Editorial for Cắt bảng


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

Code mẫu của flashmt

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

int f[1 << 16], a[4][4], m, n;

int dp(int mask)
{
    if (!mask) return 0;
    int &res = f[mask];
    if (res >= 0) return res;

    res = 0;
    for (int i = 0; i < m; i++)
        for (int j = 0; j < n; j++)
            if (mask >> (i * n + j) & 1)
            {
                // horizontal
                int x = a[i][j], usedMask = 1 << (i * n + j);
                res = max(res, dp(mask - usedMask) + x);
                for (int k = j + 1; k < n; k++)
                    if (mask >> (i * n + k) & 1)
                    {
                        x = x * 10 + a[i][k]; usedMask += 1 << (i * n + k);
                        res = max(res, dp(mask - usedMask) + x);
                    }
                    else break;

                // vertical
                x = a[i][j]; usedMask = 1 << (i * n + j);
                for (int k = i + 1; k < m; k++)
                    if (mask >> (k * n + j) & 1)
                    {
                        x = x * 10 + a[k][j]; usedMask += 1 << (k * n + j);
                        res = max(res, dp(mask - usedMask) + x);
                    }
            }

    return res;
}

int main()
{
    memset(f, -1, sizeof(f));
    cin >> m >> n;
    for (int i = 0; i < m; i++)
        for (int j = 0; j < n; j++)
            cin >> a[i][j];
    cout << dp((1 << (m * n)) - 1) << endl;
}

Code mẫu của happyboy99x

#include<cstdio>

int temp, res, a[5][5], used[5][5], m, n, step = 0;

void backtrack(int i, int j) {
    if(j == n) {
        if(i == m-1) { if(temp > res) res = temp; }
        else backtrack(i+1, 0);
    } else if(used[i][j]) backtrack(i, j+1);
    else {
        ++step; used[i][j] = step; temp += a[i][j]; backtrack(i, j+1); temp -= a[i][j];
        int x = a[i][j];
        for(int c = j + 1; ; ++c) if(used[i][c]) {
            for(int y = j + 1; y < c; ++y) used[i][y] = 0;
            break;
        } else {
            x = x * 10 + a[i][c]; used[i][c] = step; temp += x;
            backtrack(i, c+1); temp -= x;
        }
        x = a[i][j];
        for(int r = i + 1; ; ++r) if(used[r][j]) {
            for(int x = i + 1; x < r; ++x) used[x][j] = 0;
            break;
        } else {
            x = x * 10 + a[r][j]; used[r][j] = step; temp += x;
            backtrack(i, j+1); temp -= x;
        }
        used[i][j] = 0; --step;
    }
}

int main() {
    scanf("%d%d", &m, &n); for(int i = 0; i < m; ++i) for(int j = 0; j < n; ++j) scanf("%d", &a[i][j]);
    for(int j = 0; j <= n; ++j) used[m][j] = 1; for(int i = 0; i <= m; ++i) used[i][n] = 1;
    backtrack(0, 0);
    printf("%d\n", res);
    return 0;
}

Code mẫu của ladpro98

program c11cut;
uses    math;
const   fi='';
        cx:array[1..9] of longint = (0,0,0,0,1,2,3,4,0);
        cy:array[1..9] of longint = (1,2,3,4,0,0,0,0,0);
var     a:array[1..4,1..4] of longint;
        check:array[1..4,1..4] of boolean;
        m,n,res:longint;

procedure input;
var     inp:text;
        i,j:longint;
begin
        assign(inp,fi);
        reset(inp);
        readln(inp,m,n);
        for i:=1 to m do
        begin
                for j:=1 to n do
                read(inp,a[i,j]);
                readln(inp);
        end;
        close(inp);
end;

function sum(i,j,x,y:longint):longint;
var     p,t:longint;
begin
        t:=0;
        if i=x then
        for p:=j to y do
        t:=10*t+a[i,p]
        else
        for p:=i to x do
        t:=10*t+a[p,j];
        exit(t);
end;

procedure like(i,j,x,y:longint);
var     p,q:longint;
begin
        for p:=i to x do
        for q:=j to y do
        check[p,q]:=true;
end;

procedure unlike(i,j,x,y:longint);
var     p,q:longint;
begin
        for p:=i to x do
        for q:=j to y do
        check[p,q]:=false;
end;

function ok(i,j,x,y:longint):boolean;
var     p,q:longint;
begin
        for p:=i to x do
        for q:=j to y do
        if check[p,q] then exit(false);
        exit(true);
end;

procedure back(i,j,s:longint);
var     k,x,y:longint;
begin
        if i>m then
        begin
                res:=max(res,s);
                exit;
        end;
        if check[i,j] then
        begin
                if j<n then back(i,j+1,s)
                else    back(i+1,1,s);
                exit;
        end;
        for k:=1 to 9 do
        begin
                x:=i+cx[k];
                y:=j+cy[k];
                if (x<=m) and (y<=n) then
                if ok(i,j,x,y) then
                begin
                        like(i,j,x,y);
                        if j<n then back(i,j+1,s+sum(i,j,x,y))
                        else    back(i+1,1,s+sum(i,j,x,y));
                        unlike(i,j,x,y);
                end;
        end;
end;

begin
        input;
        back(1,1,0);
        write(res);
end.

