Submission #744224

#	Time	Username	Problem	Language	Result	Execution time	Memory
744224		onebit1024	Bigger segments (IZhO19_segments)	C++17	37 / 100	1561 ms	10112 KiB

segments

#include <bits/stdc++.h>
using namespace std;

#define int long long
#define pb push_back
#define all(c) c.begin(), c.end()
#define endl "\n"

const double PI=3.141592653589;


void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long 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...);}
#ifndef ONLINE_JUDGE
#define dbg(x...) cerr << "LINE(" << __LINE__ << ") -> " <<"[" << #x << "] = ["; _print(x)
#else
#define dbg(x...)
#endif

int n;
vector<int>a,pref;
struct segtree{
    int sz = 1;
    vector<int>seg,lazy;
    void init(int n){
        while(sz < n)sz*=2;
        seg = vector<int>(sz*2);
        lazy = vector<int>(sz*2);
    }

    void upd(int x, int lx, int rx, int l, int r, int v){
        // range add v
        if(lazy[x]){
            seg[x]+=lazy[x];
            if(rx-lx > 1){
                lazy[2*x+1]+=lazy[x];
                lazy[2*x+2]+=lazy[x];
            }
            lazy[x] = 0;
        }
        if(lx >= l && rx <= r){
            seg[x] += v;
            if(rx-lx > 1){
                lazy[2*x+1]+=v;
                lazy[2*x+2]+=v;
            }
            return;
        
        }
        if(rx <= l || lx >= r)return;
        int m = (lx+rx)/2;
        upd(2*x+1,lx,m,l,r,v);
        upd(2*x+2,m,rx,l,r,v);
        seg[x] = min(seg[2*x+1],seg[2*x+2]);
    }

    void upd(int l, int r, int v){
        upd(0,0,sz,l,r,v);
    }

    int sol(int x, int lx, int rx, int l, int r){
        if(lazy[x]){
            seg[x]+=lazy[x];
            if(rx-lx > 1){
                lazy[2*x+1]+=lazy[x];
                lazy[2*x+2]+=lazy[x];
            }
            lazy[x] = 0;
        }

        if(seg[x] > 0 || lx >= r || rx <= l)return -1;
        if(rx-lx == 1)return lx;
        int m = (lx+rx)/2;
        int res = sol(2*x+2,m,rx,l,r);
        if(res==-1)res = sol(2*x+1,lx,m,l,r);
        return res;
    }

    int sol(int l, int r){
        // find first elmeent <= 0 in range [l,r]
        return sol(0,0,sz,l,r);
    }
};
segtree st;
int f(int x){
    vector<pair<int,int>>dp(n+1);
    st.init(n+1);

    int pos = 0;
    for(int i = 1;i<=n;++i){
        dp[i].second = dp[i-1].second+a[i];
        st.upd(i,i+1,dp[i].second);
        st.upd(1,i,-a[i]);
        if(dp[i].second >= x){
            pos = i;
            dp[i].first = 1;
            break;
        }
    }
    if(pos==0)return 0;
    // pos denotes starting position of maxdp value so far
    vector<pair<int,int>>p;
    for(int i = pos+1;i<=n;++i){
        int l = pos, r = i-1;

        dp[i] = {dp[i-1].first,dp[i-1].second+a[i]};

        st.upd(1,i,-a[i]);
        int get = st.sol(l,r+1);
        
        if(get!=-1){
            p.pb({pos,i-1});
            pos = i;
            dp[i].first++;
            dp[i].second = pref[i]-pref[get];
            st.upd(i,i+1,dp[i].second);
            continue;
        }
        if(p.empty()){
            st.upd(i,i+1,dp[i].second);
            continue;
        }
        // can't increase segment size, so try to reduce sum of current segment
        l = p.back().first, r = p.back().second;
        get = st.sol(l,r+1);
        if(get!=-1){
            dp[i].second = pref[i]-pref[get];
            st.upd(i,i+1,dp[i].second);
        }else st.upd(i,i+1,dp[i].second);

    }
    return dp[n].first;
}
void solve()
{
    cin >> n;
    a.resize(n+1);
    pref.resize(n+1);
    for(int i = 1;i<=n;++i)cin >> a[i];
    for(int i = 1;i<=n;++i)pref[i] = pref[i-1]+a[i];

    
    int l = 1, r = 1e18;
    while(l+2 < r){
        int m1 = (l+(r-l)/3), m2 = (r-(r-l)/3);
        if(f(m1) < f(m2))l = m1;
        else r = m2;
    }
    
    int res = 0;
    for(int i = l;i<=r;++i)res = max(res, f(i));
    cout << res << endl;
}   

int32_t main()
{

    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);


    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);
    

    int T=1;
    for(int i = 1;i<=T;++i)
    {
        // cout << "Case #" << i << ": ";
        solve();
    }
}

• Subtask 1: 13 / 13
• Subtask 2: 14 / 14
• Subtask 3: 10 / 10
• Subtask 4: 0 / 36
• Subtask 5: 0 / 27