Submission #397178

#	Time	Username	Problem	Language	Result	Execution time	Memory
397178		12tqian	Road Construction (JOI21_road_construction)	C++17	100 / 100	4209 ms	676112 KiB

road_construction

#include <bits/stdc++.h>

using namespace std;

#define f1r(i, a, b) for (int i = a; i < b; ++i)
#define f0r(i, a) f1r(i, 0, a)
#define each(t, a) for (auto& t : a)

#define mp make_pair
#define f first
#define s second
#define pb push_back
#define eb emplace_back
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;

template <class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template <class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }

const int M = 4e7;
const int INF = 2e9 + 7;

struct Node {
    int lc, rc;
    int mx = -INF;
    int loc = -INF;
} t[M];

int cnt = 0;

int modify(int p, int l, int r, int x, int v) {
    int u = ++cnt;
    if (l == r) {
        t[u].mx = v;
        t[u].loc = l;
    } else {
        int m = (l + r) >> 1;
        if (x <= m) {
            t[u].lc = modify(t[p].lc, l, m, x, v);
            t[u].rc = t[p].rc;
        } else {
            t[u].lc = t[p].lc;
            t[u].rc = modify(t[p].rc, m + 1, r, x, v);
        }
        int L = t[t[u].lc].mx;
        int R = t[t[u].rc].mx;
        if (L > R) {
            t[u].mx = L;
            t[u].loc = t[t[u].lc].loc;
        } else {
            t[u].mx = R;            
            t[u].loc = t[t[u].rc].loc;
        }
    }
    return u;
}

pi query(int p, int l, int r, int lo, int hi) {
    if (hi < l || r < lo) return {-INF, -INF};;
    if (lo <= l && r <= hi) return {t[p].mx, t[p].loc};
    int m = (l + r) >> 1;
    return max(query(t[p].lc, l, m, lo, hi), query(t[p].rc, m + 1, r ,lo, hi));
}

int new_node() {
    ++cnt;
    t[cnt].lc = t[cnt].rc = cnt;
    t[cnt].mx = -INF;
    t[cnt].loc = -INF;
    return cnt;
}

template <class T> int get_pos(vector<T>& v, T x) {
    return lower_bound(all(v), x) - v.begin();
}

void reset() {
    f0r(i, cnt + 1) {
        t[i].lc = t[i].rc = 0;
        t[i].mx = t[i].loc = -INF;
    }
    cnt = 0;
}

int main() {
    cin.tie(0)->sync_with_stdio(0);
    
    int n, k; cin >> n >> k;
   
    vpi pts(n);
   
    f0r(i, n) {
        cin >> pts[i].f >> pts[i].s;
    }
   
    vi xvals;
    vi yvals;

    typedef pair<ll, int> T;

    priority_queue<T, vector<T>, greater<T>> pq;

    vl dists;
   
    { // diagonally up, not equal x or y
        reset();
        while (!pq.empty()) pq.pop();
        xvals.clear();
        yvals.clear();
        
        sort(all(pts));
        
        f0r(i, n) {
            xvals.pb(pts[i].f);
            yvals.pb(pts[i].s);
        }
        
        xvals.pb(-INF);
        yvals.pb(-INF);
        
        sort(all(xvals));
        sort(all(yvals));
        
        xvals.erase(unique(all(xvals)), xvals.end());
        yvals.erase(unique(all(yvals)), yvals.end());

        int nx = sz(xvals);
        int ny = sz(yvals);

        vector<vi> by_x(nx);
        vector<vi> by_y(ny);

        each(p, pts) {
            by_x[get_pos(xvals, p.f)].pb(p.s);
            by_y[get_pos(yvals, p.s)].pb(p.f);
        }

        each(y, by_y) sort(all(y));

        vi seg(n); // corresponding segtree for each point
       
        int rec = new_node();
       
        f0r(i, nx) { // iterate over xvals
            each(p, by_x[i]) { // this is before for exclusive
                int x = xvals[i];
                int y = p;
                int pid = get_pos(pts, mp(x, y));
                seg[pid] = rec;
            }
            each(p, by_x[i]) {
                int x = xvals[i];
                int y = p;
                int id = get_pos(yvals, y);
                rec = modify(rec, 0, ny - 1, id, x + y);
            }
        }
        
        auto add = [&](int i) {
            int x = pts[i].f;
            int y = pts[i].s;
            int yid = get_pos(yvals, y);
            
            auto res = query(seg[i], 0, ny - 1, 0, yid - 1); // check next point
            
            if (res.f == -INF) return;
            
            ll dist = 0LL + x + y - res.f;

            pq.push(mp(dist, i));  
        };

        auto nullify = [&](int i) {
            int x = pts[i].f;
            int y = pts[i].s;
            int yid = get_pos(yvals, y);

            auto res = query(seg[i], 0, ny - 1, 0, yid - 1); // exclusive

            assert(res.f != -INF);

            int loc = res.s;

            int xloc = res.f - yvals[loc]; 

            int xid = get_pos(by_y[loc], xloc);

