#34: Add explicit for some constructors

atcoder/dsu.hpp

@@ -14,7 +14,7 @@ namespace atcoder {
 struct dsu {
   public:
     dsu() : _n(0) {}
-    dsu(int n) : _n(n), parent_or_size(n, -1) {}
+    explicit dsu(int n) : _n(n), parent_or_size(n, -1) {}
 
     int merge(int a, int b) {
         assert(0 <= a && a < _n);

atcoder/fenwicktree.hpp

@@ -14,7 +14,7 @@ template <class T> struct fenwick_tree {
 
   public:
     fenwick_tree() : _n(0) {}
-    fenwick_tree(int n) : _n(n), data(n) {}
+    explicit fenwick_tree(int n) : _n(n), data(n) {}
 
     void add(int p, T x) {
         assert(0 <= p && p < _n);

atcoder/internal_csr.hpp

@@ -11,7 +11,7 @@ namespace internal {
 template <class E> struct csr {
     std::vector<int> start;
     std::vector<E> elist;
-    csr(int n, const std::vector<std::pair<int, E>>& edges)
+    explicit csr(int n, const std::vector<std::pair<int, E>>& edges)
         : start(n + 1), elist(edges.size()) {
         for (auto e : edges) {
             start[e.first + 1]++;

atcoder/internal_math.hpp

@@ -27,7 +27,7 @@ struct barrett {
     unsigned long long im;
 
     // @param m `1 <= m < 2^31`
-    barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
+    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
 
     // @return m
     unsigned int umod() const { return _m; }
@@ -177,6 +177,35 @@ constexpr int primitive_root_constexpr(int m) {
 }
 template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
 
+// @param n `n < 2^32`
+// @param m `1 <= m < 2^32`
+// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
+unsigned long long floor_sum_unsigned(unsigned long long n,
+                                      unsigned long long m,
+                                      unsigned long long a,
+                                      unsigned long long b) {
+    unsigned long long ans = 0;
+    while (true) {
+        if (a >= m) {
+            ans += n * (n - 1) / 2 * (a / m);
+            a %= m;
+        }
+        if (b >= m) {
+            ans += n * (b / m);
+            b %= m;
+        }
+
+        unsigned long long y_max = a * n + b;
+        if (y_max < m) break;
+        // y_max < m * (n + 1)
+        // floor(y_max / m) <= n
+        n = (unsigned long long)(y_max / m);
+        b = (unsigned long long)(y_max % m);
+        std::swap(m, a);
+    }
+    return ans;
+}
+
 }  // namespace internal
 
 }  // namespace atcoder

atcoder/internal_scc.hpp

@@ -15,7 +15,7 @@ namespace internal {
 // Depth-First Search and Linear Graph Algorithms
 struct scc_graph {
   public:
-    scc_graph(int n) : _n(n) {}
+    explicit scc_graph(int n) : _n(n) {}
 
     int num_vertices() { return _n; }
 

atcoder/lazysegtree.hpp

@@ -20,8 +20,8 @@ template <class S,
 struct lazy_segtree {
   public:
     lazy_segtree() : lazy_segtree(0) {}
-    lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
-    lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
+    explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
+    explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
         log = internal::ceil_pow2(_n);
         size = 1 << log;
         d = std::vector<S>(2 * size, e());

atcoder/math.hpp

@@ -80,20 +80,20 @@ std::pair<long long, long long> crt(const std::vector<long long>& r,
 }
 
 long long floor_sum(long long n, long long m, long long a, long long b) {
-    long long ans = 0;
-    if (a >= m) {
-        ans += (n - 1) * n / 2 * (a / m);
-        a %= m;
+    assert(0 <= n && n < (1LL << 32));
+    assert(1 <= m && m < (1LL << 32));
+    unsigned long long ans = 0;
+    if (a < 0) {
+        unsigned long long a2 = internal::safe_mod(a, m);
+        ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
+        a = a2;
     }
-    if (b >= m) {
-        ans += n * (b / m);
-        b %= m;
+    if (b < 0) {
+        unsigned long long b2 = internal::safe_mod(b, m);
+        ans -= 1ULL * n * ((b2 - b) / m);
+        b = b2;
     }
-
-    long long y_max = a * n + b;
-    if (y_max < m) return ans;
-    ans += floor_sum(y_max / m, a, m, y_max % m);
-    return ans;
+    return ans + internal::floor_sum_unsigned(n, m, a, b);
 }
 
