Submission #789417

#	Time	Username	Problem	Language	Result	Execution time	Memory
789417		fatemetmhr	Shortcut (IOI16_shortcut)	C++17	97 / 100	2088 ms	458772 KiB

shortcut

//  ~ Be Name Khoda ~  //
 
 
//#pragma GCC optimize ("O3")
#pragma GCC target("avx,abm,bmi,bmi2")
#pragma GCC optimize("unroll-loops,Ofast")
#include <bits/stdc++.h>
 
#include <vector> 
long long find_shortcut(int n, std::vector <int> l, std::vector <int> d, int c);
 
using namespace std;
 
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
 
 
typedef long long ll;
 
#define pb       push_back
#define mp       make_pair
#define all(x)   x.begin(), x.end()
#define fi       first
#define se       second
 
const int maxn  =  1e6   + 10;
const int maxn5 =  1e6   + 10;
const int maxnl =  1e7   + 10;
const int maxn3 =  1e3   + 10;
const ll mod   =  1e9   + 7;
const int lg    =  22;
const ll  inf   =  1e18;
 
int n, ind[maxn5];
ll c;
vector <ll> d;
ll ps[maxn5];
pair <pair<ll, int>, pair<ll, ll>> av[maxn5];
pair <ll, ll> mxx[lg][maxn5];
vector <pair<ll, int>> srt;
 
// c + d[i] + ps[i] - ps[a] + cons - ps[b] <= lim
// d[i] + ps[i] + cons <= lim - c + ps[b] + ps[a]
 
pair <ll, ll> comb(const pair <ll, ll> &a, const pair <ll, ll> &b){
    return {a.fi > b.fi? a.fi: b.fi, a.se > b.se? a.se: b.se};
}
 
 
struct RMQ{
 
    ll mx[maxn5];
    bool ty;
 
    void build(int n){
        if(ty)
            for(int i = 1; i < n; i++)
                mx[i] = max(mx[i], mx[i - 1]);
        else
            for(int i = n - 2; i >= 0; i--)
                mx[i] = max(mx[i], mx[i + 1]);
    }
 
 
} rmq[2][2];
 
pair <ll, ll> get_max(int l, int r){
    if(l > r)
        return {-inf, -inf};
    if(r == n - 1)
        return av[l].se;
    int k = 31 - __builtin_clz(r - l + 1);
    return comb(mxx[k][l], mxx[k][r - (1 << k) + 1]);
}
 
// (ty ? 1 : -1) * ps[b] <= lim - c + ps[a] - rmq[0][ty].mx[a]
// (ty ? 1 : -1) * ps[b] <= lim - c - ps[a] - rmq[1][ty].mx[a]
 
bool check2(int a, int b, int ty, ll lim){
    //cout << "for " << a << ' ' << b << ' ' << ty << ' ' << lim << endl;
    //cout << rmq[0][ty].get_max(a, n - 1) << ' ' << lim - c + (ty ? -1 : 1) * ps[b] - ps[a] << endl;
    if(rmq[0][ty].mx[a] > lim - c + (ty ? -1 : 1) * ps[b] + ps[a])
        return false;
    if(rmq[1][ty].mx[a] > lim - c + (ty ? -1 : 1) * ps[b] - ps[a])
        return false;
    //cout << "result in true " << endl;
    return true;
}
 
bool check(ll lim){
    //cout << "************** in lim " << lim << endl;
    int pt = 0;
    for(auto [w, i] : srt){
        while(pt < n && lim - w >= av[pt].fi.fi)
            pt++;
        if(i == n){
            for(int x = 0; x < 2; x++) for(int y = 0; y < 2; y++)
                rmq[x][y].mx[i] = -inf;
            continue;
        }
        pair <ll, ll> ans = {-inf, -inf};
        if(ind[i] < pt)
            ans = get_max(pt, n - 1);
        else
            ans = comb(get_max(pt, ind[i] - 1), get_max(ind[i] + 1, n - 1));
        //cout << "in " << i << ' ' << pt << ' ' << av.size() << endl;
        ll cons[2] = {ans.fi, ans.se};
        //cout << i << ' ' << cons[0] << ' ' << cons[1] << endl;
        for(int x = 0; x < 2; x++) for(int y = 0; y < 2; y++)
            rmq[x][y].mx[i] = d[i] + cons[y] + ps[i] * (x ? -1 : 1);
    }
    rmq[0][0].ty = 0;
    rmq[0][1].ty = 0;
    rmq[1][0].ty = 1;
    rmq[1][1].ty = 1;
    rmq[0][0].build(n); // 0 is suf
    rmq[0][1].build(n);
    rmq[1][0].build(n);
    rmq[1][1].build(n);
 
    int b[2][2];
    b[0][0] = n;
    b[0][1] = 0;
    b[1][0] = 0;
    b[1][1] = n - 1;
 
    for(int i = 0; i < n; i++){
 
        while(b[0][0] - 1 >= 0 && -ps[b[0][0] - 1] <= lim - c + ps[i] - rmq[0][0].mx[i])
            b[0][0]--;
        while(b[1][1] >= 0 && ps[b[1][1]] > lim - c - ps[i] - rmq[1][1].mx[i])
            b[1][1]--;
        while(b[0][1] + 1 < n && ps[b[0][1] + 1] <= lim - c + ps[i] - rmq[0][1].mx[i])
            b[0][1]++;
        while(b[1][0] < n && -ps[b[1][0]] > lim - c - ps[i] - rmq[1][0].mx[i])
            b[1][0]++;
 
        int l = max({i + 1, b[0][0], b[1][0]});
        int r = min(b[0][1], b[1][1]);
        /*
        int lo = i, hi = n;
        while(hi - lo > 1){
            int mid = (lo + hi) >> 1;
            if(check2(i, mid, 0, lim))
                hi = mid;
            else
                lo = mid;
        }
        int l = max(i + 1, hi);
 
        lo = i; hi = n;
        while(hi - lo > 1){
            int mid = (lo + hi) >> 1;
            if(check2(i, mid, 1, lim))
                lo = mid;
            else
                hi = mid;
        }
        int r = min(n, lo);
        */
        //cout << "ok " << i << ' ' << l << ' ' << r << endl;
        if(l <= r)
            return true;
    }
    return false;
 
