Submission #233873

#	Time	Username	Problem	Language	Result	Execution time	Memory
233873		anonymous	Split the sequence (APIO14_sequence)	C++14	49 / 100	77 ms	131076 KiB

sequence

#include <iostream>
#include <vector>
#define MAXN 100005
#define MAXK 205
#define LL long long
using namespace std;
int N, K, Prev[MAXN][MAXK];
LL A[MAXN], P[MAXN], dp[MAXN][MAXK];
vector <int> Out;
struct line {LL m, c, data;};
class CHT {
    int pt;
    vector<line> S;
public:
    void nuke() {
        pt = 0;
        S.clear();
    }
    bool bad(line L0) {
        line L1 = S.back(), L2 = S[S.size() - 2];
        if (L0.m == L1.m) {return(L0.c <= L1.m);}
        return((L2.c - L1.c)*(L0.m - L2.m) >= (L2.c - L0.c)*(L1.m - L2.m)); //int128?
    }
    void put(LL m, LL c, LL id) {
        while (S.size() > 1 && bad(line {m,c,id})) {S.pop_back();}
        S.push_back(line {m,c,id});
        pt = min(pt, (int) S.size()-1);
    }
    LL eval(line L, LL x) {
        return(L.m * x + L.c);
    }
    line ask(LL x) {
        while (pt + 1 < S.size() && eval(S[pt+1], x) > eval(S[pt], x)) {pt++;}
        return(S[pt]);
    }

} CHT;

int main() {
    //freopen("sequencein.txt","r",stdin);
    scanf("%d %d",&N,&K);
    for (int i=1; i<=N; i++) {
        scanf("%lld",&A[i]);
        P[i] = P[i-1] + A[i];
    }
    for (int j=1; j<=K; j++) {
        CHT.nuke();
        dp[0][j] = -(1LL << 60);
        CHT.put(0, dp[0][j],0);
        for (int i=1; i<=N; i++) {
            line res = CHT.ask(P[i]);
            dp[i][j] = res.m*P[i] + res.c;
            Prev[i][j] = res.data;
            CHT.put(P[i], dp[i][j-1] - P[i]*P[i], i);
        }
    }
    printf("%lld\n",(long long) dp[N][K]);
    for (int i=N, j=K; i>0 && j > 0; i=Prev[i][j], j--) {
        Out.push_back(Prev[i][j]);
    }
    while (Out.size()) {
        printf("%d ", Out.back());
        Out.pop_back();
    }
}

Compilation message (stderr)

sequence.cpp: In member function 'line CHT::ask(long long int)':
sequence.cpp:33:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         while (pt + 1 < S.size() && eval(S[pt+1], x) > eval(S[pt], x)) {pt++;}
                ~~~~~~~^~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:41:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d %d",&N,&K);
     ~~~~~^~~~~~~~~~~~~~~
sequence.cpp:43:14: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
         scanf("%lld",&A[i]);
         ~~~~~^~~~~~~~~~~~~~

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