feat: linear floor sum function and yosupo test

Author: a1fredbao

src/alfred/all

@@ -13,30 +13,34 @@
 #include "data_structure/dsu/cancel-dsu.hpp"
 #include "data_structure/dsu/dsu.hpp"
 #include "data_structure/dsu/weighted-dsu.hpp"
-#include "data_structure/dynamic-bitset.hpp"
+// #include "data_structure/dynamic-bitset.hpp"
 #include "data_structure/fenwick.hpp"
-#include "data_structure/hashmap.hpp"
+// #include "data_structure/hashmap.hpp"
 #include "data_structure/info.hpp"
+// #include "data_structure/persistent/partial-persistent-array.hpp"
 #include "data_structure/priority-set.hpp"
 #include "data_structure/sliding-window.hpp"
 #include "data_structure/sparse-table.hpp"
 #include "data_structure/sum.hpp"
 
-#include "graph/graph.hpp"
-#include "graph/grid.hpp"
-#include "graph/twosat.hpp"
-#include "graph/hld.hpp"
-#include "graph/lca.hpp" // Will be included after graph class is implemented well enough
+// #include "graph/graph.hpp"
+// #include "graph/grid.hpp"
+// #include "graph/hld.hpp"
+// #include "graph/lca.hpp" // Will be included after graph class is implemented well enough
 #include "graph/maxflow.hpp"
+#include "graph/twosat.hpp"
 
 #include "math/comb.hpp"
-#include "math/computation-geometry.hpp"
+// #include "math/computation-geometry.hpp"
 #include "math/conv.hpp"
+#include "math/flat-geometry.hpp" // TODO complete flat geometry
+#include "math/floor-sum.hpp"
+#include "math/gcd.hpp"
 #include "math/lagrange.hpp"
 #include "math/linear.hpp"
 #include "math/mod-int.hpp"
 #include "math/speed-of-light-power.hpp"
-#include "math/sqrt-decomposition.hpp"
+// #include "math/sqrt-decomposition.hpp"
 #include "math/utils.hpp"
 
 #include "string/fuzz-matching.hpp"

src/alfred/math/floor-sum.hpp

@@ -0,0 +1,17 @@
+#ifndef AFMT_FLOOR_SUM
+#define AFMT_FLOOR_SUM
+
+// Calculate $\sum_{i = 0}^{n - 1} \lfloor \frac{ai + b}{m} \rfloor$ in $O(\min\{a, m, n\})$
+long long floor_sum(
+    long long a, long long b, long long m, long long n
+) {
+    if (a == 0) return b / m * n;
+    if (a >= m || b >= m) {
+        return (a / m) * (n * (n - 1) / 2) + b / m * n +
+               floor_sum(a % m, b % m, m, n);
+    }
+    long long mx = (a * (n - 1) + b) / m;
+    return (n - 1) * mx - floor_sum(m, m - b - 1, a, mx);
+}
+
+#endif // !AFMT_FLOOR_SUM

verify/verify-yosupo-math/yosupo-sum-of-floor-of-linear.test.cpp

@@ -0,0 +1,16 @@
+// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/sum_of_floor_of_linear
+
+#include "../../src/alfred/config/io-sync-off.hpp"
+#include "../../src/alfred/math/floor-sum.hpp"
+#include <iostream>
+
+int main(int argc, char const *argv[]) {
+    int T;
+    optimizeIO(), std::cin >> T;
+    while (T--) {
+        int n, m, a, b;
+        std::cin >> n >> m >> a >> b;
+        std::cout << floor_sum(a, b, m, n) << '\n';
+    }
+    return 0;
+}