Add a bigint
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Math/bigint.cpp
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490
Math/bigint.cpp
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#include <bits/stdc++.h>
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#define f first
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#define s second
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using namespace std;
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using ll = long long;
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using ii = pair<int, int>;
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constexpr int MX = 125;
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using ll = long long;
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using db = long double; // or double, if TL is tight
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using str = string; // yay python!
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using pi = pair<int,int>;
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using pl = pair<ll,ll>;
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using pd = pair<db,db>;
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using vi = vector<int>;
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using vb = vector<bool>;
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using vl = vector<ll>;
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using vd = vector<db>;
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using vs = vector<str>;
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using vpi = vector<pi>;
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using vpl = vector<pl>;
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using vpd = vector<pd>;
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#define tcT template<class T
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#define tcTU tcT, class U
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// ^ lol this makes everything look weird but I'll try it
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tcT> using V = vector<T>;
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tcT, size_t SZ> using AR = array<T,SZ>;
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tcT> using PR = pair<T,T>;
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// pairs
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#define mp make_pair
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#define f first
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#define s second
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// vectors
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// oops size(x), rbegin(x), rend(x) need C++17
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#define sz(x) int((x).size())
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#define bg(x) begin(x)
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#define all(x) bg(x), end(x)
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#define rall(x) x.rbegin(), x.rend()
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#define sor(x) sort(all(x))
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#define rsz resize
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#define ins insert
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#define ft front()
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#define bk back()
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#define pb push_back
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#define eb emplace_back
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#define pf push_front
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#define rtn return
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#define lb lower_bound
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#define ub upper_bound
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tcT> int lwb(V<T>& a, const T& b) { return int(lb(all(a),b)-bg(a)); }
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// loops
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#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
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#define F0R(i,a) FOR(i,0,a)
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#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
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#define R0F(i,a) ROF(i,0,a)
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#define rep(a) F0R(_,a)
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#define each(a,x) for (auto& a: x)
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const int MOD = 1e9+7; // 998244353;
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const ll INF = 1e18; // not too close to LLONG_MAX
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const db PI = acos((db)-1);
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const int dx[4] = {1,0,-1,0}, dy[4] = {0,1,0,-1}; // for every grid problem!!
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mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
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template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;
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// bitwise ops
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// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
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constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
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constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until USACO updates ...
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return x == 0 ? 0 : 31-__builtin_clz(x); } // floor(log2(x))
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constexpr int p2(int x) { return 1<<x; }
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constexpr int msk2(int x) { return p2(x)-1; }
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ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
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ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down
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tcT> bool ckmin(T& a, const T& b) {
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return b < a ? a = b, 1 : 0; } // set a = min(a,b)
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tcT> bool ckmax(T& a, const T& b) {
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return a < b ? a = b, 1 : 0; }
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tcTU> T fstTrue(T lo, T hi, U f) {
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hi ++; assert(lo <= hi); // assuming f is increasing
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while (lo < hi) { // find first index such that f is true
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T mid = lo+(hi-lo)/2;
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f(mid) ? hi = mid : lo = mid+1;
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}
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return lo;
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}
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tcTU> T lstTrue(T lo, T hi, U f) {
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lo --; assert(lo <= hi); // assuming f is decreasing
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while (lo < hi) { // find first index such that f is true
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T mid = lo+(hi-lo+1)/2;
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f(mid) ? lo = mid : hi = mid-1;
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}
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return lo;
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}
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tcT> void remDup(vector<T>& v) { // sort and remove duplicates
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sort(all(v)); v.erase(unique(all(v)),end(v)); }
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tcTU> void erase(T& t, const U& u) { // don't erase
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auto it = t.find(u); assert(it != end(t));
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t.erase(it); } // element that doesn't exist from (multi)set
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#define tcTUU tcT, class ...U
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inline namespace Helpers {
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//////////// is_iterable
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// https://stackoverflow.com/questions/13830158/check-if-a-variable-type-is-iterable
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// this gets used only when we can call begin() and end() on that type
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tcT, class = void> struct is_iterable : false_type {};
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tcT> struct is_iterable<T, void_t<decltype(begin(declval<T>())),
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decltype(end(declval<T>()))
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>
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> : true_type {};
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tcT> constexpr bool is_iterable_v = is_iterable<T>::value;
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//////////// is_readable
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tcT, class = void> struct is_readable : false_type {};
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tcT> struct is_readable<T,
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typename std::enable_if_t<
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is_same_v<decltype(cin >> declval<T&>()), istream&>
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>
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> : true_type {};
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tcT> constexpr bool is_readable_v = is_readable<T>::value;
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//////////// is_printable
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// // https://nafe.es/posts/2020-02-29-is-printable/
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tcT, class = void> struct is_printable : false_type {};
