Submission #109774

#	Time	Username	Problem	Language	Result	Execution time	Memory
109774		PeppaPig	Split the sequence (APIO14_sequence)	C++14	100 / 100	642 ms	85488 KiB

sequence

#include <bits/stdc++.h>
 
#define long long long
 
using namespace std;
 
const int N = 1e5+5;
 
struct line {
    long m, b;
    int idx;
    line(long m, long b, int idx) : m(m), b(b), idx(idx) { }
    long f(long x) { return m * x + b; }
};
 
struct cht {
    int ptr = 0;
    vector<line> l;
    bool bad(line a, line b, line c) { return (c.b - a.b) * (a.m - b.m) <= (b.b - a.b) * (a.m - c.m); }
    void add(long m, long b, int idx) {
        line now(m, b, idx);
        while(l.size() > 1 && bad(l[l.size()-2], l[l.size()-1], now))
            l.pop_back();
        l.emplace_back(now);
    }
    line query(long x) {
        if(ptr >= l.size()) ptr = l.size() - 1;
        while(ptr + 1 < l.size() && l[ptr].f(x) < l[ptr+1].f(x)) ++ptr;
        return l[ptr];
    }
    void clear() { l.clear(), ptr = 0; }
} hull[2];
 
int n, k, pv[205][N];
long dp[N], pref[N];
 
int main() {
    scanf("%d %d", &n, &k), ++k;
    for(int i = 1; i <= n; i++) scanf("%lld", pref+i);
    for(int i = 1; i <= n; i++) pref[i] += pref[i-1];
    hull[0].add(0, 0, 0);
    for(int j = 1; j <= k; j++) {
        int now = j & 1, pre = now ^ 1;
        hull[now].clear();
        for(int i = j; i <= n; i++) {
            line ret = hull[pre].query(pref[i]);
            dp[i] = ret.f(pref[i]);
            pv[j][i] = ret.idx;
            hull[now].add(pref[i], dp[i] - pref[i] * pref[i], i);
        }
    }
    vector<int> ans;
    for(int j = k, i = n; j > 1; j--) ans.emplace_back(i = pv[j][i]);
    reverse(ans.begin(), ans.end());
    printf("%lld\n", dp[n]);
    for(int i : ans) printf("%d ", i);
    printf("\n");
 
    return 0;
}

Compilation message (stderr)

sequence.cpp: In member function 'line cht::query(long long int)':
sequence.cpp:27:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         if(ptr >= l.size()) ptr = l.size() - 1;
            ~~~~^~~~~~~~~~~
sequence.cpp:28:23: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         while(ptr + 1 < l.size() && l[ptr].f(x) < l[ptr+1].f(x)) ++ptr;
               ~~~~~~~~^~~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:38:27: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d %d", &n, &k), ++k;
     ~~~~~~~~~~~~~~~~~~~~~~^~~~~
sequence.cpp:39:38: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     for(int i = 1; i <= n; i++) scanf("%lld", pref+i);
                                 ~~~~~^~~~~~~~~~~~~~~~

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