Submission #48746

#	Time	Username	Problem	Language	Result	Execution time	Memory
48746		zadrga	Split the sequence (APIO14_sequence)	C++14	71 / 100	2063 ms	88324 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;
 
 
ll k[maxn], n[maxn];
int ind[maxn];
int best_ind, top, bot;
 
ll dp[maxn][2], pre[maxn], arr[maxn];
int from[maxn][maxk];
 
bool bad(int l1, int l2, int l3){
	return (n[l3] - n[l1]) * (k[l1] - k[l2]) < (n[l2] - n[l1]) * (k[l1] - k[l3]);
}
 
void add(ll cur_k, ll cur_n, int cur_ind){
	if(top - bot > 0 && k[top - 1] == cur_k){
		if(cur_n > n[top - 1])
			top--;
		else
			return;
	}
 
	k[top] = cur_k;
	n[top] = cur_n;
	ind[top] = cur_ind;
 
	while(top - bot >= 3 && bad(top - 2, top - 1, top)){
		k[top - 1] = k[top];
		n[top - 1] = n[top];
		ind[top - 1] = ind[top];
		top--;
	}
	top++;
}
 
inline ll val(int ind, ll x){
	return k[ind] * x + n[ind];
}
 
pair<ll, int> query(ll x){
	if(best_ind >= top)
		best_ind = top - 1;
 
	while(best_ind + 1 < top && val(best_ind, x) <= val(best_ind + 1, x))
		best_ind++;
 
	return mp(val(best_ind, x), ind[best_ind]);
}
 
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++){
		top = bot = 0;
		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] - sum(1, i - 1) * sum(1, N), i - 1);
			
			pair<ll, int> cur = query(sum(1, i));
			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 'int main()':
sequence.cpp:74:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d%d", &N, &K);
  ~~~~~^~~~~~~~~~~~~~~~
sequence.cpp:76:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%lld", arr + i);
   ~~~~~^~~~~~~~~~~~~~~~~

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