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tcT> struct is_printable<T,
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typename std::enable_if_t<
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is_same_v<decltype(cout << declval<T>()), ostream&>
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>
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> : true_type {};
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tcT> constexpr bool is_printable_v = is_printable<T>::value;
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}
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inline namespace Input {
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tcT> constexpr bool needs_input_v = !is_readable_v<T> && is_iterable_v<T>;
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tcTUU> void re(T& t, U&... u);
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tcTU> void re(pair<T,U>& p); // pairs
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// re: read
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tcT> typename enable_if<is_readable_v<T>,void>::type re(T& x) { cin >> x; } // default
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tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; } // complex
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tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i); // ex. vectors, arrays
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tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
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tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i) {
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each(x,i) re(x); }
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tcTUU> void re(T& t, U&... u) { re(t); re(u...); } // read multiple
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// rv: resize and read vectors
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void rv(size_t) {}
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tcTUU> void rv(size_t N, V<T>& t, U&... u);
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template<class...U> void rv(size_t, size_t N2, U&... u);
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tcTUU> void rv(size_t N, V<T>& t, U&... u) {
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t.rsz(N); re(t);
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rv(N,u...); }
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template<class...U> void rv(size_t, size_t N2, U&... u) {
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rv(N2,u...); }
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// dumb shortcuts to read in ints
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void decrement() {} // subtract one from each
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tcTUU> void decrement(T& t, U&... u) { --t; decrement(u...); }
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#define ints(...) int __VA_ARGS__; re(__VA_ARGS__);
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#define int1(...) ints(__VA_ARGS__); decrement(__VA_ARGS__);
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}
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inline namespace ToString {
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tcT> constexpr bool needs_output_v = !is_printable_v<T> && is_iterable_v<T>;
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// ts: string representation to print
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tcT> typename enable_if<is_printable_v<T>,str>::type ts(T v) {
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stringstream ss; ss << fixed << setprecision(15) << v;
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return ss.str(); } // default
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tcT> str bit_vec(T t) { // bit vector to string
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str res = "{"; F0R(i,sz(t)) res += ts(t[i]);
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res += "}"; return res; }
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str ts(V<bool> v) { return bit_vec(v); }
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template<size_t SZ> str ts(bitset<SZ> b) { return bit_vec(b); } // bit vector
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tcTU> str ts(pair<T,U> p); // pairs
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tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v); // vectors, arrays
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tcTU> str ts(pair<T,U> p) { return "("+ts(p.f)+", "+ts(p.s)+")"; }
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tcT> typename enable_if<is_iterable_v<T>,str>::type ts_sep(T v, str sep) {
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// convert container to string w/ separator sep
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bool fst = 1; str res = "";
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for (const auto& x: v) {
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if (!fst) res += sep;
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fst = 0; res += ts(x);
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}
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return res;
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}
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tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v) {
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return "{"+ts_sep(v,", ")+"}"; }
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// for nested DS
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template<int, class T> typename enable_if<!needs_output_v<T>,vs>::type
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ts_lev(const T& v) { return {ts(v)}; }
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template<int lev, class T> typename enable_if<needs_output_v<T>,vs>::type
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ts_lev(const T& v) {
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if (lev == 0 || !sz(v)) return {ts(v)};
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vs res;
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for (const auto& t: v) {
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if (sz(res)) res.bk += ",";
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vs tmp = ts_lev<lev-1>(t);
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res.ins(end(res),all(tmp));
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}
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F0R(i,sz(res)) {
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str bef = " "; if (i == 0) bef = "{";
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res[i] = bef+res[i];
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}
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res.bk += "}";
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return res;
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}
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}
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inline namespace Output {
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template<class T> void pr_sep(ostream& os, str, const T& t) { os << ts(t); }
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template<class T, class... U> void pr_sep(ostream& os, str sep, const T& t, const U&... u) {
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pr_sep(os,sep,t); os << sep; pr_sep(os,sep,u...); }
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// print w/ no spaces
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template<class ...T> void pr(const T&... t) { pr_sep(cout,"",t...); }
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// print w/ spaces, end with newline
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void ps() { cout << "\n"; }
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template<class ...T> void ps(const T&... t) { pr_sep(cout," ",t...); ps(); }
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// debug to cerr
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template<class ...T> void dbg_out(const T&... t) {
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pr_sep(cerr," | ",t...); cerr << endl; }
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void loc_info(int line, str names) {
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cerr << "Line(" << line << ") -> [" << names << "]: "; }
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template<int lev, class T> void dbgl_out(const T& t) {
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cerr << "\n\n" << ts_sep(ts_lev<lev>(t),"\n") << "\n" << endl; }
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#ifdef LOCAL
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#define dbg(...) loc_info(__LINE__,#__VA_ARGS__), dbg_out(__VA_ARGS__)
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#define dbgl(lev,x) loc_info(__LINE__,#x), dbgl_out<lev>(x)
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#else // don't actually submit with this
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#define dbg(...) 0
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#define dbgl(lev,x) 0
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#endif
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}
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inline namespace FileIO {
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void setIn(str s) { freopen(s.c_str(),"r",stdin); }
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void setOut(str s) { freopen(s.c_str(),"w",stdout); }
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void setIO(str s = "") {
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cin.tie(0)->sync_with_stdio(0); // unsync C / C++ I/O streams
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// cin.exceptions(cin.failbit);
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// throws exception when do smth illegal
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// ex. try to read letter into int
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if (sz(s)) setIn(s+".in"), setOut(s+".out"); // for old USACO
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}
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}
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// make sure to intialize ALL GLOBAL VARS between tcs!
