t; ans = 1; } t = y * log(z) + log(log(x)); if (t > mx + eps) { mx = t; ans = 2; } t = log(y) + log(z) + log(log(x)); if (t > mx + eps) { mx = t; ans = 3; } } if (y > 1) { t = z * log(x) + log(log(y)); if (t > mx + eps) { mx = t; ans = 5; } t = x * log(z) + log(log(y)); if (t > mx + eps) { mx = t; ans = 6; } t = log(x) + log(z) + log(log(y)); if (t > mx + eps) { mx = t; ans = 7; } } if (z > 1) { t = y * log(x) + log(log(z)); if (t > mx + eps) { mx = t; ans = 9; } t = x * log(y) + log(log(z)); if (t > mx + eps) { mx = t; ans = 10; } t = log(x) + log(y) + log(log(z)); if (t > mx + eps) { mx = t; ans = 11; } } } cout << s[ans] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const char s[12][10] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int main() { long double a[12]; long double x, y, z; cin >> x >> y >> z; a[0] = pow(y, z) * log(x); a[1] = pow(z, y) * log(x); a[2] = a[3] = y * z * log(x); a[4] = pow(x, z) * log(y); a[5] = pow(z, x) * log(y); a[6] = a[7] = x * z * log(y); a[8] = pow(x, y) * log(z); a[9] = pow(y, x) * log(z); a[10] = a[11] = x * y * log(z); int pos = 0; for (int i = 1; i < 12; i++) if (a[i] > a[pos]) pos = i; printf("%s\n", s[pos]); return 0; }
#include <bits/stdc++.h> using namespace std; long double x, y, z; vector<pair<long double, int> > V; void Print(int x) { switch (x) { case 1: printf("x^y^z\n"); break; case 2: printf("x^z^y\n"); break; case 3: printf("(x^y)^z\n"); break; case 5: printf("y^x^z\n"); break; case 6: printf("y^z^x\n"); break; case 7: printf("(y^x)^z\n"); break; case 9: printf("z^x^y"); break; case 10: printf("z^y^x"); break; case 11: printf("(z^x)^y"); break; } } int main() { cin >> x >> y >> z; long double mx = max(max(x, y), z); if (mx > 1.0l) { if (x > 1.0l) { V.push_back(pair<long double, int>(-(z * log(y) + log(log(x))), 1)); V.push_back(pair<long double, int>(-(y * log(z) + log(log(x))), 2)); V.push_back(pair<long double, int>(-(log(y * z) + log(log(x))), 3)); } if (y > 1.0l) { V.push_back(pair<long double, int>(-(z * log(x) + log(log(y))), 5)); V.push_back(pair<long double, int>(-(x * log(z) + log(log(y))), 6)); V.push_back(pair<long double, int>(-(log(x * z) + log(log(y))), 7)); } if (z > 1.0l) { V.push_back(pair<long double, int>(-(y * log(x) + log(log(z))), 9)); V.push_back(pair<long double, int>(-(x * log(y) + log(log(z))), 10)); V.push_back(pair<long double, int>(-(log(x * y) + log(log(z))), 11)); } sort(V.begin(), V.end()); Print(V[0].second); return 0; } if (mx == 1.0l) { if (x == 1.0l) Print(1); else if (y == 1.0l) Print(5); else if (z == 1.0l) Print(9); return 0; } V.push_back(pair<long double, int>((z * log(y) + log(-log(x))), 1)); V.push_back(pair<long double, int>((y * log(z) + log(-log(x))), 2)); V.push_back(pair<long double, int>((log(y * z) + log(-log(x))), 3)); V.push_back(pair<long double, int>((z * log(x) + log(-log(y))), 5)); V.push_back(pair<long double, int>((x * log(z) + log(-log(y))), 6)); V.push_back(pair<long double, int>((log(x * z) + log(-log(y))), 7)); V.push_back(pair<long double, int>((y * log(x) + log(-log(z))), 9)); V.push_back(pair<long double, int>((x * log(y) + log(-log(z))), 10)); V.push_back(pair<long double, int>((log(x * y) + log(-log(z))), 11)); sort(V.begin(), V.end()); Print(V[0].second); return 0; return 0; }
