Hướng dẫn giải của VOI 13 Bài 1 - Phần thưởng


Chỉ dùng lời giải này khi không có ý tưởng, và đừng copy-paste code từ lời giải này. Hãy tôn trọng người ra đề và người viết lời giải.
Nộp một lời giải chính thức trước khi tự giải là một hành động có thể bị ban.

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 <utility>
#include <vector>
#include <cstdlib>
using namespace std;
const int dx[] = {-2, -1, 1, 2, 2, 1, -1, -2};
const int dy[] = {1, 2, 2, 1, -1, -2, -2, -1};

int k, a[10][10], E, used[10][10], flag[100];
long long ans, total; 
pair <int,int> e[100];
vector < pair<int,int> > c[10][10][4];

int inside(int x, int y)
{
    return x > 0 && y > 0 && x < 9 && y < 9;
}

void init()
{
    for (int x = 1; x <= 8; x++)
        for (int y = 1; y <= 8; y++)
        {
            for (int i = 0; i < 8; i++)
            {
                int xx = x + dx[i], yy = y + dy[i];
                if (inside(xx, yy) && a[xx][yy]) c[x][y][0].push_back(make_pair(xx, yy));
            }

            for (int xx = 1; xx <= 8; xx++)
            {
                int yy = x + y - xx;
                if (inside(xx, yy) && a[xx][yy]) c[x][y][1].push_back(make_pair(xx, yy));
                yy = xx + y - x;
                if (inside(xx, yy) && a[xx][yy]) c[x][y][1].push_back(make_pair(xx, yy));
            }

            for (int i = 1; i <= 8; i++)
            {
                if (a[i][y]) c[x][y][2].push_back(make_pair(i, y));
                if (a[x][i]) c[x][y][2].push_back(make_pair(x, i));
            }

            for (int z = 1; z < 3; z++)
                for (int i = 0; i < int(c[x][y][z].size()); i++)
                    c[x][y][3].push_back(c[x][y][z][i]);
        }
}

void att(int z, long long score)
{
    if (z == 4)
    {
        ans = max(ans, score);
        if (ans == total)
        {
            cout << ans << endl;
            exit(0);
        }
        return;
    }

    for (int i = 0; i < E; i++)
        if (!flag[i])
        {
            flag[i] = 1;
            int x = e[i].first, y = e[i].second;
            for (int j = 0; j < int(c[x][y][z].size()); j++)
            {
                int xx = c[x][y][z][j].first, yy = c[x][y][z][j].second;
                if (!used[xx][yy]++) score += a[xx][yy];
            }

            if (z + score) att(z + 1, score);

            for (int j = 0; j < int(c[x][y][z].size()); j++)
            {
                int xx = c[x][y][z][j].first, yy = c[x][y][z][j].second;
                if (!--used[xx][yy]) score -= a[xx][yy];
            }
            flag[i] = 0;
        }
}

int main()
{
    int x, y, z;
    cin >> k;
    for (int i = 0; i < k; i++)
    {
        cin >> x >> y >> z;
        a[x][y] = z;
        total += z;
    }

    init();

    for (int i = 1; i <= 8; i++)
        for (int j = 1; j <= 8; j++)
            if (!a[i][j])
                e[E++] = make_pair(i, j);

    att(0, 0);

    cout << ans << endl;
}

Code mẫu của ladpro98

#include <cstring>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <climits>
#include <cstdlib>
#include <ctime>
#include <memory.h>
#include <cassert>
#include <climits>
#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define REP(i, a, b) for(int i = (a); i <=(b); i++)
#define FORD(i, a, b) for(int i = (a); i > (b); i--)
#define REPD(i, a, b) for(int i = (a); i >=(b); i--)
#define TR(it, a) for(typeof((a).begin()) it = (a).begin(); it != (a).end(); it++)
#define RESET(a, v) memset((a), (v), sizeof((a)))
#define SZ(a) (int((a).size()))
#define ALL(a) (a).begin(), (a).end()
#define PB push_back
#define MP make_pair
#define LL long long
#define LD long double
#define II pair<int, int>
#define X first
#define Y second
#define VI vector<int>
const int QUEEN = 1;
const int ROOK = 2;
const int BISHOP = 3;
const int KNIGHT = 4;

