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jointattack.cpp
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#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
struct rat;
bool operator<(const rat& x, const rat& y);
rat operator*(rat r1, rat r2);
rat operator*(rat r1, ll i);
rat operator/(rat r1, rat r2);
rat operator/(rat r1, ll i);
rat operator+(rat r1, rat r2);
rat operator+(rat r1, ll i);
rat operator-(rat r1, rat r2);
rat operator-(rat r1, ll i);
rat perpendicular(rat r);
rat abs(rat r);
rat neg(rat r);
void simplify(rat& r);
struct rat {
ll top;
ll bot;
rat(ll l) {
top = l;
bot = 1;
};
rat(ll a, ll b) {
top = a;
bot = b;
}
};
bool operator<(const rat& x, const rat& y) {
return tie(x.top, x.bot) < tie(y.top, y.bot);
}
void simplify(rat& r) {
ll gcd = __gcd(r.top, r.bot);
r.top /= gcd;
r.bot /= gcd;
if(r.bot < 0) {
r.top *= -1;
r.bot *= -1;
}
if(r.top == 0) {
r.bot = 1;
}
if(r.bot == 0) {
r.top = 1;
}
}
rat operator*(rat r1, rat r2) {
simplify(r1);
simplify(r2);
rat ret = {r1.top * r2.top, r1.bot * r2.bot};
simplify(ret);
return ret;
}
rat operator*(rat r1, ll i) {
simplify(r1);
rat ret = {r1.top * i, r1.bot};
simplify(ret);
return ret;
}
rat operator/(rat r1, rat r2) {
simplify(r1);
simplify(r2);
rat ret = {r1.top * r2.bot, r1.bot * r2.top};
simplify(ret);
return ret;
}
rat operator/(rat r1, ll i) {
simplify(r1);
rat ret = {r1.top, r1.bot * i};
simplify(ret);
return ret;
}
rat operator+(rat r1, rat r2) {
simplify(r1);
simplify(r2);
ll bot1 = r1.bot;
ll bot2 = r2.bot;
r1.top *= bot2;
r1.bot *= bot2;
r2.top *= bot1;
r2.bot *= bot2;
rat r = {r1.top + r2.top, r1.bot};
simplify(r);
return r;
}
rat operator+(rat r1, ll i) {
simplify(r1);
rat ret = {r1.top + (i * r1.bot), r1.bot};
simplify(ret);
return ret;
}
rat operator-(rat r1, rat r2) {
simplify(r1);
simplify(r2);
ll bot1 = r1.bot;
ll bot2 = r2.bot;
r1.top *= bot2;
r1.bot *= bot2;
r2.top *= bot1;
r2.bot *= bot2;
rat r = {r1.top - r2.top, r1.bot};
simplify(r);
return r;
}
rat operator-(rat r1, ll i) {
simplify(r1);
rat ret = {r1.top - (i * r1.bot), r1.bot};
simplify(ret);
return ret;
}
rat perpendicular(rat r) {
simplify(r);
rat ret = {-r.bot, r.top};
simplify(ret);
return ret;
}
rat abs(rat r) {
simplify(r);
if(r.top < 0) {
r.top *= -1;
}
simplify(r);
return r;
}
rat neg(rat r) {
simplify(r);
r.top *= -1;
simplify(r);
return r;
}
ostream& operator<<(ostream& o, const rat& r) {
return o << r.top << "/" << r.bot;
}
int main() {
int terms;
cin >> terms;
vector<int> v(terms);
for(auto& i : v) cin >> i;
rat ans = rat(v[terms-1]);
rat one = rat(1,1);
for(int i = terms-2; i >= 0; i--) {
ans = rat(v[i]) + (one / ans);
}
cout << ans << endl;
}