Submission #48728

#	Time	Username	Problem	Language	Result	Execution time	Memory
48728		zadrga	Split the sequence (APIO14_sequence)	C++14	0 / 100	100 ms	86196 KiB

sequence

#include <bits/stdc++.h>

using namespace std;

#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define INF (1LL << 55)
#define MOD (1000 * 1000 * 1000 + 7)
#define maxn 100111
#define maxk 211

typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;

struct line{
	ll k, n;
	int ind;
};

vector<line> env;
int best_ind;

bool bad(int l1, int l2, int l3){
	return (env[l3].n - env[l1].n) * (env[l1].k - env[l2].k) <= (env[l2].n - env[l1].n) * (env[l1].k - env[l3].k);
}

void add(line a){
	if(env.size() > 0){
		if(env.back().k == a.k){
			if(a.n > env.back().n)
				env.pop_back();
			else
				return;
		}
	}

	env.pb(a);
	while(env.size() >= 3 && bad(env.size() - 3, env.size() - 2, env.size() - 1))
		env.erase(env.end() - 2);
}

ll val(int ind, ll x){
	return env[ind].k * x + env[ind].n;
}

pair<ll, int> query(ll x){
	if(best_ind >= env.size())
		best_ind = env.size() - 1;

	while(best_ind + 1 < env.size() && val(best_ind, x) >= val(best_ind + 1, x))
		best_ind++;

	return mp(val(best_ind, x), env[best_ind].ind);
}


ll dp[maxn][2], pre[maxn], arr[maxn];
int from[maxn][maxk];

ll sum(int i, int j){
	if(i > j)
		return 0LL;

	return pre[j] - pre[i - 1];
}

int main(){
	int n, k;
	scanf("%d%d", &n, &k);
	for(int i = 1; i <= n; i++){
		scanf("%lld", arr + i);
		pre[i] = pre[i - 1] + arr[i];
	}

	for(int i = 0; i <= n; i++){
		for(int j = 0; j < 2; j++)
			dp[i][j] = -INF;
	}

	for(int i = 1; i <= n - 1; i++)
		dp[i][1] = sum(1, i) * sum(i + 1, n);

	for(int j = 2; j <= k; j++){
		env.clear();
		best_ind = 0;

		int jj = j % 2;
		int prev = 1 - jj;

		for(int i = j; i <= n - 1; i++){
			add({-(-sum(1, i - 1)), -(dp[i - 1][prev]), i - 1});
			
			pair<ll, int> cur = query( sum(i + 1, n) );
			dp[i][jj] = -cur.fi + sum(i + 1, n) * sum(1, i);
			from[i][j] = cur.se;
		}
	}

	int ans = 0;
	for(int i = 1; i <= n - 1; i++){
		if(dp[i][k % 2] > dp[ans][k % 2])
			ans = i;
	}

	printf("%lld\n", dp[ans][k % 2]);
	for(int i = k; i >= 1; i--){
		printf("%d ", ans);
		ans = from[ans][i];
	}

	return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'std::pair<long long int, int> query(ll)':
sequence.cpp:50:14: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if(best_ind >= env.size())
     ~~~~~~~~~^~~~~~~~~~~~~
sequence.cpp:53:21: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  while(best_ind + 1 < env.size() && val(best_ind, x) >= val(best_ind + 1, x))
        ~~~~~~~~~~~~~^~~~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:72:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d%d", &n, &k);
  ~~~~~^~~~~~~~~~~~~~~~
sequence.cpp:74:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%lld", arr + i);
   ~~~~~^~~~~~~~~~~~~~~~~

• Subtask 1: 0 / 11
• Subtask 2: 0 / 11
• Subtask 3: 0 / 11
• Subtask 4: 0 / 17
• Subtask 5: 0 / 21
• Subtask 6: 0 / 29