Submission #876570

#	Time	Username	Problem	Language	Result	Execution time	Memory
876570		rukashii	Split the sequence (APIO14_sequence)	C++17	71 / 100	135 ms	19032 KiB

sequence

#include <bits/stdc++.h>
using namespace std;
 
#define file  if (fopen("input.txt", "r")) { freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); }
#define int long long
#define s second
#define f first
 
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void setIO(string s = "") {
    if (s.size()) setIn(s+".in"), setOut(s+".out");
}
 
const int maxn = 1e5 + 2, maxk = 202;
 
int a[maxn], prf[maxn], n, k;
 
namespace Sub2
{
    const int s2maxn = 52, s2maxk = 52;
    int dp[s2maxn][s2maxn][s2maxk];
 
    int cal(int l, int r, int krem)
    {
        if (l == r || krem == 0)
            return dp[l][r][krem] = 0;
        
        int res = dp[l][r][krem];
        if (res != -1)
            return res;
 
        res = 0;
        for (int i = l; i < r; i++)
        {
            for (int lk = 0; lk < krem; lk++)
            {
                int rk = krem - lk - 1;
                res = max(res, cal(l, i, lk) + cal(i + 1, r, rk) + (prf[r] - prf[i]) * (prf[i] - prf[l - 1]));
            }
        }
 
        return dp[l][r][krem] = res;
    }
 
    void trace(int l, int r, int krem)
    {
        bool skip = 0;
        for (int i = l; i < r; i++)
        {
            for (int lk = 0; lk < krem; lk++)
            {
                int rk = krem - lk - 1;
                if (dp[l][r][krem] == cal(l, i, lk) + cal(i + 1, r, rk) + (prf[r] - prf[i]) * (prf[i] - prf[l - 1]))
                {
                    cout << i << ' ';
                    trace(1, i, lk);
                    trace(i + 1, r, rk);
                    skip = 1;
                    break;
                }
            }
            if (skip)
                break;
        }
    }
 
    void solve()
    {
        memset(dp, -1, sizeof(dp));
 
        cout << cal(1, n, k) << '\n';
        trace(1, n, k);
    }
} 
 
 
namespace Sub4
{
    const int s4maxn = 1002, s4maxk = 202;
    int dp[s4maxn][s4maxk];
 
    void solve()
    {
        // dp[0][0] = 0;
        memset(dp, -0x3f, sizeof(dp));
        dp[0][0] = 0;
        k++;
        for (int i = 1; i <= n; i++) 
        {
            for (int j = 1; j <= k; j++)
            {
                for (int p = 0; p < i; p++)
                {
                                                  //from n -> i + 1  //from i -> p + 1
                    dp[i][j] = max(dp[p][j - 1] + (prf[n] - prf[i]) * (prf[i] - prf[p]), dp[i][j]);
                }
            }
        }
 
        cout << dp[n][k] << '\n';
        int curk = k, curb = n;
        while (curk > 0)
        {
            for (int i = 0; i < curb; i++)
            {
                if (dp[i][curk - 1] + (prf[n] - prf[curb]) * (prf[curb] - prf[i]) == dp[curb][curk])
                {
                    if (i)
                        cout << i << ' ';
                    curk--;
                    curb = i;
                }
            }
        }
        
    }
}
 
namespace Sub5  
{
    const int s5maxn = 1e4 + 2, s5maxk = 202;
    int dp[s5maxk][s5maxn];
 
    void compute(int l, int r, int optl, int optr, int curk)
    {
        if (l > r)
            return;
        
        int mid = (l + r) / 2;
        pair <int, int> best = {LLONG_MIN, -1};
 
        for (int i = optl; i <= min(optr, mid); i++)
        {
            best = max(best, {dp[curk - 1][i] + (prf[n] - prf[mid]) * (prf[mid] - prf[i]), i});
        }
 
        int opt = best.second;
        dp[curk][mid] = best.first;
 
        compute(l, mid - 1, optl, opt, curk);
        compute(mid + 1, r, opt, optr, curk);
    }
 
    void solve()
    {
        k++;
        memset(dp, -0x3f, sizeof(dp));
        dp[0][0] = 0;
 
        for (int i = 1; i <= k; i++)
            compute(0, n, 0, n, i);
        
        cout << dp[k][n] << '\n';
        int curk = k, curb = n;
        while (curk > 0)
        {
            for (int i = 0; i < curb; i++)
            {
                if (dp[curk - 1][i] + (prf[n] - prf[curb]) * (prf[curb] - prf[i]) == dp[curk][curb])
                {
                    if (i)
                        cout << i << ' ';
                    curk--;
                    curb = i;
                }
            }
        }
    }
} 
 
