Submission #897761

#	Time	Username	Problem	Language	Result	Execution time	Memory
897761		GrindMachine	The short shank; Redemption (BOI21_prison)	C++17	70 / 100	2088 ms	140512 KiB

prison

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a,b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a,b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif

/*

read somewhere that aliens trick can be used in this problem

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

template<typename T>
struct lazysegtree {
    /*=======================================================*/
 
    struct data {
        ll mn,ind;
    };
 
    struct lazy {
        ll a;
    };
 
    data d_neutral = {inf2,-1};
    lazy l_neutral = {0};
 
    void merge(data &curr, data &left, data &right) {
        if(left.mn <= right.mn) curr = left;
        else curr = right;
    }
 
    void create(int x, int lx, int rx, T v) {
        tr[x].mn = 0;
        tr[x].ind = lx;
    }
 
    void modify(int x, int lx, int rx, T v) {
        lz[x].a = v;
    }
 
    void propagate(int x, int lx, int rx) {
        ll v = lz[x].a;
        if(!v) return;
 
        tr[x].mn += v;
        
        if(rx - lx > 1){
            lz[2*x+1].a += v;
            lz[2*x+2].a += v;
        }
 
        lz[x] = l_neutral;
    }
 
    /*=======================================================*/
 
    int siz = 1;
    vector<data> tr;
    vector<lazy> lz;
 
    lazysegtree() {
 
    }
 
    lazysegtree(int n) {
        while (siz < n) siz *= 2;
        tr.assign(2 * siz, d_neutral);
        lz.assign(2 * siz, l_neutral);
    }
 
    void build(vector<T> &a, int n, int x, int lx, int rx) {
        if (rx - lx == 1) {
            if (lx < n) {
                create(x, lx, rx, a[lx]);
            }
 
            return;
        }
 
        int mid = (lx + rx) / 2;
 
        build(a, n, 2 * x + 1, lx, mid);
        build(a, n, 2 * x + 2, mid, rx);
 
        merge(tr[x], tr[2 * x + 1], tr[2 * x + 2]);
    }
 
    void build(vector<T> &a, int n) {
        build(a, n, 0, 0, siz);
    }
 
    void rupd(int l, int r, T v, int x, int lx, int rx) {
        propagate(x, lx, rx);
 
        if (lx >= r or rx <= l) return;
        if (lx >= l and rx <= r) {
            modify(x, lx, rx, v);
            propagate(x, lx, rx);
            return;
        }
 
        int mid = (lx + rx) / 2;
 
        rupd(l, r, v, 2 * x + 1, lx, mid);
        rupd(l, r, v, 2 * x + 2, mid, rx);
 
        merge(tr[x], tr[2 * x + 1], tr[2 * x + 2]);
    }
 
    void rupd(int l, int r, T v) {
        rupd(l, r + 1, v, 0, 0, siz);
    }
 
    data query(int l, int r, int x, int lx, int rx) {
        propagate(x, lx, rx);
 
        if (lx >= r or rx <= l) return d_neutral;
        if (lx >= l and rx <= r) return tr[x];
 
        int mid = (lx + rx) / 2;
 
        data curr;
        data left = query(l, r, 2 * x + 1, lx, mid);
        data right = query(l, r, 2 * x + 2, mid, rx);
 
        merge(curr, left, right);
        return curr;
    }
 
    data query(int l, int r) {
        return query(l, r + 1, 0, 0, siz);
    }
};
 
template<typename T>
struct sparse_table {
    /*============================*/
 
    T merge(T a, T b) {
        return min(a,b);
    }
 
    /*============================*/
 
    vector<vector<T>> table;
    vector<int> bin_log;
    int LOG = 0;
 
    sparse_table() {
 
    }
 
    sparse_table(vector<T> &a, int n) {
        while ((1 << LOG) <= n) LOG++;
 
        table = vector<vector<T>>(n, vector<T>(LOG));
        bin_log = vector<int>(n + 1);
 
        rep(i, n) table[i][0] = a[i];
 
        rep1(j, LOG - 1) {
            rep(i, n) {
                int jump = 1 << (j - 1);
                if (i + jump >= n) {
                    break;
                }
 
                table[i][j] = merge(table[i][j - 1], table[i + jump][j - 1]);
            }
        }
 
        bin_log[1] = 0;
        for (int i = 2; i <= n; ++i) {
            bin_log[i] = bin_log[i / 2] + 1;
        }
    }
 
    T query(int l, int r) {
        int len = r - l + 1;
        int k = bin_log[len];
 
        T val1 = table[l][k];
        T val2 = table[r - (1 << k) + 1][k];
 
        return merge(val1, val2);
    }
};
 
void solve(int test_case)
{
    ll n,d,t; cin >> n >> d >> t;
    d++; // we need d+1 segs
    vector<ll> a(n+5);
    rep1(i,n) cin >> a[i];
 
    vector<ll> b(n+5);
    rep1(i,n) b[i] = a[i] - i;
 
    sparse_table<ll> sparse(b,n+1);
    vector<ll> lx(n+5); // lx[i] = first pos to the left of i s.t if we start making ops from this pos, a[i] <= t
 
    rep1(i,n){
        // a[j] + (i-j) = (a[j]-j) + i
        ll l = 1, r = i;
        while(l <= r){
            ll mid = (l+r) >> 1;
            if(sparse.query(mid,i) + i <= t){
                lx[i] = mid;
                l = mid + 1;
            }
            else{
                r = mid - 1;
            }
        }
    }

    vector<ll> dp(n+5), cnt(n+5);
        
    auto go = [&](ll lambda){
        fill(all(dp),0);
        fill(all(cnt),0);
        lazysegtree<ll> st(n+5);
        vector<ll> dummy(n+5);
        st.build(dummy,n+1);

        rep1(i,n){
            // range add
            st.rupd(0,lx[i]-1,1);
 
            // range min
            auto [mn,ind] = st.query(0,i-1);
            dp[i] = mn+lambda;
            cnt[i] = cnt[ind]+1;
            st.rupd(i,i,dp[i]);
        }
    };

    ll l = 0, r = n;
    ll lambda = inf2;

    while(l <= r){
        ll mid = (l+r) >> 1;
        go(mid);
        if(cnt[n] <= d){
            r = mid-1;
            lambda = mid;
        }
        else{
            l = mid+1;
        }
    }

    assert(lambda != inf2);

    go(lambda);
    ll ans = dp[n]-d*lambda;
    cout << ans << endl;
}

int main()
{
    fastio;

    int t = 1;
    // cin >> t;

    rep1(i, t) {
        solve(i);
    }

    return 0;
}

• Subtask 1: 15 / 15
• Subtask 2: 0 / 10
• Subtask 3: 20 / 20
• Subtask 4: 10 / 10
• Subtask 5: 25 / 25
• Subtask 6: 0 / 20