#include <bits/stdc++.h> const int dx[] = {1, 0, -1, 0}; const int dy[] = {0, 1, 0, -1}; using namespace std; string ans[12]; long double eps = 1e-7; int main() { cin.tie(0); ios::sync_with_stdio(false); ans[0] = "x^y^z", ans[1] = "x^z^y", ans[2] = "(x^y)^z", ans[3] = "(x^z)^y"; ans[4] = "y^x^z", ans[5] = "y^z^x", ans[6] = "(y^x)^z", ans[7] = "(y^z)^x"; ans[8] = "z^x^y", ans[9] = "z^y^x", ans[10] = "(z^x)^y", ans[11] = "(z^y)^x"; long double x, y, z; cin >> x >> y >> z; vector<long double> num(12); num[0] = powl(y, z) * log(x); num[1] = powl(z, y) * log(x); num[2] = y * z * log(x); num[4] = powl(x, z) * log(y); num[5] = powl(z, x) * log(y); num[6] = x * z * log(y); num[8] = powl(x, y) * log(z); num[9] = powl(y, x) * log(z); num[10] = x * y * log(z); int index = 0; for (int i = 1; i < 12; i++) { if (i % 4 == 3) continue; if (num[index] < num[i]) index = i; } cout << ans[index] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int INF = 1e9; const long double EPS = 1e-8; bool comp(pair<long double, int> p1, pair<long double, int> p2) { if (p1.first != p2.first) return p1.first < p2.first; return p1.second > p2.second; } int main() { double x, y, z; cin >> x >> y >> z; string ans[] = {"x^y^z", "x^z^y", "(x^y)^z", "y^x^z", "y^z^x", "(y^x)^z", "z^x^y", "z^y^x", "(z^x)^y"}; vector<pair<long double, int>> val(9); if (x > 1.0 || y > 1.0 || z > 1.0) { if (x > 1.0) { val[0] = make_pair(z * log(y) + log(log(x)), 0); val[1] = make_pair(y * log(z) + log(log(x)), 1); val[2] = make_pair(log(y * z) + log(log(x)), 2); } else { val[0] = make_pair(-INF, 0); val[1] = make_pair(-INF, 1); val[2] = make_pair(-INF, 2); } if (y > 1.0) { val[3] = make_pair(z * log(x) + log(log(y)), 3); val[4] = make_pair(x * log(z) + log(log(y)), 4); val[5] = make_pair(log(z * x) + log(log(y)), 5); } else { val[3] = make_pair(-INF, 3); val[4] = make_pair(-INF, 4); val[5] = make_pair(-INF, 5); } if (z > 1.0) { val[6] = make_pair(y * log(x) + log(log(z)), 6); val[7] = make_pair(x * log(y) + log(log(z)), 7); val[8] = make_pair(log(y * x) + log(log(z)), 8); } else { val[6] = make_pair(-INF, 6); val[7] = make_pair(-INF, 7); val[8] = make_pair(-INF, 8); } } else { val[0] = make_pair(pow(y, z) * log(x), 0); val[1] = make_pair(pow(z, y) * log(x), 1); val[2] = make_pair(y * z * log(x), 2); val[3] = make_pair(pow(x, z) * log(y), 3); val[4] = make_pair(pow(z, x) * log(y), 4); val[5] = make_pair(x * z * log(y), 5); val[6] = make_pair(pow(x, y) * log(z), 6); val[7] = make_pair(pow(y, x) * log(z), 7); val[8] = make_pair(x * y * log(z), 8); } sort((val).begin(), (val).end(), comp); cout << ans[val[8].second] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; double ta; long double x[3], eps = 1e-10, y, z, w; int main() { for (int a = 0; a < 3; a++) { scanf("%lf", &ta); x[a] = ta; } y = pow(x[1], x[2]) * log2l(x[0]); z = 0; w = pow(x[2], x[1]) * log2l(x[0]); if (w > y + eps) { y = w; z = 1; } w = x[1] * x[2] * log2l(x[0]); if (w > y + eps) { y = w; z = 2; } w = pow(x[0], x[2]) * log2l(x[1]); if (w > y + eps) { y = w; z = 4; } w = pow(x[2], x[0]) * log2l(x[1]); if (w > y + eps) { y = w; z = 5; } w = x[0] * x[2] * log2l(x[1]); if (w > y + eps) { y = w; z = 6; } w = pow(x[0], x[1]) * log2l(x[2]); if (w > y + eps) { y = w; z = 8; } w = pow(x[1], x[0]) * log2l(x[2]); if (w > y + eps) { y = w; z = 9; } w = x[0] * x[1] * log2l(x[2]); if (w > y + eps) { y = w; z = 10; } if (z == 0) printf("x^y^z"); if (z == 1) printf("x^z^y"); if (z == 2) printf("(x^y)^z"); if (z == 4) printf("y^x^z"); if (z == 5) printf("y^z^x"); if (z == 6) printf("(y^x)^z"); if (z == 8) printf("z^x^y"); if (z == 9) printf("z^y^x"); if (z == 10) printf("(z^x)^y"); return 0; }