const int N = 20;
const int gap = 8;

const int dx[] = {-1, -2, -2, -1, 1, 2, 2, 1};
const int dy[] = {-2, -1, 1, 2, 2, 1, -1, -2};

using namespace std;

int nFree, nRes; LL ans;
int val[N][N], cnt[N][N], cntX[N], cntY[N], cntDiag1[N], cntDiag2[N];
II freeCells[N * N], resCells[N * N];

void readInput() {
    ios :: sync_with_stdio(0); cin.tie(0);
    int k, u, v, c;
    cin >> k;
    FOR(i, 0, k) {
        cin >> u >> v >> c;
        val[u][v] = c;
    }
    REP(i, 1, 8) REP(j, 1, 8)
    if (val[i][j] == 0)
        freeCells[nFree++] = MP(i, j);
    else
        resCells[nRes++] = MP(i, j);
}

void update() {
    int x, y; LL sum = 0;
    FOR(i, 0, nRes) {
        x = resCells[i].X, y = resCells[i].Y;
        if (cnt[x][y] || cntX[x] || cntY[y] || cntDiag1[x + y] || cntDiag2[x - y + gap])
            sum += val[x][y];
    }
    ans = max(ans, sum);
}

void put(int type, int x, int y, int v) {
    if (type == QUEEN || type == ROOK)
        cntX[x] += v, cntY[y] += v;
    if (type == QUEEN || type == BISHOP)
        cntDiag1[x + y] += v, cntDiag2[x - y + gap] += v;
    if (type == KNIGHT)
    FOR(i, 0, 8) {
        x += dx[i]; y += dy[i];
        if (0 < x && 0 < y && x < 9 && y < 9)
            cnt[x][y] += v;
        x -= dx[i]; y -= dy[i];
    }
}

bool was[N * N];
void backtrack(int now) {
    if (now > 4) {
        update(); return;
    }
    FOR(i, 0, nFree)
    if (!was[i]) {
        was[i] = 1;
        put(now, freeCells[i].X, freeCells[i].Y, 1);
        backtrack(now + 1);
        was[i] = 0;
        put(now, freeCells[i].X, freeCells[i].Y, -1);
    }
}

int main() {
    readInput();
    backtrack(1);
    cout << ans;
    return 0;
}

Code mẫu của RR

#include <iostream>
#include <cstdio>
#include <vector>

#define FOR(i,a,b) for(int i=(a);i<=(b);++i)
#define REP(i,a) for(int i=0;i<(a);++i)
#define sqr(x) ((x)*(x))
using namespace std;

typedef pair<int,int> P;
int id[10][10];
long long board[10][10], cur[10][10], res;
int n, a[66], b[66], c[66], sum[66], diff[66], id2[66];
bool can[10][10][10][10];

int nGood;
P good[66];

vector<P> ke[5][66];
const int di[] = {-2,-2,-1,-1,1,1,2,2};
const int dj[] = {-1,1,-2,2,-2,2,-1,1};

bool inside(int u, int v) {
    return (u > 0 && u < 9 && v > 0 && v < 9);
}

void init() {
    FOR(i,1,8) FOR(j,1,8) {
        // 1 : Knight
        REP(dir,8) {
            int u = i + di[dir], v = j + dj[dir];
            if (inside(u,v))
                ke[1][id[i][j]].push_back(make_pair(u, v));
        }

        // 2 : Rook
        FOR(x,1,8) {
            ke[2][id[i][j]].push_back(make_pair(x, j));
            ke[2][id[i][j]].push_back(make_pair(i, x));
        }

        // 3 : Knight
        FOR(u,1,8) {
            int v = i + j - u;
            if (inside(u, v)) ke[3][id[i][j]].push_back(make_pair(u, v));
            v = u - (i - j);
            if (inside(u, v)) ke[3][id[i][j]].push_back(make_pair(u, v));
        }

