// #define LOCAL
#define _USE_MATH_DEFINES
#include <array>
#include <cassert>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <iomanip>
#include <string>
#include <sstream>
#include <vector>
#include <queue>
#include <stack>
#include <list>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <algorithm>
#include <complex>
#include <cmath>
#include <numeric>
#include <bitset>
#include <functional>
#include <random>
#include <ctime>
using namespace std;
template <typename A, typename B>
ostream& operator <<(ostream& out, const pair<A, B>& a) {
out << "(" << a.first << "," << a.second << ")";
return out;
}
template <typename T, size_t N>
ostream& operator <<(ostream& out, const array<T, N>& a) {
out << "["; bool first = true;
for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
return out;
}
template <typename T>
ostream& operator <<(ostream& out, const vector<T>& a) {
out << "["; bool first = true;
for (auto v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "]";
return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const set<T, Cmp>& a) {
out << "{"; bool first = true;
for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
return out;
}
template <typename T, class Cmp>
ostream& operator <<(ostream& out, const multiset<T, Cmp>& a) {
out << "{"; bool first = true;
for (auto& v : a) { out << (first ? "" : ", "); out << v; first = 0;} out << "}";
return out;
}
template <typename U, typename T, class Cmp>
ostream& operator <<(ostream& out, const map<U, T, Cmp>& a) {
out << "{"; bool first = true;
for (auto& p : a) { out << (first ? "" : ", "); out << p.first << ":" << p.second; first = 0;} out << "}";
return out;
}
#ifdef LOCAL
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
#else
#define trace(...) 42
#endif
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
cerr << name << ": " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
const char* comma = strchr(names + 1, ',');
cerr.write(names, comma - names) << ": " << arg1 << " |";
__f(comma + 1, args...);
}
template <class T> auto vect(const T& v, int n) { return vector<T>(n, v); }
template <class T, class... D> auto vect(const T& v, int n, D... m) {
return vector<decltype(vect(v, m...))>(n, vect(v, m...));
}
using int64 = long long;
using int128 = __int128_t;
using ii = pair<int, int>;
#define SZ(x) (int)((x).size())
template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
const int MOD = 1e9 + 7;
// const int MOD = 998244353;
// mt19937 mrand(random_device{}());
// int rnd(int x) { return mrand() % x; }
mt19937_64 mrand(random_device{}());
int64 rnd(int64 x) { return mrand() % x; }
template <class T> void out(const vector<T>& a) { for (int i = 0; i < SZ(a); ++i) cout << a[i] << " \n"[i + 1 == SZ(a)]; }
template <class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template <class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
template <class T> void dedup(vector<T>& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); }
void add_mod(int& x, int y) { x += y; if (x >= MOD) x -= MOD; }
void sub_mod(int& x, int y) { x += MOD - y; if (x >= MOD) x -= MOD; }
struct fast_ios {
fast_ios() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
};
} fast_ios_;
struct Line {
int64 m, b;
};
// maintain lower envolope (upper convex hull) for minimum
struct Envelop {
vector<Line> a;
int ptr = 0;
bool bad(int x, int y, int z) {
return (a[z].b - a[x].b) * (a[x].m - a[y].m) <
(a[y].b - a[x].b) * (a[x].m - a[z].m);
}
void insert(int64 m, int64 b) {
a.push_back(Line{m, b});
while (a.size() >= 3 && bad(a.size() - 3, a.size() - 2, a.size() - 1)) {
a.erase(a.end() - 2);
}
}
int64 eval(int64 x) {
ptr = min(ptr, (int)a.size() - 1);
while (ptr < a.size() - 1 &&
a[ptr + 1].m * x + a[ptr + 1].b < a[ptr].m * x + a[ptr].b) ++ptr;
return a[ptr].m * x + a[ptr].b;
}
};
int main() {
int n, m;
cin >> n >> m;
vector<int> a(n);
for (auto& x : a) cin >> x;
vector<int64> pre(n + 1);
for (int i = 0; i < n; ++i) pre[i + 1] = pre[i] + a[i];
auto dp = vect<int64>(0, m + 1, n + 1);
for (int i = 0; i < n; ++i) dp[0][i + 1] = pre[i + 1] * pre[i + 1];
trace(dp[0]);
for (int k = 1; k <= m; ++k) {
Envelop E;
E.insert(-2 * pre[k], dp[k - 1][k] + pre[k] * pre[k]);
for (int i = k + 1; i <= n; ++i) {
dp[k][i] = E.eval(pre[i]) + pre[i] * pre[i];
E.insert(-2 * pre[i], dp[k - 1][i] + pre[i] * pre[i]);
}
trace(k, dp[k]);
}
int64 ret = (pre[n] * pre[n] - dp[m][n]) / 2;
cout << ret << '\n';
auto sqr =
[&](int64 x) {
return x * x;
};
vector<int> rec;
for (int t = n, nt, k = m; k > 0; t = nt, --k) {
for (nt = t - 1; nt >= 0 && dp[k - 1][nt] + sqr(pre[t] - pre[nt]) != dp[k][t]; --nt);
trace(k, t, nt);
rec.push_back(nt);
}
reverse(rec.begin(), rec.end());
out(rec);
return 0;
}
Compilation message
sequence.cpp: In member function 'int64 Envelop::eval(int64)':
sequence.cpp:132:16: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
132 | while (ptr < a.size() - 1 &&
| ~~~~^~~~~~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:68:20: warning: statement has no effect [-Wunused-value]
68 | #define trace(...) 42
| ^~
sequence.cpp:148:3: note: in expansion of macro 'trace'
148 | trace(dp[0]);
| ^~~~~
sequence.cpp:68:20: warning: statement has no effect [-Wunused-value]
68 | #define trace(...) 42
| ^~
sequence.cpp:157:5: note: in expansion of macro 'trace'
157 | trace(k, dp[k]);
| ^~~~~
sequence.cpp:68:20: warning: statement has no effect [-Wunused-value]
68 | #define trace(...) 42
| ^~
sequence.cpp:169:5: note: in expansion of macro 'trace'
169 | trace(k, t, nt);
| ^~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
204 KB |
contestant found the optimal answer: 108 == 108 |
| 2 |
Correct |
1 ms |
204 KB |
contestant found the optimal answer: 999 == 999 |
| 3 |
Correct |
0 ms |
204 KB |
contestant found the optimal answer: 0 == 0 |
| 4 |
Correct |
0 ms |
204 KB |
contestant found the optimal answer: 1542524 == 1542524 |
| 5 |
Correct |
0 ms |
204 KB |
contestant found the optimal answer: 4500000000 == 4500000000 |
| 6 |
Incorrect |
0 ms |
204 KB |
contestant didn't find the optimal answer: 0 < 1 |
| 7 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
0 ms |
204 KB |
contestant didn't find the optimal answer: 252308 < 1093956 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
204 KB |
contestant didn't find the optimal answer: 484133 < 610590000 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
332 KB |
contestant didn't find the optimal answer: 395622 < 21503404 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
2 ms |
1100 KB |
contestant didn't find the optimal answer: 1187850 < 1818678304 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
15 ms |
8260 KB |
contestant didn't find the optimal answer: 5054352 < 19795776960 |
| 2 |
Halted |
0 ms |
0 KB |
- |