#include <bits/stdc++.h> using namespace std; struct node { int id; string n; double x; bool operator<(const node& tt) const { if (x == tt.x) return id < tt.id; return x < tt.x; } } t[15]; double x, y, z; void solve1() { int cc = 0; if (x >= 1) { t[cc].id = cc; t[cc].n = "x^y^z"; t[cc++].x = z * log(y) + log(log(x)); t[cc].id = cc; t[cc].n = "x^z^y"; t[cc++].x = y * log(z) + log(log(x)); t[cc].id = cc; t[cc].n = "(x^y)^z"; t[cc++].x = log(z) + log(y) + log(log(x)); } if (y >= 1) { t[cc].id = cc; t[cc].n = "y^x^z"; t[cc++].x = z * log(x) + log(log(y)); t[cc].id = cc; t[cc].n = "y^z^x"; t[cc++].x = x * log(z) + log(log(y)); t[cc].id = cc; t[cc].n = "(y^x)^z"; t[cc++].x = log(x) + log(z) + log(log(y)); } if (z >= 1) { t[cc].id = cc; t[cc].n = "z^x^y"; t[cc++].x = y * log(x) + log(log(z)); t[cc].id = cc; t[cc].n = "z^y^x"; t[cc++].x = x * log(y) + log(log(z)); t[cc].id = cc; t[cc].n = "(z^x)^y"; t[cc++].x = log(x) + log(y) + log(log(z)); } sort(t, t + cc); --cc; --cc; while (cc >= 0 && t[cc].x == t[cc + 1].x) --cc; if (t[cc].x != t[cc + 1].x) ++cc; printf("%s\n", t[cc].n.c_str()); } void solve2() { int cc = 0; t[cc].id = cc; t[cc].n = "x^y^z"; t[cc++].x = z * log(y) + log(log(1 / x)); t[cc].id = cc; t[cc].n = "x^z^y"; t[cc++].x = y * log(z) + log(log(1 / x)); t[cc].id = cc; t[cc].n = "(x^y)^z"; t[cc++].x = log(z) + log(y) + log(log(1 / x)); t[cc].id = cc; t[cc].n = "y^x^z"; t[cc++].x = z * log(x) + log(log(1 / y)); t[cc].id = cc; t[cc].n = "y^z^x"; t[cc++].x = x * log(z) + log(log(1 / y)); t[cc].id = cc; t[cc].n = "(y^x)^z"; t[cc++].x = log(x) + log(z) + log(log(1 / y)); t[cc].id = cc; t[cc].n = "z^x^y"; t[cc++].x = y * log(x) + log(log(1 / z)); t[cc].id = cc; t[cc].n = "z^y^x"; t[cc++].x = x * log(y) + log(log(1 / z)); t[cc].id = cc; t[cc].n = "(z^x)^y"; t[cc++].x = log(x) + log(y) + log(log(1 / z)); sort(t, t + cc); printf("%s\n", t[0].n.c_str()); } int main() { scanf("%lf%lf%lf", &x, &y, &z); if (x < 1 && y < 1 && z < 1) solve2(); else solve1(); return 0; }
#include <bits/stdc++.h> using namespace std; long double x, y, z; long double num[50]; char s[15][15] = {" ", "x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int main() { while (cin >> x >> y >> z) { long double maxn = -1; char ans[15]; num[1] = pow(y, z) * log(x); num[2] = pow(z, y) * log(x); num[3] = y * z * log(x); num[4] = y * z * log(x); num[5] = pow(x, z) * log(y); num[6] = pow(z, x) * log(y); num[7] = x * z * log(y); num[8] = x * z * log(y); num[9] = pow(x, y) * log(z); num[10] = pow(y, x) * log(z); num[11] = x * y * log(z); num[12] = x * y * log(z); for (int i = 1; i <= 12; i++) { if (num[i] > maxn) { maxn = num[i]; strcpy(ans, s[i]); } } cout << ans << endl; } }
#include <bits/stdc++.h> using namespace std; string s[12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; long double ans[15]; int main() { long double x, y, z; cin >> x >> y >> z; long double xx = logl(x); long double yy = logl(y); long double zz = logl(z); ans[1] = xx * powl(y, z); ans[2] = xx * powl(z, y); ans[3] = xx * y * z; ans[4] = xx * y * z; ans[5] = yy * powl(x, z); ans[6] = yy * powl(z, x); ans[7] = yy * x * z; ans[8] = yy * x * z; ans[9] = zz * powl(x, y); ans[10] = zz * powl(y, x); ans[11] = zz * x * y; ans[12] = zz * y * x; int j = 1; long double sum = ans[1]; for (int i = 1; i <= 12; i++) { if (sum < ans[i]) { sum = ans[i]; j = i; } } cout << s[j - 1] << endl; }
