CSES - Aalto Competitive Programming 2024 - wk8 - Wed - Results
Submission details
Task:A TIMES B!
Sender:aalto2024i_006
Submission time:2024-10-30 16:46:51 +0200
Language:C++ (C++20)
Status:READY
Result:ACCEPTED
Test results
testverdicttime
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Code

#pragma GCC optimize("O3","unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")

#include <bits/stdc++.h>
using namespace std;

#define int long long
#define rep(i, a, b) for(int i = a; i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

string to_string(string s) {
    return '"' + s + '"';
}
 
string to_string(const char* s) {
    return to_string((string) s);
}
 
string to_string(bool b) {
    return (b ? "true" : "false");
}
 
template <typename A, typename B>
string to_string(pair<A, B> p) {
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
 
template <typename A>
string to_string(A v) {
    bool first = true;
    string res = "{";
    for (const auto &x : v) {
        if (!first) {
            res += ", ";
        }
        first = false;
        res += to_string(x);
    }
    res += "}";
    return res;
}
 
void debug_out() {
    cerr << endl;
}
 
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << to_string(H);
    debug_out(T...);
}
 
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

/**
 * Author: Ludo Pulles, chilli, Simon Lindholm
 * Date: 2019-01-09
 * License: CC0
 * Source: http://neerc.ifmo.ru/trains/toulouse/2017/fft2.pdf (do read, it's excellent)
   Accuracy bound from http://www.daemonology.net/papers/fft.pdf
 * Description: fft(a) computes $\hat f(k) = \sum_x a[x] \exp(2\pi i \cdot k x / N)$ for all $k$. N must be a power of 2.
   Useful for convolution:
   \texttt{conv(a, b) = c}, where $c[x] = \sum a[i]b[x-i]$.
   For convolution of complex numbers or more than two vectors: FFT, multiply
   pointwise, divide by n, reverse(start+1, end), FFT back.
   Rounding is safe if $(\sum a_i^2 + \sum b_i^2)\log_2{N} < 9\cdot10^{14}$
   (in practice $10^{16}$; higher for random inputs).
   Otherwise, use NTT/FFTMod.
 * Time: O(N \log N) with $N = |A|+|B|$ ($\tilde 1s$ for $N=2^{22}$)
 * Status: somewhat tested
 * Details: An in-depth examination of precision for both FFT and FFTMod can be found
 * here (https://github.com/simonlindholm/fft-precision/blob/master/fft-precision.md)
 */

typedef complex<double> C;
typedef vector<double> vd;
void fft(vector<C>& a) {
    int n = sz(a), L = 31 - __builtin_clz(n);
    static vector<complex<long double>> R(2, 1);
    static vector<C> rt(2, 1);  // (^ 10% faster if double)
    for (static int k = 2; k < n; k *= 2) {
        R.resize(n); rt.resize(n);
        auto x = polar(1.0L, acos(-1.0L) / k);
        rep(i,k,2*k) rt[i] = R[i] = i&1 ? R[i/2] * x : R[i/2];
    }
    vi rev(n);
    rep(i,0,n) rev[i] = (rev[i / 2] | (i & 1) << L) / 2;
    rep(i,0,n) if (i < rev[i]) swap(a[i], a[rev[i]]);
    for (int k = 1; k < n; k *= 2)
        for (int i = 0; i < n; i += 2 * k) rep(j,0,k) {
            // C z = rt[j+k] * a[i+j+k]; // (25% faster if hand-rolled)  /// include-line
            auto x = (double *)&rt[j+k], y = (double *)&a[i+j+k];        /// exclude-line
            C z(x[0]*y[0] - x[1]*y[1], x[0]*y[1] + x[1]*y[0]);           /// exclude-line
            a[i + j + k] = a[i + j] - z;
            a[i + j] += z;
        }
}
vd conv(const vd& a, const vd& b) {
    if (a.empty() || b.empty()) return {};
    vd res(sz(a) + sz(b) - 1);
    int L = 32 - __builtin_clz(sz(res)), n = 1 << L;
    vector<C> in(n), out(n);
    copy(all(a), begin(in));
    rep(i,0,sz(b)) in[i].imag(b[i]);
    fft(in);
    for (C& x : in) x *= x;
    rep(i,0,n) out[i] = in[-i & (n - 1)] - conj(in[i]);
    fft(out);
    rep(i,0,sz(res)) res[i] = imag(out[i]) / (4 * n);
    return res;
}

signed main() {
    cin.tie(0)->sync_with_stdio(0);
    cin.exceptions(cin.failbit); // RTE if input wrong datatype

    string sa, sb;
    cin >> sa >> sb;

    vd a, b;
    for (char c : sa) a.push_back(c - '0');
    for (char c : sb) b.push_back(c - '0');
    reverse(all(a));
    reverse(all(b));

