Editorial for VOI 14 Bài 2 - Dãy con chung bội hai dài nhất


Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.

Lưu ý: Các code mẫu dưới đây chỉ mang tính tham khảo và có thể không AC được bài tập này

Code mẫu của happyboy99x

#include<algorithm>
#include<iostream>
#include<vector>
using namespace std;

struct BIT2D {
    vector<vector<int> > data;
    int m, n;

    BIT2D(int m, int n): data (m, vector<int>(n, 0)), m (m), n (n) {}

    void update(int idx, int idy, int val) {
        for(int x = idx; x < m; x |= x + 1)
            for(int y = idy; y < n; y |= y + 1)
                data[x][y] = max(data[x][y], val);
    }

    int get(int idx, int idy) const {
        int res = 0;
        for(int x = idx; x >= 0; x -= ~x & (x + 1))
            for(int y = idy; y >= 0; y -= ~y & (y + 1))
                res = max(res, data[x][y]);
        return res;
    }
};

const int N = 1500;
int a[N], b[N], f[N + 1][N + 1];

int main() {
    ios::sync_with_stdio(false);
    int tc; cin >> tc;
    while(tc--) {
        int m, n; cin >> m >> n;
        for(int i = 0; i < m; ++i) cin >> a[i];
        for(int i = 0; i < n; ++i) cin >> b[i];
        vector<int> v (b, b + n);
        sort(v.begin(), v.end());
        v.erase(unique(v.begin(), v.end()), v.end());
        BIT2D bit (n, v.size());
        for(int i = 0; i < m; ++i) {
            vector<int> toUpdate;
            for(int j = 0; j < n; ++j) {
                if(a[i] == b[j]) {
                    int p = upper_bound(v.begin(), v.end(), b[j] / 2) - v.begin() - 1;
                    f[i + 1][j + 1] = bit.get(j - 1, p) + 1;
                    toUpdate.push_back(j);
                } else {
                    f[i + 1][j + 1] = max(f[i][j + 1], f[i + 1][j]);
                }
            }
            for(unsigned k = 0; k < toUpdate.size(); ++k) {
                int j = toUpdate[k];
                int p = lower_bound(v.begin(), v.end(), b[j]) - v.begin();
                bit.update(j, p, f[i + 1][j + 1]);
            }
        }
        cout << f[m][n] << endl;
    }
    return 0;
}

Code mẫu của ladpro98

#include <bits/stdc++.h>

using namespace std;

const int N = 1505;

int BIT[N][N];
int a[N], b[N];
int n, m, SIZE;

void update(int i, int y, int v) {
    for (; i <= n; i += i & -i) for (int j = y; j <= SIZE; j += j & -j)
        BIT[i][j] = max(BIT[i][j], v);
}

int getMax(int i, int y) {
    int ans = 0;
    for (; i; i -= i & -i) for (int j = y; j; j -= j & -j)
        ans = max(ans, BIT[i][j]);
    return ans;
}

void solve() {
    cin >> m >> n;
    for (int i = 1; i <= m; ++i) cin >> a[i];
    for (int i = 1; i <= n; ++i) cin >> b[i];
    vector<int> V (b + 1, b + 1 + n);
    sort(V.begin(), V.end());
    V.resize(unique(V.begin(), V.end()) - V.begin());
    SIZE = V.size();
    for (int i = 1; i <= n; ++i) for (int j = 1; j <= SIZE; ++j)
        BIT[i][j] = 0;
    int ans = 0;
    for (int i = 1; i <= m; ++i) {
        vector<pair<pair<int, int>, int> > buffer;
        for (int j = 1; j <= n; ++j) if (a[i] == b[j]) {
            int value = lower_bound(V.begin(), V.end(), a[i]) - V.begin() + 1;
            int half = int(upper_bound(V.begin(), V.end(), a[i] >> 1) - V.begin());
            int cur = getMax(j - 1, half) + 1;
            ans = max(ans, cur);
            buffer.push_back(make_pair(make_pair(j, value), cur));
        }
        while (!buffer.empty()) {
            update(buffer.back().first.first, buffer.back().first.second, buffer.back().second);
            buffer.pop_back();
        }
    }
    cout << ans << '\n';
}

 int main() {
    ios::sync_with_stdio(0); cin.tie(0);
#ifndef ONLINE_JUDGE
    freopen("LCS2X.txt", "r", stdin);
#endif // ONLINE_JUDGE
    int nTest; cin >> nTest;
    while (nTest--) solve();
    return 0;
 }

