Submission #96106

#	Time	Username	Problem	Language	Result	Execution time	Memory
96106		gs14004	Split the sequence (APIO14_sequence)	C++17	100 / 100	150 ms	6348 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
typedef long long lint;
typedef long double llf;
typedef pair<lint, int> pi;
const int MAXN = 100005;

struct line{ lint x, y; int cnt, idx; };

struct cht{
	vector<line> v;
	int p = 0;
	void clear(){ v.clear(); p = 0; }
	bool bad(line x, line y, line z){
		return (llf)(x.y - y.y) / (y.x - x.x) >= (llf)(z.y - y.y) / (y.x - z.x);
	}
	void add(line l){
		if(v.size() > p && v.back().x == l.x){
			if(l.y < v.back().y) l = v.back();
			v.pop_back();
		}
		while(v.size() >= p + 2 && bad(v[v.size()-2], v.back(), l)){
			v.pop_back();
		}
		v.push_back(l);
	}
	tuple<lint, int, int> query(lint x){
		while(p + 1 < v.size() && v[p].x * x + v[p].y <= v[p+1].x * x + v[p+1].y) p++;
		return make_tuple(v[p].x * x + v[p].y, v[p].cnt, v[p].idx);
	}
}cht;

int n, k, a[MAXN], trk[MAXN];
pi dp[MAXN];

pi trial(lint l){
	cht.clear();
	for(int i=1; i<=n; i++){
		cht.add({a[i-1], dp[i-1].first - l, dp[i-1].second, i-1});
		lint x; int y, z; 
		tie(x, y, z) = cht.query(2 * (a[i] - a[n]));
		dp[i] = pi(x + 2ll * (a[n] - a[i]) * a[i], y + 1);
		trk[i] = z;
	}
	return dp[n];
}

vector<int> trace(lint l){
	trial(l);
	vector<int> v;
	for(int i=n; i; i=trk[i]){
		v.push_back(i);
	}
	v.push_back(0);
	return vector<int>(v.rbegin(), v.rend());
}

void printv(vector<int> v){
	lint ret = 0;
	for(int i=1; i<v.size(); i++){
		ret += 1ll * (a[v[i]] - a[v[i-1]]) * (a[n] - a[v[i]]);
	}
	printf("%lld\n", ret);
	for(int i=1; i+1<v.size(); i++) printf("%d ", v[i]);
	exit(0);
}

int main(){
	scanf("%d %d",&n,&k); k++;
	for (int i=0; i<n; i++) {
		int t;
		scanf("%d",&t);
		a[i+1] = a[i] + t;
	}
	lint s = 0, e = 1e17;
	while(s != e){
		lint m = (s+e)/2;
		if(trial(2 * m + 1).second <= k) e = m;
		else s = m + 1;
	}
	vector<int> l = trace(2 * s + 1);
	vector<int> r = trace(2 * s - 1);
	if(l.size() == k + 1) printv(l);
	if(r.size() == k + 1) printv(r);
	for(int i=0; i+1<r.size(); i++){
		auto idx = upper_bound(l.begin(), l.end(), r[i]) - l.begin();
		if(l[idx] >= r[i+1] && (i + 1) + (l.size() - idx) == k + 1){
			vector<int> v;
			for(int j=0; j<=i; j++) v.push_back(r[j]);
			for(int j=idx; j<l.size(); j++) v.push_back(l[j]);
			printv(v);
		}
	}
	assert(0);
}

Compilation message (stderr)

sequence.cpp: In member function 'void cht::add(line)':
sequence.cpp:18:15: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if(v.size() > p && v.back().x == l.x){
      ~~~~~~~~~^~~
sequence.cpp:22:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(v.size() >= p + 2 && bad(v[v.size()-2], v.back(), l)){
         ~~~~~~~~~^~~~~~~~
sequence.cpp: In member function 'std::tuple<long long int, int, int> cht::query(lint)':
sequence.cpp:28:15: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   while(p + 1 < v.size() && v[p].x * x + v[p].y <= v[p+1].x * x + v[p+1].y) p++;
         ~~~~~~^~~~~~~~~~
sequence.cpp: In function 'void printv(std::vector<int>)':
sequence.cpp:60:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=1; i<v.size(); i++){
               ~^~~~~~~~~
sequence.cpp:64:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=1; i+1<v.size(); i++) printf("%d ", v[i]);
               ~~~^~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:83:14: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if(l.size() == k + 1) printv(l);
     ~~~~~~~~~^~~~~~~~
sequence.cpp:84:14: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if(r.size() == k + 1) printv(r);
     ~~~~~~~~~^~~~~~~~
sequence.cpp:85:18: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  for(int i=0; i+1<r.size(); i++){
               ~~~^~~~~~~~~
sequence.cpp:87:53: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   if(l[idx] >= r[i+1] && (i + 1) + (l.size() - idx) == k + 1){
                          ~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~
sequence.cpp:90:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
    for(int j=idx; j<l.size(); j++) v.push_back(l[j]);
                   ~^~~~~~~~~
sequence.cpp:69:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d %d",&n,&k); k++;
  ~~~~~^~~~~~~~~~~~~~~
sequence.cpp:72:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d",&t);
   ~~~~~^~~~~~~~~

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