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/**
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* Description: Big Integer
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* Source: https://github.com/indy256/codelibrary/blob/master/cpp/numeric/bigint.cpp
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* oops that one uses FFT instead of Karatsuba now ....
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* Verification: https://oj.uz/problem/view/IOI11_parrots
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*/
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// base and base_digits must be consistent
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const int base = 1e9, base_digits = 9;
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struct bigint { // value == 0 is represented by empty z
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vi z; // digits
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int sign; // sign == 1 <==> value >= 0
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bigint() : sign(1) {} // sign == -1 <==> value < 0
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bigint(ll v) { *this = v; }
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bigint &operator=(ll v) {
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sign = v < 0 ? -1 : 1; v *= sign; // make v positive
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z.clear(); for (;v;v/=base) z.pb(v%base);
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return *this;
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}
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bigint(const str &s) { read(s); } // add char by char
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bigint &operator+=(const bigint &other) {
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//dbg("ADDING",*this,other,sign,other.sign);
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if (sign == other.sign) {
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for (int i = 0, carry = 0; i < sz(other.z) || carry; ++i) {
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if (i == sz(z)) z.pb(0);
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z[i] += carry+(i<sz(other.z)?other.z[i]:0);
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carry = z[i] >= base; if (carry) z[i] -= base;
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}
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} else if (other != 0 /* prevent infinite loop */) *this -= -other;
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return *this;
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}
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friend bigint operator+(bigint a, const bigint &b) { return a += b; }
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bigint &operator-=(const bigint &other) {
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if (sign == other.sign) {
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if ((sign == 1 && *this >= other) || (sign == -1 && *this <= other)) {
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for (int i = 0, carry = 0; i < sz(other.z) || carry; ++i) {
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z[i] -= carry+(i<sz(other.z)?other.z[i]:0);
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carry = z[i]<0; if (carry) z[i] += base;
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}
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trim();
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} else { // result will change sign
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*this = other-*this;
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this->sign = -this->sign;
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}
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} else *this += -other;
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return *this;
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}
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friend bigint operator-(bigint a, const bigint &b) { return a -= b; }
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bigint &operator*=(int v) { // oops make sure not to multiply by ll ...
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if (v < 0) sign = -sign, v = -v;
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for (int i = 0, carry = 0; i < sz(z) || carry; ++i) {
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if (i == sz(z)) z.pb(0);
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ll cur = (ll)z[i]*v+carry;
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carry = cur/base; z[i] = cur%base;
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}
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trim(); return *this;
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}
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bigint operator*(int v) const { return bigint(*this) *= v; }
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friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
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int norm = base/(b1.z.bk+1);
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bigint a = a1.abs()*norm, b = b1.abs()*norm, q, r; // make last element of b big
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q.z.rsz(sz(a.z));
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R0F(i,sz(a.z)) {
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r *= base; r += a.z[i];
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int s1 = sz(b.z) < sz(r.z) ? r.z[sz(b.z)] : 0;
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int s2 = sz(b.z)-1 < sz(r.z) ? r.z[sz(b.z)-1] : 0;
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int d = ((ll)s1*base+s2)/b.z.bk; // best approximation
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r -= b*d; while (r < 0) r += b, --d;
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q.z[i] = d;
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}
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q.sign = a1.sign*b1.sign; r.sign = a1.sign;
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q.trim(); r.trim(); return {q,r/norm};
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}
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friend bigint sqrt(const bigint &a1) {
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bigint a = a1; while (!sz(a.z) || sz(a.z)&1) a.z.pb(0);
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int n = sz(a.z), firstDigit = ::sqrt((db)a.z[n-1]*base+a.z[n-2]);
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int norm = base/(firstDigit+1); a *= norm; a *= norm;
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while (!sz(a.z) || sz(a.z)&1) a.z.pb(0);
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bigint r = (ll)a.z[n-1]*base+a.z[n-2];
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firstDigit = (int)::sqrt((db)a.z[n-1]*base+a.z[n-2]);
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int q = firstDigit; bigint res;
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R0F(j,n/2) {
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for (;; --q) {
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bigint r1 = (r-(res*2*base+q)*q)*base*base +
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(j>0?(ll)a.z[2*j-1]*base+a.z[2*j-2]:0);
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if (r1 >= 0) { r = r1; break; }
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}
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res *= base; res += q; // add a bit to sqrt
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if (j > 0) {
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int d1 = sz(res.z)+2 < sz(r.z) ? r.z[sz(res.z)+2] : 0; // always 0/1?
