Submission #998523

#	Time	Username	Problem	Language	Result	Execution time	Memory
998523		Arapak	Carnival Tickets (IOI20_tickets)	C++17	67 / 100	589 ms	132256 KiB

tickets

// Author: Kajetan Ramsza
#include "bits/stdc++.h"
#include "tickets.h"
using namespace std;

#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;

template<typename F, typename S> ostream& operator<<(ostream& os, const pair<F, S> &p) { return os<<"("<<p.first<<", "<<p.second<<")"; }
template<typename T> ostream &operator<<(ostream & os, const vector<T> &v) { os << "{"; typename vector< T > :: const_iterator it;
    for( it = v.begin(); it != v.end(); it++ ) { if( it != v.begin() ) os << ", "; os << *it; } return os << "}"; }

void dbg_out() { cerr<<'\n'; }
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr<<' '<<H; dbg_out(T...); }

#ifdef DEBUG
#define dbg(...) cerr<<"(" << #__VA_ARGS__ <<"):", dbg_out(__VA_ARGS__)
#else
#define dbg(...) 
#endif

const ll inf = ll(1e18) + 7;

int n, m, k;
vector<vi> answer;
vector<pii> used;
vector<vector<ll>> tickets;

void update_used(vector<vector<ll>> &dp, int ind) {
	int curr = n / 2;
	for(int i=n-1;i>=0;i--) {
		if(dp[i+1][curr] == dp[i][curr] + tickets[i][used[i].second]) {
			answer[i][used[i].second] = ind;
			used[i].second--;
		} else {
			answer[i][used[i].first] = ind;
			used[i].first++;
			curr--;
		}
	}
}

ll solve_k1() {
	used.assign(n, {0, m-1});
	vector<vector<ll>> dp(n+1, vector<ll>(n+1, -inf));
	dp[0][0] = 0;
	ll result = 0;
	rep(ind,0,k) {
		rep(i,0,n) {
			dp[i+1][0] = -inf;
			rep(j,0,i+1) {
				dp[i+1][j] = max(dp[i+1][j], dp[i][j] + tickets[i][used[i].second]);
				dp[i+1][j+1] = dp[i][j] - tickets[i][used[i].first];
			}
		}
		dbg(used);
		dbg(dp);
		update_used(dp, ind);
		result += dp[n][n / 2];
	}
	return result;
}


ll solve_1() {
	vector<vi> ones(n);
	vector<vi> zeros(n);
	rep(i,0,n) rep(j,0,m) {
		if(tickets[i][j] == 1)
			ones[i].push_back(j);
		else if(tickets[i][j] == 0)
			zeros[i].push_back(j);
	}
	ll res = 0;
	rep(ind,0,k) {
		vector<pii> num(n);
		rep(i,0,n) num[i] = {sz(ones[i]), i};
		sort(all(num));
		rep(i,0,n) {
			int index = num[i].second;
			if((i < n/2 && sz(zeros[index])) || sz(ones[index]) == 0) {
				answer[index][zeros[index].back()] = ind;
				zeros[index].pop_back();
			} else {
				answer[index][ones[index].back()] = ind;
				ones[index].pop_back();
				res += i < n/2 ? -1 : 1;
			}
		}	
	}
	return res;
}

ll solve_km() {
	vector<tuple<ll, int, int>> vals;
	rep(i,0,n) rep(j,0,m)
		vals.push_back({tickets[i][j], i ,j});
	sort(all(vals));
	ll result = 0;
	rep(ind,0,n*m) {
		auto [val, i, j] = vals[ind];
		if(ind >= n*m / 2) {
			result += val;
			tickets[i][j] = 1;
		} else {
			result -= val;
			tickets[i][j] = 0;
		}
	}
	dbg(result);
	solve_1();
	return result;
}

ll solve() {
	vector<vector<ll>> dp(n+1, vector<ll>(n*k+1, -inf));
	vector<vector<ll>> curr_dp(n, vector<ll>(k+1, 0));
	dp[0][0] = 0;
	rep(i,0,n) {
		rep(j,m-k,m) curr_dp[i][0] += tickets[i][j];
		rep(j,0,k) curr_dp[i][j+1] = curr_dp[i][j] - tickets[i][m - k + j] - tickets[i][j];
		dbg(curr_dp[i]);
		rep(j,0,n*k+1)
			rep(o,0,min(k,j)+1)
				dp[i+1][j] = max(dp[i+1][j], curr_dp[i][o] + dp[i][j-o]); 
	}
	int curr = n * k / 2;
	for(int i=n-1;i>=0;i--) {
		int index = -1;
		rep(j,0,min(k, curr) + 1)
			if(dp[i+1][curr] == curr_dp[i][j] + dp[i][curr - j]) {
				index = j;
				break;
			}
		dbg(index);
		curr -= index;
		rep(j,0,index) tickets[i][j] = 0;
		rep(j,index,m-k+index) tickets[i][j] = -1;
		rep(j,m-k+index,m) tickets[i][j] = 1;
	}
	solve_1();
	return dp[n][n*k / 2];
}

ll find_maximum(int k_, vector<vi> tickets_) {
	k = k_;
	n = tickets_.size();
	m = tickets_[0].size();
	tickets.assign(n, vector<ll>(m));
	rep(i,0,n) rep(j,0,m) tickets[i][j] = tickets_[i][j];
	answer.assign(n, vi(m, -1));
	ll res;
	if(k == 1) res = solve_k1();
	else if(k == m) res = solve_km();
	else if(n <= 80 && m <= 80) res = solve();
	else res = solve_1();
	allocate_tickets(answer);
	return res;
}

• Subtask 1: 11 / 11
• Subtask 2: 16 / 16
• Subtask 3: 14 / 14
• Subtask 4: 14 / 14
• Subtask 5: 12 / 12
• Subtask 6: 0 / 23
• Subtask 7: 0 / 10