    vd c = conv(a, b);
    // debug(a);
    // debug(b);
    // debug(c);

    vi cc(sz(c));
    for (int i = 0; i < sz(cc); i++) {
        if (i < sz(c)) cc[i] += round(c[i]);
        if (cc[i] >= 10) {
            if (i + 1 >= sz(cc)) cc.push_back(0);
            cc[i + 1] += cc[i] / 10;
            cc[i] %= 10;
        }
    }

    reverse(all(cc));
    for (auto x : cc) cout << x;
}

Test details

Test 1

Verdict: ACCEPTED

input
8
5

correct output
40

user output
40

Test 2

Verdict: ACCEPTED

input
9
1

correct output
9

user output
9

Test 3

Verdict: ACCEPTED

input
9
5

correct output
45

user output
45

Test 4

Verdict: ACCEPTED

input
2
5

correct output
10

user output
10

Test 5

Verdict: ACCEPTED

input
8
7

correct output
56

user output
56

Test 6

Verdict: ACCEPTED

input
48
92

correct output
4416

user output
4416

Test 7

Verdict: ACCEPTED

input
1
40

correct output
40

user output
40

Test 8

Verdict: ACCEPTED

input
97
74

correct output
7178

user output
7178

Test 9

Verdict: ACCEPTED

input
58
8

correct output
464

user output
464

Test 10

Verdict: ACCEPTED

input
15
24

correct output
360

user output
360

Test 11

Verdict: ACCEPTED

input
4
7

correct output
28

user output
28

Test 12

Verdict: ACCEPTED

input
906
417

correct output
377802

user output
377802

Test 13

Verdict: ACCEPTED

input
778
105

correct output
81690

user output
81690

Test 14

Verdict: ACCEPTED

input
2
989

correct output
1978

user output
1978

Test 15

Verdict: ACCEPTED

input
2830
5329

correct output
15081070

user output
15081070

Test 16

Verdict: ACCEPTED

input
9
51382

correct output
462438

user output
462438

Test 17

Verdict: ACCEPTED

input
25053
71372

correct output
1788082716

user output
1788082716

Test 18

Verdict: ACCEPTED

input
258180
674616

correct output
174172358880

user output
174172358880

Test 19

Verdict: ACCEPTED

input
8821
2

correct output
17642

user output
17642

Test 20

Verdict: ACCEPTED

input
1742712
9600618

correct output
16731112196016

user output
16731112196016

Test 21

Verdict: ACCEPTED

input
8898606
2936506

correct output
26130809910636

user output
26130809910636

Test 22

Verdict: ACCEPTED

input
82670092
60138633

correct output
4971666322864236

user output
4971666322864236

Test 23

Verdict: ACCEPTED

input
54746871
83822602

correct output
4589025178578342

user output
4589025178578342

Test 24

Verdict: ACCEPTED

input
477252461
1032684

correct output
492850980435324

user output
492850980435324

Test 25

Verdict: ACCEPTED

input
5932935
379

correct output
2248582365

user output
2248582365

Test 26

Verdict: ACCEPTED

input
620114
3126641

correct output
1938873857074

user output
1938873857074

Test 27

Verdict: ACCEPTED

input
452757081
222748761

correct output
100851078826726641

user output
100851078826726641

Test 28

Verdict: ACCEPTED

input
689748332
888826746

correct output
613066765490487672

user output
613066765490487672

Test 29

Verdict: ACCEPTED

input
111337
25

correct output
2783425

user output
2783425

Test 30

Verdict: ACCEPTED

input
809
84435378

correct output
68308220802

user output
68308220802

Test 31

Verdict: ACCEPTED

input
9641697369926504411
425970950212942028697061039529...

correct output
410708299033321711216812810174...

user output
410708299033321711216812810174...

Test 32

Verdict: ACCEPTED

input
793769623129909085108356241071...

correct output
264404012608186879272715560773...

user output
264404012608186879272715560773...
Truncated

Test 33

Verdict: ACCEPTED

input
8539777831492675800
436

correct output
3723343134530806648800

user output
3723343134530806648800

Test 34

Verdict: ACCEPTED

input
946492187160898604892390431179...

correct output
585982368537725512535970251461...

user output
585982368537725512535970251461...
Truncated

Test 35

Verdict: ACCEPTED

input
874046401974324184707688863838...

correct output
174556202198322810668657866310...

user output
174556202198322810668657866310...
Truncated

Test 36

Verdict: ACCEPTED

input
168584663428092347854539803060...

correct output
235958453587245776929148968707...

user output
235958453587245776929148968707...
Truncated

Test 37

Verdict: ACCEPTED

input
279013912031336395843652482056...

correct output
856375236460411618343887929304...

user output
856375236460411618343887929304...
Truncated

Test 38

Verdict: ACCEPTED

input
909594443312661242668561455177...

correct output
801297086685128929836268694647...

user output
801297086685128929836268694647...
Truncated

Test 39

Verdict: ACCEPTED

input
521558480102200460144622364590...

correct output
403176935665359352292583479223...

user output
403176935665359352292583479223...

