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OI-codes/S2OJ/1824/1824.cpp

153 lines
2.7 KiB
C++

#include <iostream>
#include <algorithm>
using std::cin;
using std::cout;
const char endl = '\n';
const unsigned long long mod = 1ull << 63,
mod_mask = mod - 1;
/**
* Calculates the sum of i from 1 to x
*
* res = x * (x + 1) / 2
*/
unsigned long long sum_i_1(unsigned long long x) {
unsigned long long t1 = x,
t2 = x + 1;
if (x % 2 == 0) t1 /= 2;
else t2 /= 2;
return t1 * t2;
}
/**
* Calculates the sum of i^2 from 1 to x
*
* res = x * (x + 1) * (2 * x + 1) / 6
*/
unsigned long long sum_i_2(unsigned long long x) {
unsigned long long t1 = x,
t2 = x + 1,
t3 = x * 2 + 1;
if (t1 % 2 == 0) t1 /= 2;
else t2 /= 2;
if (t1 % 3 == 0) t1 /= 3;
else if (t2 % 3 == 0) t2 /= 3;
else t3 /= 3;
return t1 * t2 * t3;
}
/**
* Calculates the sum of i^3 from 1 to x
*
* res = (x * (x + 1) / 2) * (x * (x + 1) / 2)
*/
unsigned long long sum_i_3(unsigned long long x) {
return sum_i_1(x) * sum_i_1(x);
}
/**
* Calculates this:
*
* @code
* --#+
* |
* |
* @endcode
*
* #: (2x + 1)^2
*/
unsigned long long calc_all(unsigned long long x) {
if (x < 0) return 0;
return sum_i_3(x) * 8 + sum_i_2(x) * 16 + sum_i_1(x) * 11 + (x + 1) * 3;
}
/**
* Calculates this:
*
* @code
* --#(+)
* (|)
* (|)
* @endcode
*
* #: (2x + 1)^2
* (): not included
*/
unsigned long long calc_top(unsigned long long x, unsigned long long y) {
unsigned long long res = sum_i_2(y) * 8 + sum_i_1(y) * 6 + (y - x + 1) * (x + 2),
t = x + 1;
if (x > 0) {
res -= sum_i_2(x - 1) * 8 + sum_i_1(x - 1) * 6;
}
if (res % 2 == 0) res /= 2;
else t /= 2;
return res * t;
}
/**
* Calculates this:
*
* @code
* (--#)+
* |
* |
* @endcode
*
* #: (2x + 1)^2
* (): not included
*/
unsigned long long calc_right(unsigned long long x, unsigned long long y) {
unsigned long long res = sum_i_2(x - 1) * 8 + sum_i_1(x - 1) * 10 + (x - y - 1) * (4 - y),
t = y + 1;
if (y > 0) {
res -= sum_i_2(y) * 8 + sum_i_1(y) * 10;
}
if (res % 2 == 0) res /= 2;
else t /= 2;
return res * t;
}
unsigned long long calc(long long x, long long y) {
if (x < 0 || y < 0) return 0;
if (x - 1 <= y) {
return calc_all(x - 1) + calc_top(x, y);
}
// x - 1 > y
return calc_all(y) + calc_right(x, y);
}
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
int q;
cin >> q;
while (q--) {
long long x1, x2, y1, y2;
cin >> x1 >> x2 >> y1 >> y2;
cout << ((calc(x2, y2) - calc(x1 - 1, y2) - calc(x2, y1 - 1) + calc(x1 - 1, y1 - 1)) & mod_mask) << endl;
}
return 0;
}