Submission #48490

#	Time	Username	Problem	Language	Result	Execution time	Memory
48490		zadrga	Split the sequence (APIO14_sequence)	C++14	0 / 100	108 ms	86144 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{
	int type;
	double x;
	ll k, n;
	int ind;
};

bool operator<(line a, line b){
	if(a.type + b.type > 0)
		return a.x < b.x;

	return a.k > b.k;
}

set<line> env;
typedef set<line>::iterator sit;

double intersect(sit a, sit b){
	return (double) (b -> n - a -> n) / (a -> k - b -> k);
}

bool has_prev(sit it){
	return it != env.begin();
}

bool has_next(sit it){
	return it != env.end() && next(it) != env.end();
}

void calc_x(sit it){
	if(has_prev(it)){
		line l = *it;
		l.x = intersect(prev(it), it);
		env.insert(env.erase(it), l);
	}
}

bool irrelevant(sit it){
	if(has_next(it) && next(it) -> n <= it -> n)
		return 1;

	return has_prev(it) && has_next(it) && intersect(prev(it), next(it)) <= intersect(prev(it), it);
}

void add(ll k, ll n, int id){
	sit it = env.lower_bound({0, 0, k, n, -1});
	if(it != env.end() && it -> k == k){
		if(it -> n <= n)
			return;
		else
			env.erase(it);
	}

	it = env.insert({0, 0, k, n, id}).fi;
	if(irrelevant(it)){
		env.erase(it);
		return;
	}

	while(has_prev(it) && irrelevant(prev(it)))
		env.erase(prev(it));

	while(has_next(it) && irrelevant(next(it)))
		env.erase(next(it));

	if(has_next(it))
		calc_x(next(it));

	calc_x(it);
}

pair<int, int> query(ll x){
	if(env.size() == 0)
		return mp(INF, -1);

	sit it = env.upper_bound({1, double(x), 0, 0, -1});
	it--;

//	cout <<  it -> k << "  " << it -> n  <<  "  " << it -> ind << endl;
	return mp(it -> k * x + it -> n, it -> 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();

		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;
		}
	}
	
/*
	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++){
		for(int i = j; i <= n - 1; i++){
			for(int z = 1; z < i; z++){
				if(dp[i][j] < sum(i + 1, n) * (sum(1, i) - sum(1, z)) + dp[z][j - 1]){
					dp[i][j] = sum(i + 1, n) * (sum(1, i) - sum(1, z)) + dp[z][j - 1];
					from[i][j] = z;
				}
			}
		}
	} */


/*	for(int i = 0; i <= k; i++){
		for(int j = 0; j <= n; j++)
			printf("%lld ", dp[j][i]);
		printf("\n");
	} */

	int ans = 0;
	for(int i = 1; i <= n - 1; i++){
		if(dp[i][k % 2] > dp[ans][k])
			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:112:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d%d", &n, &k);
  ~~~~~^~~~~~~~~~~~~~~~
sequence.cpp:114:8: 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