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Submission #971196

# Submission time Handle Problem Language Result Execution time Memory
971196 2024-04-28T06:31:10 Z _rain_ Split the sequence (APIO14_sequence) C++14
100 / 100
 1681 ms 94952 KB 
/** 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 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] = LLONG_MAX;
    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];
    memset(dp , 0x3f , sizeof dp);
    g[1] = 0;
    for (int i = 1; i <= k; ++i) solve(i);
    i64 answer = LLONG_MAX;
    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

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
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5208 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 5212 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 5212 KB contestant found the optimal answer: 0 == 0
4 Correct 1 ms 5212 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 1 ms 7260 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 5212 KB contestant found the optimal answer: 1 == 1
7 Correct 1 ms 5212 KB contestant found the optimal answer: 1 == 1
8 Correct 1 ms 5208 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 5212 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 3 ms 5212 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 1 ms 5212 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 5208 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 5208 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 5212 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 5212 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 5212 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 1 ms 5212 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5212 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 5212 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 7 ms 23824 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 5212 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 7260 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 1 ms 7260 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 13400 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 9308 KB contestant found the optimal answer: 687136 == 687136
9 Correct 1 ms 7260 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 1 ms 9308 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5212 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 1 ms 5212 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 29 ms 81244 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 1 ms 5212 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 9 ms 58656 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 10 ms 75100 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 11 ms 81244 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 3 ms 21596 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 15452 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 4 ms 25692 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5464 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 5208 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 16 ms 81240 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 5212 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 18 ms 81232 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 16 ms 71004 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 17 ms 81304 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 16 ms 81240 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 4 ms 19804 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 8 ms 36188 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 6116 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 3 ms 5920 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 152 ms 82516 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 6908 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 90 ms 51240 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 120 ms 59404 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 129 ms 64052 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 108 ms 53900 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 113 ms 60060 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 149 ms 76616 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 27 ms 17116 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 25 ms 16488 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1442 ms 93680 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 29 ms 17240 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1681 ms 94952 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 991 ms 65980 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1248 ms 74804 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 1081 ms 65668 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 1080 ms 72212 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1415 ms 88004 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845