        // 4 : Queen
        FOR(t,2,3)
            REP(x,ke[t][id[i][j]].size())
                ke[4][id[i][j]].push_back(ke[t][id[i][j]][x]);
    }
}

bool mark[10][10];

void solve2() {
    FOR(i,1,n) {
        int a, b, c; scanf("%d%d%d", &a, &b, &c);
        board[a][b] += c;
    }
    FOR(i,1,8) FOR(j,1,8) {
        if (!board[i][j]) {
            good[++nGood] = make_pair(i,j);
            id[i][j] = nGood;
        }
        cur[i][j] = board[i][j];
    }

    init();

    res = 0;
    int u, v;
    FOR(knight_id,1,nGood)
    FOR(rook_id,1,nGood) if (rook_id != knight_id)
    FOR(bishop_id,1,nGood) if (bishop_id != knight_id && bishop_id != rook_id)
    FOR(queen_id,1,nGood) if (queen_id != knight_id && queen_id != rook_id && queen_id != bishop_id) {
        FOR(i,1,8) FOR(j,1,8) cur[i][j] = board[i][j];

        long long now = 0;
        REP(x,ke[1][knight_id].size()) {
            u = ke[1][knight_id][x].first, v = ke[1][knight_id][x].second;
            now += cur[u][v];
            cur[u][v] = 0;
        }
        REP(x,ke[2][rook_id].size()) {
            u = ke[2][rook_id][x].first, v = ke[2][rook_id][x].second;
            now += cur[u][v];
            cur[u][v] = 0;
        }
        REP(x,ke[3][bishop_id].size()) {
            u = ke[3][bishop_id][x].first, v = ke[3][bishop_id][x].second;
            now += cur[u][v];
            cur[u][v] = 0;
        }
        REP(x,ke[4][queen_id].size()) {
            u = ke[4][queen_id][x].first, v = ke[4][queen_id][x].second;
            now += cur[u][v];
            cur[u][v] = 0;
        }
        res = max(res, now);
    }
    cout << res << endl;
}

void solve1() {
    for(int i = 1; i <= 8; ++i)
        for(int j = 1; j <= 8; ++j)
            for(int u = 1; u <= 8; ++u)
                for(int v = 1; v <= 8; ++v)
                    can[i][j][u][v] = sqr(i-u) + sqr(j-v) == 5;

    for(int i = 1; i <= n; ++i) {
        scanf("%d%d%d", &a[i], &b[i], &c[i]);
        sum[i] = a[i] + b[i];
        diff[i] = a[i] - b[i];
        board[a[i]][b[i]] += c[i];
    }

    long long res = 0, cur;
    for(int rooki = 1; rooki <= 8; ++rooki)
        for(int rookj = 1; rookj <= 8; ++rookj) if (!board[rooki][rookj]) {
            for(int bishopi = 1; bishopi <= 8; ++bishopi)
                for(int bishopj = 1; bishopj <= 8; ++bishopj)
                    if (!board[bishopi][bishopj])
                    if (bishopi != rooki || bishopj != rookj) {
                        int bishop_sum = bishopi + bishopj, bishop_diff = bishopi - bishopj;
                        for(int queeni = 1; queeni <= 8; ++queeni)
                            for(int queenj = 1; queenj <= 8; ++queenj)
                                if (!board[queeni][queenj])
                                if (queeni != rooki || queenj != rookj)
                                    if (queeni != bishopi || queenj != bishopj) {
                                        int queen_sum = queeni + queenj, queen_diff = queeni - queenj;
                                        long long cursum = 0;
                                        int nId = 0;
                                        for(int i = 1; i <= n; ++i) {
                                            if (a[i] == rooki || b[i] == rookj
                                                || sum[i] == bishop_sum || diff[i] == bishop_diff
                                                || a[i] == queeni || b[i] == queenj
                                                || sum[i] == queen_sum || diff[i] == queen_diff)
                                                    cursum += c[i];
                                            else id2[++nId] = i;
                                        }