Code mẫu của RR

#include <bits/stdc++.h>

#define FOR(i,a,b) for(int i=(a),_b=(b); i<=_b; i++)
#define FORD(i,a,b) for(int i=(a),_b=(b); i>=_b; i--)
#define REP(i,a) for(int i=0,_a=(a); i<_a; i++)

#define DEBUG(x) { cout << #x << " = "; cout << x << endl; }
#define PR(a,n) { cout << #a << " = "; FOR(_,1,n) cout << a[_] << ' '; cout << endl; }
#define PR0(a,n) { cout << #a << " = "; REP(_,n) cout << a[_] << ' '; cout << endl; }
using namespace std;

//Buffer reading
int INP,AM,REACHEOF;
const int BUFSIZE = (1<<12) + 17;
char BUF[BUFSIZE+1], *inp=BUF;
#define GETCHAR(INP) { \
    if(!*inp && !REACHEOF) { \
        memset(BUF,0,sizeof BUF);\
        int inpzzz = fread(BUF,1,BUFSIZE,stdin);\
        if (inpzzz != BUFSIZE) REACHEOF = true;\
        inp=BUF; \
    } \
    INP=*inp++; \
}
#define DIG(a) (((a)>='0')&&((a)<='9'))
#define GN(j) { \
    AM=0;\
    GETCHAR(INP); while(!DIG(INP) && INP!='-') GETCHAR(INP);\
    if (INP=='-') {AM=1;GETCHAR(INP);} \
    j=INP-'0'; GETCHAR(INP); \
    while(DIG(INP)){j=10*j+(INP-'0');GETCHAR(INP);} \
    if (AM) j=-j;\
}
//End of buffer reading
const int MN = 3011;

int a[MN], b[MN], m, n, c[MN], s;
int nextb[MN][MN];
int ca[MN], cb[MN], f[MN][55];

void init() {
    FOR(i,1,m) ca[i] = ca[i-1] + (a[i] == 0);
    FOR(i,1,n) cb[i] = cb[i-1] + (b[i] == 0);

    s = 0;
    FOR(i,1,m) c[++s] = a[i];
    FOR(i,1,n) c[++s] = b[i];
    sort(c+1, c+s+1);
    s = unique(c+1, c+s+1) - c - 1;

    FOR(i,1,m) a[i] = lower_bound(c+1, c+s+1, a[i]) - c;
    FOR(i,1,n) b[i] = lower_bound(c+1, c+s+1, b[i]) - c;

    memset(nextb, 0, sizeof nextb);
    FORD(i,n,1) {
        FOR(j,1,i) nextb[i][b[j]] = j;
    }
}

void solve() {
    int res = min(ca[m], cb[n]);
    // DEBUG(res);

    FORD(i,m,1) FOR(h,1,31) if (c[a[i]]) {
        if (h == 1) {
            f[i][1] = nextb[n][a[i]];
        }
        else {
            f[i][h] = 0;
            if (f[i][h-1] == 0) continue;

            FOR(ii,i+1,m) if (c[a[i]] * 2 <= c[a[ii]]) {
                int u = f[ii][h-1];
                f[i][h] = max(f[i][h], nextb[u][a[i]]);
            }
        }
        if (f[i][h]) {
            res = max(res, h + min(ca[i-1], cb[f[i][h]-1]));
            // cout << i << ' ' << h << ' ' << f[i][h] << ' ' << res << endl;
        }
    }

    cout << res << endl;
}

int main() {
    ios :: sync_with_stdio(false);
    int ntest; cin >> ntest;
    while (ntest--) {
        cin >> m >> n;
        FOR(i,1,m) cin >> a[i];
        FOR(i,1,n) cin >> b[i];

        init();
        solve();
    }
    return 0;
}

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