Submission #852126

#	Time	Username	Problem	Language	Result	Execution time	Memory
852126		chanhchuong123	Split the sequence (APIO14_sequence)	C++14	50 / 100	832 ms	131072 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
#define task ""

const long long INF = 1e18 + 0702;
const int MAX = 100010;
int n, k;
int a[MAX];
long long pf[MAX];
int trace[MAX][202];
long long dp[MAX][202];

//struct Line {
//    long long m, c; int id;
//
//    Line(long long _m = 0, long long _c = 0, int _id = 0) {
//        m = _m;
//        c = _c;
//        id = _id;
//    }
//
//    long long eval(long long x) {
//        return m * x + c;
//    }
//
//    double intersect(const Line &other) const {
//        return 1.0 * (c - other.c) / (other.m - m);
//    }
//};
//
//struct ConvexHullTrick {
//    vector<Line> lines;
//    int pt = 0;
//
//    bool bad(const Line &l1, const Line &l2, const Line &l3) {
//        return l1.intersect(l3) <= l1.intersect(l2);
//    }
//
//    void add(long long m, long long c, int id) {
//        Line line(m, c, id); while (lines.size() >= 2 && bad(lines[lines.size() - 2], lines.back(), line)) lines.pop_back();
//        lines.push_back(line); pt = min(pt, int(lines.size()) - 1);
//    }
//
//    pair<long long, int> get(long long x) {
//        if (lines.size() == 1) return make_pair(lines[0].eval(x), lines[0].id); while (pt + 1 < lines.size() && lines[pt + 1].eval(x) >= lines[pt].eval(x)) ++pt;
//        return make_pair(lines[pt].eval(x), lines[pt].id);
//    }
//} cht[202];

struct Line {
  mutable long long m, b, p, id;
  bool operator<(const Line& o) const { return m < o.m; }
  bool operator<(long long x) const { return p < x; }
};

struct LineContainer : multiset<Line, less<>> {
  // (for doubles, use inf = 1/.0, div(a,b) = a/b)
  const long long inf = LLONG_MAX;
  long long div(long long a, long long b) { // floored division
    return a / b - ((a ^ b) < 0 && a % b);
  }
  bool isect(iterator x, iterator y) {
    if (y == end()) { x->p = inf; return false; }
    if (x->m == y->m) x->p = x->b > y->b ? inf : -inf;
    else x->p = div(y->b - x->b, x->m - y->m);
    return x->p >= y->p;
  }
  void add(long long m, long long b, int id) {
    auto z = insert({m, b, 0, id}), y = z++, x = y;
    while (isect(y, z)) z = erase(z);
    if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
    while ((y = x) != begin() && (--x)->p >= y->p) isect(x, erase(y));
  }
  pair<long long, int> get(long long x) {
    assert(!empty());
    auto l = *lower_bound(x);
    return make_pair(l.m * x + l.b, l.id);
  }
} cht[202];

int main() {
	ios_base::sync_with_stdio(false); cin.tie(nullptr);

	if (fopen(task".inp", "r")) {
		freopen(task".inp", "r", stdin);
		freopen(task".out", "w", stdout);
	}

	cin >> n >> k; ++k;
	for (int i = 1; i <= n; ++i) {
        cin >> a[i];
        pf[i] = pf[i - 1] + a[i];
	}
	cht[0].add(0, 0, 0);
    for (int i = 1; i <= n; ++i) {
        for (int j = min(i, k); j >= 1; --j) {
            pair<long long, int> cur = cht[j - 1].get(pf[i]);
            trace[i][j] = cur.second;
            dp[i][j] = cur.first;
            cht[j].add(pf[i], - pf[i] * pf[i] + dp[i][j], i);
        }
    }
    cout << dp[n][k] << '\n';
    vector<int> posAns;
    do {
        n = trace[n][k--];
        posAns.push_back(n);
    } while (k > 1);
    for (int &id: posAns) {
        cout << id << ' ';
    }
	return 0;
}

/*
7 3
4 1 3 4 0 2 3
*/

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:85:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   85 |   freopen(task".inp", "r", stdin);
      |   ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:86:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   86 |   freopen(task".out", "w", stdout);
      |   ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

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