Submission #852160

#	Time	Username	Problem	Language	Result	Execution time	Memory
852160		chanhchuong123	Split the sequence (APIO14_sequence)	C++14	100 / 100	393 ms	90120 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];
int pf[MAX];
int trace[MAX][202];
long long dp[2][MAX];

struct Line {
    int m; long long c; int id;

    Line(int _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;
    }
};

struct ConvexHullTrick {
    vector<Line> lines;
    int pt = 0;

    bool bad(const Line &l1, const Line &l2, const Line &l3) {
        return 1LL * (l1.c - l3.c) * (l2.m - l1.m) <= 1LL * (l1.c - l2.c) * (l3.m - l1.m);
    }

   void add(long long m, long long c, int id) {
        if (lines.size() && lines.back().m == m) {
            long long minC = c;
            while (lines.size() && lines.back().m == m) {
                minC = min(minC, lines.back().c);
                lines.pop_back();
            }
            lines.push_back(Line(m, minC, id));
            return;
        }
        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(int 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[2];

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];
	}
	memset(dp, -1, sizeof dp);
	dp[0][0] = 0;
	long long res = 0;
	for (int j = 1; j <= k; ++j) {
        int prv = (j - 1) & 1, cur = j & 1;
        cht[prv].lines.clear();
        cht[prv].pt = 0;
        memset(dp[cur], -1, sizeof dp[cur]);
        for (int i = j; i <= n; ++i) {
            if (dp[prv][i - 1] > -1) cht[prv].add(pf[i - 1], -1LL * pf[i - 1] * pf[i - 1] + dp[prv][i - 1], i - 1);
            pair<long long, int> ans = cht[prv].get(pf[i]);
            if (i == n && j == k) res = ans.first;
            dp[cur][i] = ans.first;
            trace[i][j] = ans.second;
        }
	}
    cout << res << '\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 member function 'std::pair<long long int, int> ConvexHullTrick::get(int)':
sequence.cpp:50:9: warning: this 'if' clause does not guard... [-Wmisleading-indentation]
   50 |         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;
      |         ^~
sequence.cpp:50:81: note: ...this statement, but the latter is misleadingly indented as if it were guarded by the 'if'
   50 |         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;
      |                                                                                 ^~~~~
sequence.cpp:50:95: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<Line>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   50 |         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;
      |                                                                                        ~~~~~~~^~~~~~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:59:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   59 |   freopen(task".inp", "r", stdin);
      |   ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:60:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   60 |   freopen(task".out", "w", stdout);
      |   ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

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