namespace Sub6
{
 
    int dp[6][maxn], pt, trace[202][maxn];
    vector <pair <int, int>> A, B;
 
    bool ccw(int l1, int l2, int l3)
    {
        return (B[l1].f - B[l2].f) * (A[l3].f - A[l1].f) >= (B[l1].f - B[l3].f) * (A[l2].f - A[l1].f);
    }
 
    void add(int a, int b, int id)
    {
        // if (A.size() && A.back().f == a)
        // {
        //     if (B.back().f >= b)
        //         return;
        //     else
        //         A.pop_back(), B.pop_back();
        // }
 
        A.push_back({a, id}), B.push_back({b, id});
        pt++;
        while (A.size() >= 3 && ccw(A.size() - 3, A.size() - 2, A.size() - 1))
        {
            A.erase(A.end() - 2);
            B.erase(B.end() - 2);
        }
    }
 
    pair <int, int> query(int x)
    {
        pt = min(pt, (int)A.size() - 1);
        
        int sz = A.size();
        while (pt && ((A[pt - 1].f - A[pt].f) * x ) > (B[pt].f - B[pt - 1].f))
            pt--;
        
        return {A[pt].f * x + B[pt].f, A[pt].s};
    }
 
    /*
    * dp[j][i] = 0..i with j-th split happening at between a[i] and a[i+1]
    *
    * dp[j][i] = max(dp[j-1][k] + (p[i] - p[k]) * (p[n] - p[i]))
    *          = p[i]p[n] - p[i]p[i] + max(p[i]p[k] + dp[j-1][k] - p[k]p[n])
    **/
    void solve()
    {
        k++;
        for (int i = 1;i <= n;i++) 
            dp[1][i] = prf[i] * (prf[n] - prf[i]);
        for (int i = 2; i <= k; i++)
        {
            A.clear(), B.clear(); pt = 0;
            add(prf[i - 1], -prf[i - 1] * prf[n] + dp[!(i & 1)][i - 1], i - 1);
            
            for (int j = i; j <= n; j++)
            {
                auto tmp = query(prf[j]);
                dp[(i & 1)][j] = prf[j] * prf[n] - prf[j] * prf[j] + tmp.f;
 
                trace[i][j] = tmp.s;
                if (i > 1)
                    add(prf[j], dp[!(i & 1)][j] - prf[j] * prf[n], j);
            }
            
        }
 
        cout << dp[k % 2][n] << '\n';
        int curk = k, curb = n;
        while (curk > 0)
        {
            if (trace[curk][curb])
                cout << trace[curk][curb] << ' ';
            curb = trace[curk][curb];
            curk--;
        }
    }
}
 
 
signed main()
{
    // setIO();
    file;
    ios::sync_with_stdio(0); cin.tie(0);
 
    cin >> n >> k;
    for (int i = 1; i <= n; i++)
        cin >> a[i], prf[i] = prf[i - 1] + a[i];
 
    if (n <= 50)
        return Sub2::solve(), 0;
    if (n <= 1000)
        return Sub4::solve(), 0;
    if (n <= 10000)
        return Sub5::solve(), 0;
    if (n <= 100000)
        return Sub6::solve(), 0;
 
    cout << "From ITK20 w love UwU";
}

Compilation message (stderr)

sequence.cpp: In function 'std::pair<long long int, long long int> Sub6::query(long long int)':
sequence.cpp:206:13: warning: unused variable 'sz' [-Wunused-variable]
  206 |         int sz = A.size();
      |             ^~
sequence.cpp: In function 'void setIn(std::string)':
sequence.cpp:9:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
    9 | void setIn(string s) { freopen(s.c_str(),"r",stdin); }
      |                        ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
sequence.cpp: In function 'void setOut(std::string)':
sequence.cpp:10:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   10 | void setOut(string s) { freopen(s.c_str(),"w",stdout); }
      |                         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:4:53: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
    4 | #define file  if (fopen("input.txt", "r")) { freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); }
      |                                              ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:257:5: note: in expansion of macro 'file'
  257 |     file;
      |     ^~~~
sequence.cpp:4:87: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
    4 | #define file  if (fopen("input.txt", "r")) { freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); }
      |                                                                                ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:257:5: note: in expansion of macro 'file'
  257 |     file;
      |     ^~~~

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