Test 40

Verdict: ACCEPTED

input
198766521920629467015839613580...

correct output
197951285207558548760833360414...

user output
197951285207558548760833360414...
Truncated

Test 41

Verdict: ACCEPTED

input
388239940637354291806784217812...

correct output
354893636094929851749498258576...

user output
354893636094929851749498258576...
Truncated

Test 42

Verdict: ACCEPTED

input
580031950564534684773525167998...

correct output
225288306472433597677862095876...

user output
225288306472433597677862095876...
Truncated

Test 43

Verdict: ACCEPTED

input
673497493525004204568833306269...

correct output
104167516519697053781119530996...

user output
104167516519697053781119530996...
Truncated

Test 44

Verdict: ACCEPTED

input
583582406474458495157747860432...

correct output
355985267949419682046226194863...

user output
355985267949419682046226194863...
Truncated

Test 45

Verdict: ACCEPTED

input
154401310284121033413839709675...

correct output
472687322036571910421947159369...

user output
472687322036571910421947159369...
Truncated

Test 46

Verdict: ACCEPTED

input
964784520177212016698
135881607827957154173561484162...

correct output
131096471809203739325264543904...

user output
131096471809203739325264543904...
Truncated

Test 47

Verdict: ACCEPTED

input
506417941420848908877158785176...

correct output
124940484872553056181800567857...

user output
124940484872553056181800567857...
Truncated

Test 48

Verdict: ACCEPTED

input
278205703909200971326699489015...

correct output
213362541886605761113025837459...

user output
213362541886605761113025837459...
Truncated

Test 49

Verdict: ACCEPTED

input
488919747667763730629078434642...

correct output
244261035002054726047225565934...

user output
244261035002054726047225565934...
Truncated

Test 50

Verdict: ACCEPTED

input
683013292533355268532590162229...

correct output
271255985219635665074840248062...

user output
271255985219635665074840248062...
Truncated

Test 51

Verdict: ACCEPTED

input
701382950383712289025758984281...

correct output
396240397875971182850884660551...

user output
396240397875971182850884660551...
Truncated

Test 52

Verdict: ACCEPTED

input
950530137216618089651057517232...

correct output
525100658977646195130452101103...

user output
525100658977646195130452101103...
Truncated

Test 53

Verdict: ACCEPTED

input
758180874616256083097058082046...

correct output
612777382638418549100062437996...

user output
612777382638418549100062437996...
Truncated

Test 54

Verdict: ACCEPTED

input
282198270649528096385750216226...

correct output
878945962031578099916769892430...

user output
878945962031578099916769892430...
Truncated

Test 55

Verdict: ACCEPTED

input
374271236006180996628555027124...

correct output
205927043926518428842129271440...

user output
205927043926518428842129271440...
Truncated

Test 56

Verdict: ACCEPTED

input
789860669365068182777748873091...

correct output
369460448033120451265094062370...

user output
369460448033120451265094062370...
Truncated

Test 57

Verdict: ACCEPTED

input
826700926013863385104801713448...

correct output
291751287859134397942962144651...

user output
291751287859134397942962144651...
Truncated

Test 58

Verdict: ACCEPTED

input
947468718382260248801518078140...

correct output
226868697296935607336651841496...

user output
226868697296935607336651841496...
Truncated

Test 59

Verdict: ACCEPTED

input
177252461103268440789803954968...

correct output
111876380249200192763403085310...

user output
111876380249200192763403085310...
Truncated

Test 60

Verdict: ACCEPTED

input
393293577943612353036749957226...

correct output
336630505716557163667422969707...

user output
336630505716557163667422969707...
Truncated

Test 61

Verdict: ACCEPTED

input
320114112664152374910455416563...

correct output
136407754249269979820422504376...

user output
136407754249269979820422504376...
Truncated

Test 62

Verdict: ACCEPTED

input
152757081122748761316522074282...

correct output
107712372482584798763194835348...

user output
107712372482584798763194835348...
Truncated

Test 63

Verdict: ACCEPTED

input
889748332988826746683887083103...

correct output
729454517423131565738173030712...

user output
729454517423131565738173030712...
Truncated

Test 64

Verdict: ACCEPTED

input
311337350148998951898280698942...

correct output
245742878826375358332482490843...

user output
245742878826375358332482490843...
Truncated

Test 65

Verdict: ACCEPTED

input
709744353788876782171034561202...

correct output
198288295923437797210097622398...

user output
198288295923437797210097622398...
Truncated