Code mẫu của RR

#include <sstream>
#include <iomanip>
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <string>
#include <deque>
#include <complex>

#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 FORN(i,a,b) for(int i=(a),_b=(b);i<_b;i++)
#define DOWN(i,a,b) for(int i=a,_b=(b);i>=_b;i--)
#define SET(a,v) memset(a,v,sizeof(a))
#define sqr(x) ((x)*(x))
#define ll long long
#define F first
#define S second
#define PB push_back
#define MP make_pair

#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;
#define BUFSIZE (1<<12)
char BUF[BUFSIZE+1], *inp=BUF;
#define GETCHAR(INP) { \
    if(!*inp) { \
        if (REACHEOF) return 0;\
        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 long double PI = acos((long double) -1.0);

int f[10][10][10][10];
int m, n, a[10][10];

int row(int i, int l, int r) {
    int res = 0;
    FOR(j,l,r)
        res = res * 10 + a[i][j];
    return res;
}

int col(int j, int l, int r) {
    int res = 0;
    FOR(i,l,r)
        res = res * 10 + a[i][j];
    return res;
}

int get(int u, int v, int x, int y) {
    if (f[u][v][x][y] >= 0) return f[u][v][x][y];
    if (u == x && v == y) return a[u][v];

    int res = 0;
    if (u < x) {
        res = max(res, row(u, v, y) + get(u+1, v, x, y));
        res = max(res, row(x, v, y) + get(u, v, x-1, y));
    }
    else res = max(res, row(u, v, y));

    if (v < y) {
        res = max(res, col(v, u, x) + get(u, v+1, x, y));
        res = max(res, col(y, u, x) + get(u, v, x, y-1));
    }
    else res = max(res, col(v, u, x));

    return f[u][v][x][y] = res;
}

int main() {
    scanf("%d%d", &m, &n);
    FOR(i,1,m) FOR(j,1,n) scanf("%d", &a[i][j]);

    memset(f, -1, sizeof f);
    cout << get(1, 1, m, n) << endl;
    return 0;
}

Code mẫu của hieult

#include <set>
#include <map>
#include <list>
#include <cmath>
#include <queue>
#include <stack>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <sstream>
#include <iomanip>
#include <iostream>
#include <algorithm>

#include <ctime>
#include <deque>
#include <bitset>
#include <cctype>
#include <utility>
#include <cassert>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef unsigned int ui;
typedef unsigned long long ull;

#define Rep(i,n) for(int i = 0; i < (n); ++i)
#define Repd(i,n) for(int i = (n)-1; i >= 0; --i)
#define For(i,a,b) for(int i = (a); i <= (b); ++i)
#define Ford(i,a,b) for(int i = (a); i >= (b); --i)
//#define Fit(i,v) for(__typeof((v).begin()) i = (v).begin(); i != (v).end(); ++i)
//#define Fitd(i,v) for(__typeof((v).rbegin()) i = (v).rbegin(); i != (v).rend(); ++i)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define sz(a) ((int)(a).size())
#define all(a) (a).begin(), (a).end()
#define ms(a,x) memset(a, x, sizeof(a))

template<class F, class T> T convert(F a, int p = -1) { stringstream ss; if (p >= 0) ss << fixed << setprecision(p); ss << a; T r; ss >> r; return r; }
template<class T> T gcd(T a, T b) { T r; while (b != 0) { r = a % b; a = b; b = r; } return a; }
template<class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
template<class T> T sqr(T x) { return x * x; }
template<class T> T cube(T x) { return x * x * x; }
template<class T> int getbit(T s, int i) { return (s >> i) & 1; }
template<class T> T onbit(T s, int i) { return s | (T(1) << i); }
template<class T> T offbit(T s, int i) { return s & (~(T(1) << i)); }
template<class T> int cntbit(T s) { return s == 0 ? 0 : cntbit(s >> 1) + (s & 1); }