                                        for(int knighti = 1; knighti <= 8; ++knighti)
                                            for(int knightj = 1; knightj <= 8; ++knightj)
                                                if (!board[knighti][knightj])
                                                if (knighti != rooki || knightj != rookj)
                                                    if (knighti != bishopi || knightj != bishopj)
                                                        if (knighti != queeni || knightj != queenj) {
                                                            cur = 0;
                                                            for(int i = 1; i <= nId; ++i) {
                                                                if (can[knighti][knightj][a[id2[i]]][b[id2[i]]])
                                                                    cur += c[id2[i]];
                                                            }
                                                            res = max(res, cur + cursum);
                                                        }
                                    }
                    }
        }

    cout << res << endl;
}

int main() {
    scanf("%d", &n);
    if (n >= 30) {
        solve2();
    }
    else solve1();
}

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-9;

const int dr[] = {+2, +1, +2, +1, -2, -1, -2, -1};
const int dc[] = {+1, +2, -1, -2, +1, +2, -1, -2};

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

#define maxn 105

ull X[64], H[64], T[64], M[64];
ll f[64], d[64];

ull cal(int r, int c){
    ull t = 1;
    t <<= (r * 8 + c);
    return t;
}

ull cal1(int r, int c){
    int t = r * 8 + c;
    if(d[t] != -1) return ((ull)(1) << d[t]);
    return 0;
}

bool inside(int r, int c){
    return r >= 0 && r < 8 && c >= 0 && c < 8;
}

void getX(int id){
    int r = id / 8, c = id % 8;
    X[id] = 0;
    Rep(i, 8){
        X[id] |= cal1(r, i);
        X[id] |= cal1(i, c);
    }
}

void getH(int id){
    int r = id / 8, c = id % 8;
    H[id] = 0;
    Rep(i, 8){
        H[id] |= cal1(r, i);
        H[id] |= cal1(i, c);
    }
    Rep(i, 8) Rep(j, 8){
        if(i - j == r - c || i + j == r + c){
            H[id] |= cal1(i, j);
        }
    }
}

void getT(int id){
    int r = id / 8, c = id % 8;
    T[id] = 0;
    Rep(i, 8) Rep(j, 8){
        if(i - j == r - c || i + j == r + c){
            T[id] |= cal1(i, j);
        }
    }
}

void getM(int id){
    int r = id / 8, c = id % 8;
    M[id] = 0;
    Rep(h, 8){
        int rr = r + dr[h], cc = c + dc[h];
        if(inside(rr, cc)){
            M[id] |= cal1(rr, cc);
        }
    }
}

void init(){
    Rep(i, 64){
        getX(i);
        getH(i);
        getT(i);
        getM(i);
    }
}

ull mask;
ll res = 0;
int num, r, c, g;

void go(int id, ull Mask, ull mask1){
    if(id == 4){
        if(Mask){
            ll ret = 0;
            Rep(i, num) if(getbit(Mask, i)){
                ret += f[i];
            }
            res = max(res, ret);
        }
        return;
    }

    Rep(i, 64) if(!getbit(mask, i) && !getbit(mask1, i)){
        ull Maskt = Mask, mask1t = mask1;
        mask1t |= ((ull)(1) << i);
        if(id == 0) Maskt |= X[i];
        if(id == 1) Maskt |= H[i];
        if(id == 2) Maskt |= T[i];
        if(id == 3) Maskt |= M[i];
        go(id + 1, Maskt, mask1t);
    }
}


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

    cin >> num;
    mask = 0;
    ms(f, 0);
    ms(d, -1);
    Rep(i, num){
        cin >> r >> c >> g;
        r--; c--;
        int x = r * 8 + c;
        mask |= cal(r, c);
        d[x] = i;
        f[i] = g;
    }
    init();
    go(0, 0, 0);
    cout << res << endl;
//  cout << clock() << endl;

    return 0;
}

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