 }  // namespace atcoder

atcoder/maxflow.hpp

@@ -14,7 +14,7 @@ namespace atcoder {
 template <class Cap> struct mf_graph {
   public:
     mf_graph() : _n(0) {}
-    mf_graph(int n) : _n(n), g(n) {}
+    explicit mf_graph(int n) : _n(n), g(n) {}
 
     int add_edge(int from, int to, Cap cap) {
         assert(0 <= from && from < _n);

atcoder/mincostflow.hpp

@@ -15,7 +15,7 @@ namespace atcoder {
 template <class Cap, class Cost> struct mcf_graph {
   public:
     mcf_graph() {}
-    mcf_graph(int n) : _n(n) {}
+    explicit mcf_graph(int n) : _n(n) {}
 
     int add_edge(int from, int to, Cap cap, Cost cost) {
         assert(0 <= from && from < _n);

atcoder/modint.hpp

@@ -247,7 +247,7 @@ template <int id> struct dynamic_modint : internal::modint_base {
     static internal::barrett bt;
     static unsigned int umod() { return bt.umod(); }
 };
-template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
+template <int id> internal::barrett dynamic_modint<id>::bt(998244353);
 
 using modint998244353 = static_modint<998244353>;
 using modint1000000007 = static_modint<1000000007>;

atcoder/scc.hpp

@@ -12,7 +12,7 @@ namespace atcoder {
 struct scc_graph {
   public:
     scc_graph() : internal(0) {}
-    scc_graph(int n) : internal(n) {}
+    explicit scc_graph(int n) : internal(n) {}
 
     void add_edge(int from, int to) {
         int n = internal.num_vertices();

atcoder/segtree.hpp

@@ -12,8 +12,8 @@ namespace atcoder {
 template <class S, S (*op)(S, S), S (*e)()> struct segtree {
   public:
     segtree() : segtree(0) {}
-    segtree(int n) : segtree(std::vector<S>(n, e())) {}
-    segtree(const std::vector<S>& v) : _n(int(v.size())) {
+    explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
+    explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
         log = internal::ceil_pow2(_n);
         size = 1 << log;
         d = std::vector<S>(2 * size, e());

atcoder/twosat.hpp

@@ -15,7 +15,7 @@ namespace atcoder {
 struct two_sat {
   public:
     two_sat() : _n(0), scc(0) {}
-    two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}
+    explicit two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}
 
     void add_clause(int i, bool f, int j, bool g) {
         assert(0 <= i && i < _n);

document_en/appendix.md

@@ -134,6 +134,10 @@ vector<long long> c = convolution<924844033>(a, b);
 In the first case, $m$ is automatically set to be $998244353$.
 In the second case, $m$ becomes the value that is explicitly specified, which is $924844033$ here.
 
+### 💻 explicit specifier
+
+Constructors of structs except `modint` are declared with the explicit specifier.
+
 ## Precise requirements in Segtree / LazySegtree
 
 In some situations, the cardinality of algebraic structures for Segtree / LazySegtree would be infinite. In precise meaning, it may break the constraints in the document.

