#1824. 【2021首师附省选集训4月23日】qiu

https://sjzezoj.com/submission/71911

S2OJ/1824/1824.cpp

@@ -0,0 +1,152 @@
+#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;
+}