#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
const int MOD = 1000000007;
const ll INF = 1e18;
const int MX = 100001;
constexpr int base = 1000000000;
constexpr int base_digits = 9;
struct bigint {
// value == 0 is represented by empty z
vector<int> z; // digits
// sign == 1 <==> value >= 0
// sign == -1 <==> value < 0
int sign;
bigint() : sign(1) {
}
bigint(long long v) {
*this = v;
}
bigint &operator=(long long v) {
sign = v < 0 ? -1 : 1;
v *= sign;
z.clear();
for (; v > 0; v = v / base)
z.push_back((int) (v % base));
return *this;
}
bigint(const string &s) {
read(s);
}
bigint &operator+=(const bigint &other) {
if (sign == other.sign) {
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
if (i == z.size())
z.push_back(0);
z[i] += carry + (i < other.z.size() ? other.z[i] : 0);
carry = z[i] >= base;
if (carry)
z[i] -= base;
}
} else if (other != 0 /* prevent infinite loop */) {
*this -= -other;
}
return *this;
}
friend bigint operator+(bigint a, const bigint &b) {
return a += b;
}
bigint &operator-=(const bigint &other) {
if (sign == other.sign) {
if (sign == 1 && *this >= other || sign == -1 && *this <= other) {
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
z[i] -= carry + (i < other.z.size() ? other.z[i] : 0);
carry = z[i] < 0;
if (carry)
z[i] += base;
}
trim();
} else {
*this = other - *this;
this->sign = -this->sign;
}
} else {
*this += -other;
}
return *this;
}
friend bigint
operator-(bigint a, const bigint &b) {
return a -= b;
}
bigint &operator*=(int v) {
if (v < 0)
sign = -sign, v = -v;
for (int i = 0, carry = 0; i < z.size() || carry; ++i) {
if (i == z.size())
z.push_back(0);
long long cur = (long long) z[i] * v + carry;
carry = (int) (cur / base);
z[i] = (int) (cur % base);
}
trim();
return *this;
}
bigint operator*(int v) const {
return bigint(*this) *= v;
}
friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
int norm = base / (b1.z.back() + 1);
bigint a = a1.abs() * norm;
bigint b = b1.abs() * norm;
bigint q, r;
q.z.resize(a.z.size());
for (int i = (int) a.z.size() - 1; i >= 0; i--) {
r *= base;
r += a.z[i];
int s1 = b.z.size() < r.z.size() ? r.z[b.z.size()] : 0;
int s2 = b.z.size() - 1 < r.z.size() ? r.z[b.z.size() - 1] : 0;
int d = (int) (((long long) s1 * base + s2) / b.z.back());
r -= b * d;
while (r < 0)
r += b, --d;
q.z[i] = d;
}
q.sign = a1.sign * b1.sign;
r.sign = a1.sign;
q.trim();
r.trim();
return {q, r / norm};
}
friend bigint sqrt(const bigint &a1) {
bigint a = a1;
while (a.z.empty() || a.z.size() % 2 == 1)
a.z.push_back(0);
int n = a.z.size();
int firstDigit = (int) ::sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
int norm = base / (firstDigit + 1);
a *= norm;
a *= norm;
while (a.z.empty() || a.z.size() % 2 == 1)
a.z.push_back(0);
bigint r = (long long) a.z[n - 1] * base + a.z[n - 2];
firstDigit = (int) ::sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
int q = firstDigit;
bigint res;
for (int j = n / 2 - 1; j >= 0; j--) {
for (;; --q) {
bigint r1 = (r - (res * 2 * base + q) * q) * base * base +
(j > 0 ? (long long) a.z[2 * j - 1] * base + a.z[2 * j - 2] : 0);
if (r1 >= 0) {
r = r1;
break;
}
}
res *= base;
res += q;
if (j > 0) {
int d1 = res.z.size() + 2 < r.z.size() ? r.z[res.z.size() + 2] : 0;
int d2 = res.z.size() + 1 < r.z.size() ? r.z[res.z.size() + 1] : 0;
int d3 = res.z.size() < r.z.size() ? r.z[res.z.size()] : 0;
q = (int) (((long long) d1 * base * base + (long long) d2 * base + d3) / (firstDigit * 2));
}
}
res.trim();
return res / norm;
}
bigint operator/(const bigint &v) const {
return divmod(*this, v).first;
}
bigint operator%(const bigint &v) const {
return divmod(*this, v).second;
}
bigint &operator/=(int v) {
if (v < 0)
sign = -sign, v = -v;
for (int i = (int) z.size() - 1, rem = 0; i >= 0; --i) {
long long cur = z[i] + rem * (long long) base;
z[i] = (int) (cur / v);
rem = (int) (cur % v);
}
trim();
return *this;
}
bigint operator/(int v) const {
return bigint(*this) /= v;
}
int operator%(int v) const {
if (v < 0)
v = -v;
int m = 0;
for (int i = (int) z.size() - 1; i >= 0; --i)
m = (int) ((z[i] + m * (long long) base) % v);
return m * sign;
}
bigint &operator*=(const bigint &v) {
*this = *this * v;
return *this;
}
bigint &operator/=(const bigint &v) {
*this = *this / v;
return *this;
}
bool operator<(const bigint &v) const {