            if (xid == 0) {
                seg[i] = modify(seg[i], 0, ny - 1, loc, -INF); // set to null
            } else {                
                seg[i] = modify(seg[i], 0, ny - 1, loc, yvals[loc] + by_y[loc][xid - 1]); // set to null
            }
        };
        
        f0r(i, n) {
            int x = pts[i].f;
            int y = pts[i].s;
            int yid = get_pos(yvals, y);
            
            auto res = query(seg[i], 0, ny - 1, 0, yid - 1); // exclusive

            if (res.f == -INF) continue;
            
            ll dist = 0LL + x + y - res.f;
            dists.pb(dist); // initial dist
            
            nullify(i);
            add(i);
        }
        
        int t = 0;
        
        while (t < k && !pq.empty()) {
            auto top = pq.top();
            pq.pop();
            dists.pb(top.f);
            
            int i = top.s;

            nullify(i);
            add(i);            

            t++;
        }
    }
    { // possibly equal x, y
        reset();
        while (!pq.empty()) pq.pop();
        xvals.clear();
        yvals.clear();

        f0r(i, n) pts[i].f *= -1;
        
        sort(all(pts));
        
        f0r(i, n) {
            xvals.pb(pts[i].f);
            yvals.pb(pts[i].s);
        }
        
        xvals.pb(-INF);
        yvals.pb(-INF);
        
        sort(all(xvals));
        sort(all(yvals));
        
        xvals.erase(unique(all(xvals)), xvals.end());
        yvals.erase(unique(all(yvals)), yvals.end());

        int nx = sz(xvals);
        int ny = sz(yvals);

        vector<vi> by_x(nx);
        vector<vi> by_y(ny);

        each(p, pts) {
            by_x[get_pos(xvals, p.f)].pb(p.s);
            by_y[get_pos(yvals, p.s)].pb(p.f);
        }

        each(y, by_y) sort(all(y));

        vi seg(n); // corresponding segtree for each point
       
        int rec = new_node();
       
        f0r(i, nx) { // iterate over xvals
            each(p, by_x[i]) {
                int x = xvals[i];
                int y = p;
                int id = get_pos(yvals, y);
                rec = modify(rec, 0, ny - 1, id, x + y);
            }
         
            each(p, by_x[i]) { // this is before for exclusive
                int x = xvals[i];
                int y = p;
                int pid = get_pos(pts, mp(x, y));
                seg[pid] = rec;
            }
        }

        auto add = [&](int i) {
            int x = pts[i].f;
            int y = pts[i].s;
            int yid = get_pos(yvals, y);
            
            auto res = query(seg[i], 0, ny - 1, 0, yid); // check next point
            
            if (res.f == -INF) return;
            
            ll dist = 0LL + x + y - res.f;

            pq.push(mp(dist, i));  
        };

        auto nullify = [&](int i) {
            int x = pts[i].f;
            int y = pts[i].s;
            int yid = get_pos(yvals, y);

            auto res = query(seg[i], 0, ny - 1, 0, yid); 

            assert(res.f != -INF);

            int loc = res.s;

            int xloc = res.f - yvals[loc]; 

            int xid = get_pos(by_y[loc], xloc);

            if (xid == 0) {
                seg[i] = modify(seg[i], 0, ny - 1, loc, -INF); // set to null
            } else {                
                seg[i] = modify(seg[i], 0, ny - 1, loc, yvals[loc] + by_y[loc][xid - 1]); // set to null
            }
        };
        
        f0r(i, n) { 
            int x = pts[i].f;
            int y = pts[i].s;
            int yid = get_pos(yvals, y);
            
            auto res = query(seg[i], 0, ny - 1, 0, yid); // exclusive

            if (res.f == -INF) continue;
            
            int loc = res.s;

            ll dist = 0LL + x + y - res.f;
            
            assert(dist == 0);

            nullify(i);
            add(i);
        }
        
        int t = 0;
        
        while (t < k && !pq.empty()) {
            auto top = pq.top();
            pq.pop();
            dists.pb(top.f);
            
            int i = top.s;

            nullify(i);
            add(i);            

            t++;
        }
    }

    sort(all(dists));

    f0r(i, k) {
        cout << dists[i] << '\n';
    }
    return 0;
}

/**
 * we have to pursue from a few directions
 * can have equal y coordinate, but not x coordinate
 * 
 */

Compilation message (stderr)

road_construction.cpp: In lambda function:
road_construction.cpp:182:17: warning: unused variable 'x' [-Wunused-variable]
  182 |             int x = pts[i].f;
      |                 ^
road_construction.cpp: In lambda function:
road_construction.cpp:306:17: warning: unused variable 'x' [-Wunused-variable]
  306 |             int x = pts[i].f;
      |                 ^
road_construction.cpp: In function 'int main()':
road_construction.cpp:336:17: warning: unused variable 'loc' [-Wunused-variable]
  336 |             int loc = res.s;
      |                 ^~~

• Subtask 1: 5 / 5
• Subtask 2: 6 / 6
• Subtask 3: 7 / 7
• Subtask 4: 20 / 20
• Subtask 5: 27 / 27
• Subtask 6: 35 / 35