Submission #1155696

#	Time	Username	Problem	Language	Result	Execution time	Memory
1155696		Sang	Split the sequence (APIO14_sequence)	C++20	100 / 100	686 ms	96188 KiB

sequence

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

#define int long long
#define FOR(i, a, b) for (int i = (a), _b = (b); i <= _b; i++)
#define FORD(i, a, b) for (int i = (a), _b = (b); i >= _b; i--)
#define fi first
#define se second
#define pb push_back
#define ALL(a) (a).begin(), (a).end()
#define task "kbsiudthw"

typedef vector<int> vi;
typedef pair<int, int> ii;
typedef pair<int, ii> pii;

const int N = 1e5 + 5;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 2277;

int n, k, a[N], dp[205];
int32_t opt[N][205];

struct Line{
    int a, b, pos;
    Line(int a = 0, int b = 0, int pos = -1) : a(a), b(b), pos(pos) {};
    int eval(int x){ return a * x + b ;}
    long double intersectX(Line A){
        return (long double)(b - A.b)/(A.a - a);
    }
};

deque<Line> hull[205];

bool bad(Line A, Line B, Line C){
    return A.intersectX(C) <= A.intersectX(B);
}

void addLine(int x, int y, int pos, int id){
    Line nw(x, y, pos);
    while (hull[id].size() >= 2 && bad(hull[id][hull[id].size() - 2], hull[id].back(), nw)) hull[id].pop_back();
    hull[id].pb(nw);
}

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    if (fopen(task".inp", "r")){
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }
    cin >> n >> k;
    FOR (i, 1, n) cin >> a[i], a[i] += a[i-1];
    addLine(0, 0, 0, 0);
    int pos = 1, val = -1e9;
    FOR (i, 1, n){
        FOR (j, 1, k) dp[j] = -1e9;
        FORD (j, k, 1){
            if (hull[j-1].empty()) continue;
            while (hull[j-1].size() >= 2 && hull[j-1][0].eval(a[i]) <= hull[j-1][1].eval(a[i])) hull[j-1].pop_front();
            dp[j] = hull[j-1][0].eval(a[i]) - a[i] * a[i] + a[i] * a[n];
            opt[i][j] = hull[j-1][0].pos;
            addLine(a[i], -a[i] * a[n] + dp[j], i, j);
        }
        if (dp[k] > val){
            val = dp[k];
            pos = i;
        }   
    }
    cout << val << '\n';
    vi ans;
    while (pos){
        ans.pb(pos);
        pos = opt[pos][k--];
    }
    reverse(ALL(ans));
    for (int &x : ans) cout << x << ' ';

    return 0;
}

Compilation message (stderr)

sequence.cpp: In function 'int main()':
sequence.cpp:49:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   49 |         freopen(task".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:50:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   50 |         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