CodeForces 903D Almost Difference

题目描述

Let's denote a function

You are given an array $d(a_{i},a_{j})d(ai,aj) over all pairs (i,j)(i,j) such that 1<=i<=j<=n1<=i<=j<=n .$

输入输出格式

输入格式：

The first line contains one integer

The second line contains $a_{1}a1 , a_{2}a2 , ..., a_{n}an ( 1<=a_{i}<=10^{9}1<=ai<=109 ) — elements of the array.$

输出格式：

Print one integer — the sum of $d(a_{i},a_{j})d(ai,aj) over all pairs (i,j)(i,j) such that 1<=i<=j<=n1<=i<=j<=n .$

输入输出样例

输入样例#1：

5
1 2 3 1 3

输出样例#1：

输入样例#2：

4
6 6 5 5

输出样例#2：

输入样例#3：

4
6 6 4 4

输出样例#3：

-8

说明

In the first example:

$d(a_{1},a_{2})=0d(a1,a2)=0 ;$
$d(a_{1},a_{3})=2d(a1,a3)=2 ;$
$d(a_{1},a_{4})=0d(a1,a4)=0 ;$
$d(a_{1},a_{5})=2d(a1,a5)=2 ;$
$d(a_{2},a_{3})=0d(a2,a3)=0 ;$
$d(a_{2},a_{4})=0d(a2,a4)=0 ;$
$d(a_{2},a_{5})=0d(a2,a5)=0 ;$
$d(a_{3},a_{4})=-2d(a3,a4)=−2 ;$
$d(a_{3},a_{5})=0d(a3,a5)=0 ;$
$d(a_{4},a_{5})=2d(a4,a5)=2 .$

#include<bits/stdc++.h>
#define maxn 200005
#define ll long long
using namespace std;  
const int base = 1000000000;
const int base_digits = 9;struct bigint {vector<int> z;int sign;bigint() : sign(1) { }bigint(long long v) { *this = v; }bigint(const string &s) { read(s); }void operator=(const bigint &v) {sign = v.sign;z = v.z;}void operator=(long long v) {sign = 1;if (v < 0)sign = -1, v = -v;z.clear();for (; v > 0; v = v / base)z.push_back(v % base);}bigint operator+(const bigint &v) const {if (sign == v.sign) {bigint res = v;for (int i = 0, carry = 0; i < (int) max(z.size(), v.z.size()) || carry; ++i) {if (i == (int) res.z.size())res.z.push_back(0);res.z[i] += carry + (i < (int) z.size() ? z[i] : 0);carry = res.z[i] >= base;if (carry)res.z[i] -= base;}return res;}return *this - (-v);}bigint operator-(const bigint &v) const {if (sign == v.sign) {if (abs() >= v.abs()) {bigint res = *this;for (int i = 0, carry = 0; i < (int) v.z.size() || carry; ++i) {res.z[i] -= carry + (i < (int) v.z.size() ? v.z[i] : 0);carry = res.z[i] < 0;if (carry)res.z[i] += base;}res.trim();return res;}return -(v - *this);}return *this + (-v);}void operator*=(int v) {if (v < 0)sign = -sign, v = -v;for (int i = 0, carry = 0; i < (int) z.size() || carry; ++i) {if (i == (int) z.size())z.push_back(0);long long cur = z[i] * (long long) v + carry;carry = (int) (cur / base);z[i] = (int) (cur % base);//asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));}trim();}bigint operator*(int v) const {bigint res = *this;res *= v;return res;}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 = 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 = ((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 make_pair(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 = ((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;}void 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();}bigint operator/(int v) const {bigint res = *this;res /= v;return res;}int operator%(int v) const {if (v < 0)v = -v;int m = 0;for (int i = z.size() - 1; i >= 0; --i)m = (z[i] + m * (long long) base) % v;return m * sign;}void operator+=(const bigint &v) {*this = *this + v;}void operator-=(const bigint &v) {*this = *this - v;}void operator*=(const bigint &v) {*this = *this * v;}void operator/=(const bigint &v) {*this = *this / v;}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 = 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() || (z.size() == 1 && !z[0]);}bigint operator-() const {bigint res = *this;res.sign = -sign;return res;}bigint abs() const {bigint res = *this;res.sign *= res.sign;return res;}long long longValue() const {long long res = 0;for (int i = 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 < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {if (s[pos] == '-')sign = -sign;++pos;}for (int i = 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 < (int) p.size(); i++)p[i] = p[i - 1] * 10;vector<int> res;long long cur = 0;int cur_digits = 0;for (int i = 0; i < (int) a.size(); i++) {cur += a[i] * 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 < (int) a1b1.size(); i++)r[i] -= a1b1[i];for (int i = 0; i < (int) a2b2.size(); i++)r[i] -= a2b2[i];for (int i = 0; i < (int) r.size(); i++)res[i + k] += r[i];for (int i = 0; i < (int) a1b1.size(); i++)res[i] += a1b1[i];for (int i = 0; i < (int) 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 < (int) 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;}
}ans;ll a[maxn],num[maxn],n,ky;
ll tot,cal,del,cnt[maxn];
int main(){scanf("%lld",&n);for(int i=1;i<=n;i++){scanf("%lld",a+i);num[i]=a[i];}sort(num+1,num+n+1);ky=unique(num+1,num+n+1)-num-1;ans=0;for(int i=1;i<=n;cnt[a[i]]++,tot+=num[a[i]],i++){a[i]=lower_bound(num+1,num+ky+1,a[i])-num;ans+=num[a[i]]*(ll)(i-1);ans-=tot;if(num[a[i]+1]==num[a[i]]+1) ans+=cnt[a[i]+1];if(num[a[i]-1]==num[a[i]]-1) ans-=cnt[a[i]-1];}cout<<ans<<endl;return 0;
}

转载于:https://www.cnblogs.com/JYYHH/p/8422709.html