if (sign != v.sign)
return sign < v.sign;
if (z.size() != v.z.size())
return z.size() * sign < v.z.size() * v.sign;
for (int i = (int) z.size() - 1; i >= 0; i--)
if (z[i] != v.z[i])
return z[i] * sign < v.z[i] * sign;
return false;
}
bool operator>(const bigint &v) const {
return v < *this;
}
bool operator<=(const bigint &v) const {
return !(v < *this);
}
bool operator>=(const bigint &v) const {
return !(*this < v);
}
bool operator==(const bigint &v) const {
return !(*this < v) && !(v < *this);
}
bool operator!=(const bigint &v) const {
return *this < v || v < *this;
}
void trim() {
while (!z.empty() && z.back() == 0)
z.pop_back();
if (z.empty())
sign = 1;
}
bool isZero() const {
return z.empty();
}
friend bigint operator-(bigint v) {
if (!v.z.empty())
v.sign = -v.sign;
return v;
}
bigint abs() const {
return sign == 1 ? *this : -*this;
}
long long longValue() const {
long long res = 0;
for (int i = (int) z.size() - 1; i >= 0; i--)
res = res * base + z[i];
return res * sign;
}
friend bigint gcd(const bigint &a, const bigint &b) {
return b.isZero() ? a : gcd(b, a % b);
}
friend bigint lcm(const bigint &a, const bigint &b) {
return a / gcd(a, b) * b;
}
void read(const string &s) {
sign = 1;
z.clear();
int pos = 0;
while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) {
if (s[pos] == '-')
sign = -sign;
++pos;
}
for (int i = (int) s.size() - 1; i >= pos; i -= base_digits) {
int x = 0;
for (int j = max(pos, i - base_digits + 1); j <= i; j++)
x = x * 10 + s[j] - '0';
z.push_back(x);
}
trim();
}
friend istream &operator>>(istream &stream, bigint &v) {
string s;
stream >> s;
v.read(s);
return stream;
}
friend ostream &operator<<(ostream &stream, const bigint &v) {
if (v.sign == -1)
stream << '-';
stream << (v.z.empty() ? 0 : v.z.back());
for (int i = (int) v.z.size() - 2; i >= 0; --i)
stream << setw(base_digits) << setfill('0') << v.z[i];
return stream;
}
static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
vector<long long> p(max(old_digits, new_digits) + 1);
p[0] = 1;
for (int i = 1; i < p.size(); i++)
p[i] = p[i - 1] * 10;
vector<int> res;
long long cur = 0;
int cur_digits = 0;
for (int v : a) {
cur += v * p[cur_digits];
cur_digits += old_digits;
while (cur_digits >= new_digits) {
res.push_back(int(cur % p[new_digits]));
cur /= p[new_digits];
cur_digits -= new_digits;
}
}
res.push_back((int) cur);
while (!res.empty() && res.back() == 0)
res.pop_back();
return res;
}
typedef vector<long long> vll;
static vll karatsubaMultiply(const vll &a, const vll &b) {
int n = a.size();
vll res(n + n);
if (n <= 32) {
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
res[i + j] += a[i] * b[j];
return res;
}
int k = n >> 1;
vll a1(a.begin(), a.begin() + k);
vll a2(a.begin() + k, a.end());
vll b1(b.begin(), b.begin() + k);
vll b2(b.begin() + k, b.end());
vll a1b1 = karatsubaMultiply(a1, b1);
vll a2b2 = karatsubaMultiply(a2, b2);
for (int i = 0; i < k; i++)
a2[i] += a1[i];
for (int i = 0; i < k; i++)
b2[i] += b1[i];
vll r = karatsubaMultiply(a2, b2);
for (int i = 0; i < a1b1.size(); i++)
r[i] -= a1b1[i];
for (int i = 0; i < a2b2.size(); i++)
r[i] -= a2b2[i];
for (int i = 0; i < r.size(); i++)
res[i + k] += r[i];
for (int i = 0; i < a1b1.size(); i++)
res[i] += a1b1[i];
for (int i = 0; i < a2b2.size(); i++)
res[i + n] += a2b2[i];
return res;
}
bigint operator*(const bigint &v) const {
vector<int> a6 = convert_base(this->z, base_digits, 6);
vector<int> b6 = convert_base(v.z, base_digits, 6);
vll a(a6.begin(), a6.end());
vll b(b6.begin(), b6.end());
while (a.size() < b.size())
a.push_back(0);
while (b.size() < a.size())
b.push_back(0);
while (a.size() & (a.size() - 1))
a.push_back(0), b.push_back(0);
vll c = karatsubaMultiply(a, b);
bigint res;
res.sign = sign * v.sign;
for (int i = 0, carry = 0; i < c.size(); i++) {
long long cur = c[i] + carry;
res.z.push_back((int) (cur % 1000000));
carry = (int) (cur / 1000000);
}
res.z = convert_base(res.z, 6, base_digits);
res.trim();
return res;
}
};
int main() {
ios_base::sync_with_stdio(0); cin.tie(0);
bigint s; cin >> s;
bigint z = sqrt(s*2);
while ((z-1)*z/2 >= s) z -= 1;
while (z*(z+1)/2 < s) z += 1;
cout << z*z-(z*(z+1)/2-s)*2;
}
/* Look for:
* the exact constraints (multiple sets are too slow for n=10^6 :( )
* special cases (n=1?)