#include <bits/stdc++.h> using namespace std; int main() { long double x, y, z; cin >> x >> y >> z; string s[12]; s[0] = "x^y^z", s[1] = "x^z^y", s[2] = "(x^y)^z", s[3] = "(x^z)^y"; s[4] = "y^x^z", s[5] = "y^z^x", s[6] = "(y^x)^z", s[7] = "(y^z)^x"; s[8] = "z^x^y", s[9] = "z^y^x", s[10] = "(z^x)^y", s[11] = "(z^y)^x"; long double a[12]; long double lx = log(x); long double ly = log(y); long double lz = log(z); a[0] = lx * pow(y, z); a[1] = lx * pow(z, y); a[2] = lx * y * z; a[3] = a[2]; a[4] = ly * pow(x, z); a[5] = ly * pow(z, x); a[6] = ly * x * z; a[7] = a[6]; a[8] = lz * pow(x, y); a[9] = lz * pow(y, x); a[10] = lz * x * y; a[11] = a[10]; long double max = a[0]; int idx = 0; for (int i = 1; i < 12; i++) { if (a[i] > max) { max = a[i]; idx = i; } } cout << s[idx] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const long double eps = 1e-8; long double a[12]; char w[12][10] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; bool isEqual(long double a, long double b) { return fabs(a - b) < eps; } int cmp(long double a, long double b) { if (isEqual(a, b)) return 0; if (a < b) return -1; return 1; } int main() { long double x, y, z; cin >> x >> y >> z; a[0] = pow(y, z) * log(x); a[1] = pow(z, y) * log(x); a[2] = a[3] = y * z * log(x); a[4] = pow(x, z) * log(y); a[5] = pow(z, x) * log(y); a[6] = a[7] = x * z * log(y); a[8] = pow(x, y) * log(z); a[9] = pow(y, x) * log(z); a[10] = a[11] = x * y * log(z); int pos = 0; for (int i = 1; i < 12; i++) { if (cmp(a[i], a[pos]) > 0) pos = i; } printf("%s\n", w[pos]); return 0; }
#include <bits/stdc++.h> using namespace std; template <typename Arg1> void __f(const char* name, Arg1&& arg1) { cerr << name << " : " << arg1 << std::endl; } template <typename Arg1, typename... Args> void __f(const char* names, Arg1&& arg1, Args&&... args) { const char* comma = strchr(names + 1, ','); cerr.write(names, comma - names) << " : " << arg1 << " | "; __f(comma + 1, args...); } long double x, y, z, ans = -1 * (1e9); string out[12] = {"x^y^z", "x^z^y", "(x^y)^z", "(x^z)^y", "y^x^z", "y^z^x", "(y^x)^z", "(y^z)^x", "z^x^y", "z^y^x", "(z^x)^y", "(z^y)^x"}; int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cin >> x >> y >> z; int pos = -1; if (log(x) * pow(y, z) > ans) { ans = log(x) * pow(y, z); pos = 0; } if (log(x) * pow(z, y) > ans) { ans = log(x) * pow(z, y); pos = 1; } if (log(x) * y * z > ans) { ans = log(x) * y * z; pos = 2; } if (log(x) * z * y > ans) { ans = log(x) * z * y; pos = 2; } if (log(y) * pow(x, z) > ans) { ans = log(y) * pow(x, z); pos = 4; } if (log(y) * pow(z, x) > ans) { ans = log(y) * pow(z, x); pos = 5; } if (log(y) * x * z > ans) { ans = log(y) * x * z; pos = 6; } if (log(y) * x * z > ans) { ans = log(y) * x * z; pos = 6; } if (log(z) * pow(x, y) > ans) { ans = log(z) * pow(x, y); pos = 8; } if (log(z) * pow(y, x) > ans) { ans = log(z) * pow(y, x); pos = 9; } if (log(z) * x * y > ans) { ans = log(y) * x * y; pos = 10; } if (log(z) * x * y > ans) { ans = log(y) * x * y; pos = 10; } cout << out[pos] << endl; return 0; }