const int bfsz = 1 << 16;
char bf[bfsz + 5];
int rsz = 0;
int ptr = 0;
char gc() {
    if (rsz <= 0) {
        ptr = 0;
        rsz = (int) fread(bf, 1, bfsz, stdin);
        if (rsz <= 0)
            return EOF;
    }
    --rsz;
    return bf[ptr++];
}
void ga(char &c) {
    c = EOF;
    while (!isalpha(c))
        c = gc();
}
int gs(char s[]) {
    int l = 0;
    char c = gc();
    while (isspace(c))
        c = gc();
    while (c != EOF && !isspace(c)) {
        s[l++] = c;
        c = gc();
    }
    s[l] = '\0';
    return l;
}
template<class T> bool gi(T &v) {
    v = 0;
    char c = gc();
    while (c != EOF && c != '-' && !isdigit(c))
        c = gc();
    if (c == EOF)
        return false;
    bool neg = c == '-';
    if (neg)
        c = gc();
    while (isdigit(c)) {
        v = v * 10 + c - '0';
        c = gc();
    }
    if (neg)
        v = -v;
    return true;
}

typedef pair<int, int> II;

const ld PI = acos(-1.0);
const ld eps = 1e-13;

const int dr[] = {0, +1, 0, -1};
const int dc[] = {+1, 0, -1, 0};

const int inf = (int)1e9 + 5;
const ll linf = (ll)1e16 + 5;
const ll mod = (ll)1e9 + 7;

int n, m, a[5][5], f[5][5][5][5];

int cal(int r1, int c1, int r2, int c2){
    int res = 0;
    if(r1 == r2){
        For(i, c1, c2) res = res * 10 + a[r1][i];
    }
    else{
        For(i, r1, r2) res = res * 10 + a[i][c1];
    }
    return res;
}

int main(){
//  freopen("in.txt", "r", stdin);

    cin >> n >> m;
    For(i, 1, n) For(j, 1, m) cin >> a[i][j];
    For(r, 0, n - 1) For(c, 0, m - 1) For(i, 1, n - r) For(j, 1, m - c){
        if(r == 0 || c == 0) {
            f[i][j][i + r][j + c] = cal(i, j, i + r, j + c);
            continue;
        }

        f[i][j][i + r][j + c] = 0;
        f[i][j][i + r][j + c] = max(f[i][j][i + r][j + c], cal(i, j, i, j + c) + f[i + 1][j][i + r][j + c]);
        f[i][j][i + r][j + c] = max(f[i][j][i + r][j + c], cal(i, j, i + r, j) + f[i][j + 1][i + r][j + c]);
        f[i][j][i + r][j + c] = max(f[i][j][i + r][j + c], cal(i + r, j, i + r, j + c) + f[i][j][i + r - 1][j + c]);
        f[i][j][i + r][j + c] = max(f[i][j][i + r][j + c], cal(i, j + c, i + r, j + c) + f[i][j][i + r][j + c - 1]);
    }

    cout << f[1][1][n][m];

    return 0;
}

Code mẫu của skyvn97

#include<stdio.h>
#define MAX   17
int a[MAX][MAX];
int x[MAX][MAX];
long best;
int m,n;
void update(void)
{
     int i,j,k;
     long sum,val;
     bool saw[MAX][MAX];
     for (i=1;i<=m;i=i+1)
         for (j=1;j<=n;j=j+1)
             saw[i][j]=false;
     sum=0;
     for (i=1;i<=m;i=i+1)
         for (j=1;j<=n;j=j+1)         
             {
              if (saw[i][j]) continue;
              val=a[i][j];
              if (x[i][j]==1)
                 {
                  for (k=j+1;k<=n;k=k+1)
                      {
                       if (x[i][k]!=1) break;
                       else
                           {
                            val=val*10+a[i][k];
                            saw[i][k]=true;
                           }
                      }                  
                 }
              if (x[i][j]==2)
                 {
                  for (k=i+1;k<=m;k=k+1)
                      {
                       if (x[k][j]!=2) break;
                       else
                           {
                            val=val*10+a[k][j];
                            saw[k][j]=true;
                           }
                      }
                 }
              sum=sum+val;
              saw[i][j]=true;
             }
     if (sum>best) best=sum;        

}
void btrk(int r,int c)
{
     int i;
     for (i=1;i<=2;i=i+1)
         {
          x[r][c]=i;
          if (c==n)
             {
              if (r==m) update();
              else btrk(r+1,1);
             }
          else btrk(r,c+1);              
         }
}
void init(void)
{
     int i,j;
     scanf("%d",&m);
     scanf("%d",&n);
     for (i=1;i<=m;i=i+1)
         for (j=1;j<=n;j=j+1) scanf("%d",&a[i][j]);
     best=0;
}
int main(void)
{
    init();
    btrk(1,1);
    printf("%ld",best); 
}

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