    /*
 
    for(int i = 0; i < n; i++) if(pt[i] < av[i].size()){
        int b = 0;
        for(auto [w, a] : srt[i]){
            while(b + 1 < n && c + d[i] + w + av[i][pt[i]].se.fi - ps[b] > lim)
                b++;
            l[a] = max(l[a], b);
        }
        b = n - 1;
        for(auto [w, a] : srt[i]){
            while(b && c + d[i] + w + av[i][pt[i]].se.se + ps[b] > lim)
                b--;
            r[a] = min(r[a], b);
        }
 
 
 
        /*
        int lo = i, hi = n;
        while(hi - lo > 1){
            int mid = (lo + hi) >> 1;
            if(check(i, mid, 0, lim))
                hi = mid;
            else
                lo = mid;
        }
        l = max(i + 1, hi);
 
        lo = i; hi = n;
        while(hi - lo > 1){
            int mid = (lo + hi) >> 1;
            if(check(i, mid, 1, lim))
                lo = mid;
            else
                hi = mid;
        }
        r = min(n, lo);
        //////cout << "ok " << lim << ' ' << i << ' ' << l << ' ' << r << endl;
        if(l <= r)
            return true;
 
 
 
        /*
        bool re = true;
        for(int j = 0; j < n && re; j++) for(int k = j + 1; k < n && re; k++) if(dis(j, k) + d[j] + d[k] > lim){
            ll dis1 = dis(i, j);
            ll need = lim - c - d[j] - d[k] - dis1;
            if(need < 0)
                re = false;
            int ptl = k - (upper_bound(all(av[k][0]), need) - av[k][0].begin() - 1);
            int ptr = k + (upper_bound(all(av[k][1]), need) - av[k][1].begin() - 1);
            l = max(l, ptl);
            r = min(r, ptr);
            //////cout << lim << ' ' << i << ' ' << j << ' ' << k << ' ' << l << ' ' << r << endl;
            if(l > r)
                re = false;
        }
        if(re)
            return true;
    }
    */
}
 
long long find_shortcut(int N, std::vector<int> l, std::vector<int> D, int C)
{
    n = N;
    c = C;
    for(auto u : D)
        d.pb(u);
    ps[0] = 0;
    for(int i = 0; i < n; i++){
        if(i)
            ps[i] = ps[i - 1] + l[i - 1];
        av[i] = {{d[i] + ps[i], i}, {d[i] + ps[i], d[i] - ps[i]}};
        srt.pb({d[i] - ps[i], i});
    }
    sort(all(srt));
    reverse(all(srt));
    sort(av, av + n);
    for(int i = n - 1; i >= 0; i--){
        ind[av[i].fi.se] = i;
        mxx[0][i] = av[i].se;
        if(i != n - 1)
            av[i].se = comb(av[i].se, av[i + 1].se);
    }
    for(int i = 1; i < lg; i++) for(int j = 0; j < n; j++)
        mxx[i][j] = comb(mxx[i - 1][j], j + (1 << (i - 1)) < n ? mxx[i - 1][j + (1 << (i - 1))] : mp(-inf, -inf));
    /*
    for(int i = 0; i < n; i++){
        for(int j = i + 1; j < n; j++)
            av[i].pb({dis(i, j) + d[i] + d[j], {d[j] + ps[j], d[j] - ps[j]}});
        //if(i == 1)
        //    ////cout << av[i][1].back().se << ' ' << av[i][1].back().fi << endl;
        sort(all(av[i]));
        for(int j = int(av[i].size()) - 2; j >= 0; j--){
            //if(i == 1)
            //    ////cout << j << endl;
            av[i][j].se.fi = max(av[i][j].se.fi, av[i][j + 1].se.fi);
            av[i][j].se.se = max(av[i][j].se.se, av[i][j + 1].se.se);
        }
        //if(i == 1)
        //    ////cout << av[i][1].back().se << ' ' << av[i][1].back().fi << endl;
    }
    */
    ll lo = -1, hi = mod * (n + 3);
    while(hi - lo > 1){
        ll mid = (lo + hi) >> 1;
        if(check(mid))
            hi = mid;
        else
            lo = mid;
    }
    return hi;
}

Compilation message (stderr)

shortcut.cpp:184:9: warning: "/*" within comment [-Wcomment]
  184 |         /*
      |          
shortcut.cpp:210:9: warning: "/*" within comment [-Wcomment]
  210 |         /*
      |

• Subtask 1: 9 / 9
• Subtask 2: 14 / 14
• Subtask 3: 8 / 8
• Subtask 4: 7 / 7
• Subtask 5: 33 / 33
• Subtask 6: 22 / 22
• Subtask 7: 4 / 4
• Subtask 8: 0 / 3