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int d2 = sz(res.z)+1 < sz(r.z) ? r.z[sz(res.z)+1] : 0;
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int d3 = sz(res.z) < sz(r.z) ? r.z[sz(res.z)] : 0;
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q = ((ll) d1*base*base+(ll)d2*base+d3)/(firstDigit*2);
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}
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}
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res.trim(); return res/norm;
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}
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bigint operator/(const bigint &v) const { return divmod(*this, v).f; }
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bigint operator%(const bigint &v) const { return divmod(*this, v).s; }
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bigint &operator/=(int v) {
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if (v < 0) sign = -sign, v = -v;
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for (int i = sz(z)-1, rem = 0; i >= 0; --i) {
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ll cur = z[i]+rem*(ll)base;
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z[i] = cur/v; rem = cur%v;
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}
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trim(); return *this;
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}
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bigint operator/(int v) const { return bigint(*this) /= v; }
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||||
int operator%(int v) const {
|
||||
if (v < 0) v = -v;
|
||||
int m = 0; R0F(i,sz(z)) m = (z[i]+m*(ll)base)%v;
|
||||
return m*sign; }
|
||||
bigint &operator*=(const bigint &v) { return *this = *this*v; }
|
||||
bigint &operator/=(const bigint &v) { return *this = *this/v; }
|
||||
|
||||
bool operator<(const bigint &v) const {
|
||||
if (sign != v.sign) return sign < v.sign;
|
||||
if (sz(z) != sz(v.z)) return sz(z)*sign < sz(v.z) * v.sign;
|
||||
R0F(i,sz(z)) if (z[i] != v.z[i]) return z[i]*sign < v.z[i]*sign;
|
||||
return 0; // equal
|
||||
}
|
||||
bool operator>(const bigint &v) const { return v < *this; }
|
||||
bool operator<=(const bigint &v) const { return !(v < *this); }
|
||||
bool operator>=(const bigint &v) const { return !(*this < v); }
|
||||
bool operator==(const bigint &v) const { return !(*this < v) && !(v < *this); }
|
||||
bool operator!=(const bigint &v) const { return *this < v || v < *this; }
|
||||
void trim() {
|
||||
while (sz(z) && z.bk == 0) z.pop_back();
|
||||
if (!sz(z)) sign = 1; // don't output -0
|
||||
}
|
||||
bool isZero() const { return !sz(z); }
|
||||
friend bigint operator-(bigint v) {
|
||||
if (sz(v.z)) v.sign = -v.sign;
|
||||
return v; }
|
||||
bigint abs() const { return sign == 1 ? *this : -*this; }
|
||||
ll longValue() const {
|
||||
ll res = 0; R0F(i,sz(z)) res = res*base+z[i];
|
||||
return res*sign; }
|
||||
friend bigint gcd(const bigint &a, const bigint &b) {
|
||||
return b.isZero() ? a : gcd(b, a % b); } // euclidean algo
|
||||
friend bigint lcm(const bigint &a, const bigint &b) {
|
||||
return a/gcd(a, b) * b; }
|
||||
|
||||
void read(const str &s) {
|
||||
sign = 1; z.clear(); int pos = 0;
|
||||
while (pos < sz(s) && (s[pos] == '-' || s[pos] == '+')) {
