Submission #625227

#	Time	Username	Problem	Language	Result	Execution time	Memory
625227		IvanJ	Split the sequence (APIO14_sequence)	C++17	0 / 100	79 ms	86428 KiB

sequence

#include<bits/stdc++.h>

#define x first
#define y second
#define pb push_back
#define all(a) (a).begin(), (a).end()

using namespace std;

typedef long long ll;
typedef pair<int, int> ii;

const int maxn = 1e5 + 5;
const double inf = 1e18, eps = 1e-9;

struct line {double a, b, p, idx;};

int n, k;
int A[maxn];
double pref[maxn];
double dp[maxn], dp1[maxn];
int opt[maxn][205];
vector<line> lines;

double getX(double a1, double b1, double a2, double b2) {
	return (b1 - b2) / (a2 - a1);	
}

void addLine(double a, double b, double idx) {
	double p = -inf;
	while(lines.size()) {
		p = getX(a, b, lines.back().a, lines.back().b);
		if(p < lines.back().p) lines.pop_back();
		else break;
	}
	lines.pb({a, b, p, idx});
}

pair<double, int> getAns(double x) {
	int lo = 0, hi = (int)lines.size() - 1, ans = 0;
	while(lo <= hi) {
		int mid = (lo + hi) / 2;
		if(lines[mid].p <= x) ans = mid, lo = mid + 1;
		else hi = mid - 1;
	}
	return {lines[ans].a * x + lines[ans].b, (int)lines[ans].idx};
}

int main() {
	scanf("%d%d", &n, &k);
	for(int i = 0;i < n;i++) scanf("%d", A + i);
	
	pref[0] = A[0];
	for(int i = 1;i < n;i++) pref[i] = pref[i - 1] + A[i];
	
	double ans = 0;
	for(int i = 1;i < k + 1;i++) {
		addLine(pref[i - 1], dp[i - 1] - pref[i - 1] * pref[i - 1], i - 1);
		for(int j = i;j < n;j++) {
			pair<double, int> p = getAns(pref[j]);
			dp1[j] = p.x;
			opt[j][i] = p.y;
			addLine(pref[j], dp[j] - pref[j] * pref[j], j);
		}
		for(int j = i;j < n;j++) dp[j] = dp1[j];
		ans = dp[n - 1];
		lines.clear();
	}
	printf("%lld\n", (ll)ans);
	int pos = n - 1;
	for(int i = k;i >= 1;i--) 
		printf("%d ", opt[pos][i] + 1), pos = opt[pos][i];
	return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:50:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   50 |  scanf("%d%d", &n, &k);
      |  ~~~~~^~~~~~~~~~~~~~~~
sequence.cpp:51:32: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
   51 |  for(int i = 0;i < n;i++) scanf("%d", A + 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