Submission #951463

#	Time	Username	Problem	Language	Result	Execution time	Memory
951463		yeediot	Split the sequence (APIO14_sequence)	C++14	100 / 100	568 ms	84048 KiB

sequence

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define F first
#define S second
#define all(x) x.begin(),x.end()
#define pii pair<int,int>
#define pb push_back
#define sz(x) (int)(x.size())
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
#define vi vector<int>
#define vp vector<pii>
#define vvi vector<vi>
#define ykh mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count())
#define __lg(x) 63-__builtin_clzll(x)
#define pow2(x) (1LL<<x)
void __print(int x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifdef local
void setio(){freopen("/Users/iantsai/Library/Mobile Documents/com~apple~CloudDocs/cpp/Empty.md","r",stdin);}
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
void setio(){}
#define debug(x...)
#endif
void setIO(string s) {
    freopen((s + ".in").c_str(), "r", stdin);
    freopen((s + ".out").c_str(), "w", stdout);
}
struct line{
    ll a,b,c;
    ll operator()(const int x)const{
        return a*x+b;
    }
};
/*
cb<=ab
cx+d=ax+b;
x=(d-b)/(a-c)
(c.b-b.b)/(b.a-c.a)<=(a.b-b.b)/(b.a-a.a)
*/
bool check(line a,line b,line c){
    return (c.b-b.b)*(b.a-a.a)>=(a.b-b.b)*(b.a-c.a);
}
signed main(){
    setio();
    ios::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
    ll n,k;
    cin>>n>>k;
    vector<ll>a(n+1),pre(n+1);
    for(int i=1;i<=n;i++){
        cin>>a[i];  
        pre[i]=pre[i-1]+a[i];
    }
    ll dp[2][n+1];
    int from[k+2][n+1];
    memset(dp,0,sizeof(dp));
    memset(from,0,sizeof(from));
    int nxt=0,now=1;
    for(int j=1;j<=k+1;j++){
        deque<line>dq;
        dq.push_back({0,0,0});
        for(int i=1;i<=n;i++){
            while(sz(dq)>1 and dq[0](pre[i])<=dq[1](pre[i])){
                dq.pop_front();
            }
            dp[nxt][i]=dq.front()(pre[i])+pre[i]*pre[n]-pre[i]*pre[i];
            from[j][i]=dq.front().c;
            line l={2*pre[i],dp[now][i]-pre[i]*pre[i]-pre[i]*pre[n],i};
            while(sz(dq)>1 and check(dq[sz(dq)-2],dq.back(),l)){
                dq.pop_back();
            }
            dq.push_back(l);
        }
        swap(now,nxt);
    }
    cout<<dp[now][n]/2<<'\n';
    vector<int>ans;
    int cur=n;
    int dick=k+1;
    debug(from[dick][n]);
    while(cur!=0){
        cur=from[dick][cur];
        dick--;
        if(cur==0)break;
        ans.pb(cur);
        if(sz(ans)==k)break;
    }
    reverse(all(ans));
    for(auto i:ans){
        cout<<i<<' ';
    }
    cout<<'\n';
}
 /*
 input:
 dp[i]=dp[j]+(pre[i]-pre[j])*(sum-pre[i]+pre[j])
 dp[i]=dp[j]+pre[i]*sum-pre[i]*pre[i]+pre[i]pre[j]+pre[i]*pre[j]-pre[j]*pre[j]
 =(dp[j]-pre[j]pre[j])+2*pre[i]*pre[j]+(pre[i]*sum-pre[i]*pre[i])
 */















 

Compilation message (stderr)

sequence.cpp: In function 'void setIO(std::string)':
sequence.cpp:42:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   42 |     freopen((s + ".in").c_str(), "r", stdin);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:43:12: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   43 |     freopen((s + ".out").c_str(), "w", stdout);
      |     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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