Submission #971195

#	Time	Username	Problem	Language	Result	Execution time	Memory
971195		_rain_	Split the sequence (APIO14_sequence)	C++14	100 / 100	1641 ms	94480 KiB

sequence

/** author : _RAIN_ **/
#include<bits/stdc++.h>
using namespace std;
 
using i64 = long long;
using ui64 = unsigned long long;
 
#define MASK(x) ((i64)(1) << (x))
#define BIT(mask , x) (((mask) >> (x)) & (1))
 
template<class T>
    bool maximize(T &a , T b) {if (a < b) return a = b , true; else return false;}
template<class T>
    bool minimize(T &a , T b) {if (a > b) return a = b , true; else return false;}
template<class T>
    T gcd(T x , T y) {while (y) swap(y , x %= y); return x;}
template<class T>
    T lcm(T x , T y) {return (x * y) / gcd(x , y);}
#define sz(x) (int)((x).size())
struct Line
{
    i64 a , b;
    Line(i64 a , i64 b) : a(a) , b(b) {};
};
struct Hull
{
    Line X;
    long double intersec;
    int idx;
};
class Convex_hull
{
    public:
        vector<Hull> line;
        long double getintersec(Line x , Line y)
        {
            return (long double)(y.b - x.b) / (x.a - y.a);
        }
        i64 getval(Line a , i64 x)
        {
            return a.a * x + a.b;
        }
        void addline(Line a , int idx)
        {
            int n = sz(line);
            while (n > 1 && getintersec(line[n - 2].X , a) <= getintersec(line[n - 1].X , line[n - 2].X))
                line.pop_back() , --n;
            if (!sz(line))
                line.push_back({a , LLONG_MIN , idx});
            else line.push_back({a , getintersec(a , line[n - 1].X), idx});
            return;
        }
        pair<i64 , int> find(i64 val)
        {
            int low = 0 , high = sz(line) - 1 , p = 0;
            while (low <= high)
            {
                int mid = low + high >> 1;
                if (line[mid].intersec <= val) p = mid , low = mid + 1;
                    else high = mid - 1;
            }
            return {getval(line[p].X , val) , line[p].idx};
        }
        void add(i64 a , i64 b , int idx)
        {
            addline(Line{a , b} , idx);
            return;
        }
};
const i64 limit = LLONG_MAX;
const int maxn = 1e5;
const int maxk = 200;
i64 dp[maxn + 2] , g[maxn + 2] , a[maxn + 2] , pre[maxn + 2];
int trace[maxk + 2][maxn + 2];
int n , k;
 
void solve(int idx)
{
    Convex_hull bag1;
    for (int i = 1; i <= n; ++i) dp[i] = limit;
    for (int i = 1; i <= n; ++i)
    {
        if (bag1.line.size())
        {
            pair<i64 , int> val = bag1.find(pre[i - 1]);
            dp[i] = val.first - pre[n] * pre[i - 1] + pre[i - 1] * pre[i - 1];
            trace[idx][i] = val.second;
        }
        if (i > 1)
        {
            int j = 1;
            if (minimize(dp[i] , dp[1] - pre[n] * pre[i - 1] + pre[i - 1] * pre[i - 1] - pre[i - 1] * pre[j - 1] + pre[n] * pre[j - 1]))
                trace[idx][i] = 1;
        }
        bag1.add(-pre[i - 1] , pre[n] * pre[i - 1] + g[i] , i);
    }
    for (int i = 1; i <= n; ++i) g[i] = dp[i];
}
 
int32_t main(void)
{
    cin.tie(nullptr)->sync_with_stdio(false);
    const string name = "main";
    if (fopen((name + ".inp").c_str() , "r"))
    {
        (void)!freopen((name + ".inp").c_str() , "r" , stdin);
        (void)!freopen((name + ".out").c_str() , "w+", stdout);
    }
    cin >> n >> k; 
    int bug = 0;
    memset(pre , 0 , sizeof pre);
    
    for (int i = 1; i <= n; ++i) cin >> a[i];
    for (int i = 1; i <= n; ++i) pre[i] = pre[i - 1] + a[i];
    g[1] = 0;
    for (int i = 1; i <= k; ++i) solve(i);
    i64 answer = limit;
    int v = 1 , ks = 1;
    for (int i = 1; i <= n; ++i) 
        if (minimize(answer , g[i]))
            v = i - 1 , ks = i;
    cout << -g[ks] << '\n';
    vector<int> recall;
    while (k > bug)
    {
        recall.emplace_back(v);
        v = trace[k][ks] - 1;
        ks = trace[k][ks];
        --k;
    }
    reverse(recall.begin() , recall.end());
    for (auto& v : recall) cout << v << ' ';
}

Compilation message (stderr)

sequence.cpp: In member function 'std::pair<long long int, int> Convex_hull::find(i64)':
sequence.cpp:58:31: warning: suggest parentheses around '+' inside '>>' [-Wparentheses]
   58 |                 int mid = low + high >> 1;
      |                           ~~~~^~~~~~

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