|
||||
if (s[pos] == '-') sign = -sign;
|
||||
++pos; } // account for sign
|
||||
for (int i = sz(s)-1; i >= pos; i -= base_digits) {
|
||||
int x = 0;
|
||||
for (int j = max(pos, i-base_digits+1); j <= i; j++)
|
||||
x = x*10+s[j]-'0';
|
||||
z.pb(x);
|
||||
}
|
||||
trim();
|
||||
}
|
||||
friend istream &operator>>(istream &is, bigint &v) {
|
||||
str s; is >> s; v.read(s); return is; }
|
||||
friend ostream &operator<<(ostream &os, const bigint &v) {
|
||||
if (v.sign == -1) os << '-';
|
||||
os << (!sz(v.z) ? 0 : v.z.bk);
|
||||
R0F(i,sz(v.z)-1) os << setw(base_digits) << setfill('0') << v.z[i];
|
||||
return os; // pad with zeroes
|
||||
}
|
||||
static vi convert_base(const vi &a, int old_digits, int new_digits) {
|
||||
vl p(max(old_digits, new_digits) + 1); // blocks of 10^{old} -> 10^{new}
|
||||
p[0] = 1; FOR(i,1,sz(p)) p[i] = p[i-1]*10;
|
||||
vi res; ll cur = 0; int cur_digits = 0;
|
||||
for (int v:a) {
|
||||
cur += v*p[cur_digits]; cur_digits += old_digits;
|
||||
while (cur_digits >= new_digits) {
|
||||
res.pb(cur%p[new_digits]);
|
||||
cur /= p[new_digits]; cur_digits -= new_digits;
|
||||
}
|
||||
}
|
||||
res.pb(cur); while (sz(res) && res.bk == 0) res.pop_back();
|
||||
return res;
|
||||
}
|
||||
static vl karatMul(const vl &a, const vl &b) { // karatsuba
|
||||
int n = sz(a); vl res(2*n);
|
||||
if (n <= 32) { // naive multiply
|
||||
F0R(i,n) F0R(j,n) res[i+j] += a[i]*b[j];
|
||||
return res; }
|
||||
int k = n/2;
|
||||
vl a1(begin(a),begin(a)+k), a2(k+all(a));
|
||||
vl b1(begin(b),begin(b)+k), b2(k+all(b));
|
||||
vl a1b1 = karatMul(a1, b1), a2b2 = karatMul(a2, b2);
|
||||
F0R(i,k) a2[i] += a1[i], b2[i] += b1[i];
|
||||
vl r = karatMul(a2, b2); // three instead of four products
|
||||
F0R(i,sz(a1b1)) r[i] -= a1b1[i];
|
||||
F0R(i,sz(a2b2)) r[i] -= a2b2[i];
|
||||
F0R(i,sz(r)) res[i+k] += r[i];
|
||||
F0R(i,sz(a1b1)) res[i] += a1b1[i];
|
||||
F0R(i,sz(a2b2)) res[i+n] += a2b2[i];
|
||||
return res;
|
||||
}
|
||||
bigint operator*(const bigint &v) const {
|
||||
if (min(sz(z),sz(v.z)) < 150) return mul_simple(v);
|
||||
bigint res; res.sign = sign*v.sign; // should work as long as # of digits isn't too large (> LLONG_MAX/10^{12})
|
||||
vi a6 = convert_base(this->z, base_digits, 6); // blocks of 10^6 instead of 10^9
|
||||
vi b6 = convert_base(v.z, base_digits, 6);
|
||||
vl a(all(a6)), b(all(b6));
|
||||
while (sz(a) < sz(b)) a.pb(0);
|
||||
while (sz(b) < sz(a)) b.pb(0);
|
||||
while (sz(a)&(sz(a)-1)) a.pb(0), b.pb(0); // make size power of 2
|
||||
vl c = karatMul(a, b);
|
||||
ll cur = 0; F0R(i,sz(c)) { // process carries
|
||||
cur += c[i]; res.z.pb(cur%1000000); cur /= 1000000; }
|
||||
res.z = convert_base(res.z,6,base_digits);
|
||||
res.trim(); return res;
|
||||
}
|
||||
bigint mul_simple(const bigint &v) const {
|
||||
bigint res; res.sign = sign*v.sign;
|
||||
res.z.rsz(sz(z)+sz(v.z));
|
||||
F0R(i,sz(z)) if (z[i]) {
|
||||
ll cur = 0; for (int j = 0; j < sz(v.z) || cur; ++j) {
|
||||
cur += res.z[i+j]+(ll)z[i]*(j<sz(v.z)?v.z[j]:0);
|
||||
res.z[i+j] = cur%base; cur /= base;
|
||||
}
|
||||
}
|
||||
res.trim(); return res;
|
||||
}
|
||||
friend str ts(const bigint& v) {
|
||||
stringstream ss; ss << v;
|
||||
str s; ss >> s; return s; }
|
||||
};
|
||||
Loading…
Reference in a new issue