* overflow (ll vs int?)
* array bounds
*/
Compilation message
oddeven.cpp: In member function 'bigint& bigint::operator+=(const bigint&)':
oddeven.cpp:77:42: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
~~^~~~~~~~~~~~~~~~
oddeven.cpp:78:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
if (i == z.size())
~~^~~~~~~~~~~
oddeven.cpp:80:36: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
z[i] += carry + (i < other.z.size() ? other.z[i] : 0);
~~^~~~~~~~~~~~~~~~
oddeven.cpp: In member function 'bigint& bigint::operator-=(const bigint&)':
oddeven.cpp:97:27: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
if (sign == 1 && *this >= other || sign == -1 && *this <= other) {
~~~~~~~~~~^~~~~~~~~~~~~~~~~
oddeven.cpp:98:46: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
~~^~~~~~~~~~~~~~~~
oddeven.cpp:99:40: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
z[i] -= carry + (i < other.z.size() ? other.z[i] : 0);
~~^~~~~~~~~~~~~~~~
oddeven.cpp: In member function 'bigint& bigint::operator*=(int)':
oddeven.cpp:124:38: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0, carry = 0; i < z.size() || carry; ++i) {
~~^~~~~~~~~~
oddeven.cpp:125:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
if (i == z.size())
~~^~~~~~~~~~~
oddeven.cpp: In member function 'void bigint::read(const string&)':
oddeven.cpp:322:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) {
~~~~^~~~~~~~~~
oddeven.cpp: In static member function 'static std::vector<int> bigint::convert_base(const std::vector<int>&, int, int)':
oddeven.cpp:355:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 1; i < p.size(); i++)
~~^~~~~~~~~~
oddeven.cpp: In static member function 'static bigint::vll bigint::karatsubaMultiply(const vll&, const vll&)':
oddeven.cpp:402:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0; i < a1b1.size(); i++)
~~^~~~~~~~~~~~~
oddeven.cpp:404:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0; i < a2b2.size(); i++)
~~^~~~~~~~~~~~~
oddeven.cpp:407:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0; i < r.size(); i++)
~~^~~~~~~~~~
oddeven.cpp:409:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0; i < a1b1.size(); i++)
~~^~~~~~~~~~~~~
oddeven.cpp:411:27: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0; i < a2b2.size(); i++)
~~^~~~~~~~~~~~~
oddeven.cpp: In member function 'bigint bigint::operator*(const bigint&) const':
oddeven.cpp:430:38: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
for (int i = 0, carry = 0; i < c.size(); i++) {
~~^~~~~~~~~~
| # |
결과 |
실행 시간 |
메모리 |
Grader output |
| 1 |
Correct |
3 ms |
376 KB |
Output is correct |
| 2 |
Correct |
2 ms |
488 KB |
Output is correct |
| 3 |
Correct |
2 ms |
728 KB |
Output is correct |
| 4 |
Correct |
2 ms |
728 KB |
Output is correct |
| 5 |
Correct |
2 ms |
784 KB |
Output is correct |
| 6 |
Correct |
2 ms |
788 KB |
Output is correct |
| 7 |
Correct |
2 ms |
912 KB |
Output is correct |
| 8 |
Correct |
2 ms |
916 KB |
Output is correct |
| 9 |
Correct |
2 ms |
916 KB |
Output is correct |
| 10 |
Correct |
2 ms |
916 KB |
Output is correct |
| 11 |
Correct |
2 ms |
916 KB |
Output is correct |
| 12 |
Correct |
3 ms |
916 KB |
Output is correct |
| 13 |
Correct |
3 ms |
916 KB |
Output is correct |
| 14 |
Correct |
3 ms |
916 KB |
Output is correct |
| 15 |
Correct |
3 ms |
916 KB |
Output is correct |
| 16 |
Correct |
3 ms |
916 KB |
Output is correct |
| 17 |
Correct |
3 ms |
916 KB |
Output is correct |
| 18 |
Correct |
3 ms |
916 KB |
Output is correct |
| 19 |
Correct |
2 ms |
916 KB |
Output is correct |
| 20 |
Correct |
3 ms |
920 KB |
Output is correct |
| 21 |
Correct |
3 ms |
924 KB |
Output is correct |
| 22 |
Correct |
4 ms |
928 KB |
Output is correct |