document_en/math.md

@@ -65,17 +65,20 @@ $y, z$ $(0 \leq y < z = \mathrm{lcm}(m[i]))$. It returns this $(y, z)$ as a pair
 ll floor_sum(ll n, ll m, ll a, ll b)
 ```
 
-It returns $\sum_{i = 0}^{n - 1} \mathrm{floor}(\frac{a \times i + b}{m})$.
+It returns
+
+$$\sum_{i = 0}^{n - 1} \left\lfloor \frac{a \times i + b}{m} \right\rfloor$$
+
+It returns the answer in $\bmod 2^{\mathrm{64}}$, if overflowed.
 
 **@{keyword.constraints}**
 
-- $0 \leq n \leq 10^9$
-- $1 \leq m \leq 10^9$
-- $0 \leq a, b \lt m$
+- $0 \leq n \lt 2^{32}$
+- $1 \leq m \lt 2^{32}$
 
 **@{keyword.complexity}**
 
-- $O(\log{(n+m+a+b)})$
+- $O(\log{(m+a)})$
 
 ## @{keyword.examples}
 

document_ja/appendix.md

@@ -141,6 +141,10 @@ vector<long long> c = convolution<924844033>(a, b);
 上段のように使った場合は、$m$ の値は自動的に $998244353$ となります。
 下段のように使った場合は、$m$ の値は明示的に与えた値 (この場合は $924844033$) となります。
 
+### 💻 explicit 指定子
+
+`modint` 以外の構造体のコンストラクタには explicit が付いています。
+
 ## Segtree / LazySegtree の厳密な要件
 
 Segtree / LazySegtree を使いたい状況において、扱う代数構造が無限集合である場合があります。たとえば、与えられた区間の $\mathrm{max}$ を求める、与えられた区間内の全ての要素に定数を足す、の二種類のクエリに対応する LazySegtree はよくありますが、このときたとえば $S = \mathrm{int}$ としてしまうと、$S$ は加法について閉じていない (overflow を起こす可能性がある) ため、厳密な意味でドキュメント本編の制約を満たしません。そこで、AC Library では以下のような場合正しく動くことを保証しています。

document_ja/math.md

@@ -64,19 +64,18 @@ $$x \equiv r[i] \pmod{m[i]}, \forall i \in \lbrace 0,1,\cdots, n - 1 \rbrace$$
 ll floor_sum(ll n, ll m, ll a, ll b)
 ```
 
-$\sum_{i = 0}^{n - 1} \mathrm{floor}(\frac{a \times i + b}{m})$
+$$\sum_{i = 0}^{n - 1} \left\lfloor \frac{a \times i + b}{m} \right\rfloor$$
 
-を返します。
+を返します。答えがオーバーフローしたならば $\bmod 2^{\mathrm{64}}$ で等しい値を返します。
 
 **@{keyword.constraints}**
 
-- $0 \leq n \leq 10^9$
-- $1 \leq m \leq 10^9$
-- $0 \leq a, b \lt m$
+- $0 \leq n \lt 2^{32}$
+- $1 \leq m \lt 2^{32}$
 
 **@{keyword.complexity}**
 
-- $O(\log{(n+m+a+b)})$
+- $O(\log{(m+a)})$
 
 ## @{keyword.examples}
 

test/unittest/math_test.cpp

@@ -27,7 +27,8 @@ ll pow_mod_naive(ll x, ull n, uint mod) {
 ll floor_sum_naive(ll n, ll m, ll a, ll b) {
     ll sum = 0;
     for (ll i = 0; i < n; i++) {
-        sum += (a * i + b) / m;
+        ll z = a * i + b;
+        sum += (z - internal::safe_mod(z, m)) / m;
     }
     return sum;
 }
@@ -93,8 +94,8 @@ TEST(MathTest, InvModZero) {
 TEST(MathTest, FloorSum) {
     for (int n = 0; n < 20; n++) {
         for (int m = 1; m < 20; m++) {
-            for (int a = 0; a < 20; a++) {
-                for (int b = 0; b < 20; b++) {
+            for (int a = -20; a < 20; a++) {
+                for (int b = -20; b < 20; b++) {
                     ASSERT_EQ(floor_sum_naive(n, m, a, b),
                               floor_sum(n, m, a, b));
                 }