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