Submission #1051667

#	Time	Username	Problem	Language	Result	Execution time	Memory
1051667		Alihan_8	Shortcut (IOI16_shortcut)	C++17	71 / 100	2063 ms	54364 KiB

shortcut

#include "shortcut.h"

#include <bits/stdc++.h>

using namespace std;

#define pb push_back
#define ar array
#define all(x) x.begin(), x.end()

using i64 = long long;

const i64 inf = 1e15;

struct square{
	i64 x1, x2, y1, y2;
	
	square(i64 x1 = 0, i64 x2 = 0, i64 y1 = 0, i64 y2 = 0) : x1(x1), x2(x2), y1(y1), y2(y2) {}
	
	square f(square q){
		return square(max(x1, q.x1), min(x2, q.x2), max(y1, q.y1), min(y2, q.y2));
	}
	
	bool check(i64 x, i64 y){
		return x1 <= x && x2 >= x && y1 <= y && y2 >= y;
	}
};

struct SegTree{
	vector <ar<i64,2>> T;
	
	int n;
	
	bool isMax;
	
	SegTree(int n, bool isMax = false) : n(n), isMax(isMax) {
		T.resize(n * 4 + 5, {inf, -1});
	}
	
	void upd(int v, int l, int r, int p, i64 x, int j){
		if ( l == r ){
			if ( T[v][0] > x ){
				T[v] = {x, j};
			}
			
			return;
		}	
		
		int m = (l + r) / 2;
		
		if ( p <= m ) upd(v * 2, l, m, p, x, j);
		else  upd(v * 2 + 1, m + 1, r, p, x, j);
		
		T[v] = min(T[v * 2], T[v * 2 + 1]);
	}	
	
	void upd(int p, i64 x, int j){
		if ( isMax ) x = -x;
		upd(1, 0, n, p, x, j);
	}
	
	ar <i64,2> get(int v, int l, int r, int tl, int tr){
		ar <i64,2> ret = {inf, -1};
		
		if ( l > tr or r < tl ) return ret;
		
		if ( tl <= l && tr >= r ){
			return T[v];
		}
		
		int m = (l + r) / 2;
		
		return min(get(v * 2, l, m, tl, tr), get(v * 2 + 1, m + 1, r, tl, tr));
	}
	
	int get(int l, int r){
		return get(1, 0, n, l, r)[1];
	}
};

long long find_shortcut(int n, std::vector<int> L, std::vector<int> d, int C){
	vector <i64> x(n), A(n), B(n);
	
	for ( int i = 1; i < n; i++ ){
		x[i] = x[i - 1] + L[i - 1];
	}
	
	for ( int i = 0; i < n; i++ ){
		A[i] = x[i] + d[i];
		B[i] = x[i] - d[i];
	}
	
	auto P = B;
	
	P.pb(-inf), P.pb(inf);
	
	sort(all(P));
	P.resize(unique(all(P)) - P.begin());
	
	int m = P.size();
	
	auto get = [&](i64 x){
		return lower_bound(all(P), x) - P.begin();
	};
	
	auto ok = [&](i64 k){
		i64 kk = k - C;
		
		vector <ar<i64,3>> pt;
		
		auto add = [&](int i, int j){
			if ( i == -1 ) return;
			pt.pb({x[i] + x[j], x[i] - x[j], kk - (d[i] + d[j])});
		};
		
		vector <SegTree> seg(4, SegTree(m));
		
		seg[1] = seg[3] = SegTree(m, 1);
		
		for ( int i = 0; i < n; i++ ){
			int u = get(A[i] - k) - 1, v = get(B[i]);
			
			vector <i64> q = {A[i], A[i], B[i], B[i]};
			
			for ( int j = 0; j < 4; j++ ){
				add(seg[j].get(0, u), i);
				seg[j].upd(v, q[j], i);
			}
		}
		
		if ( pt.empty() ) return true;
		
		auto [X, Y, d] = pt[0];
		
		square t = square(X - d, X + d, Y - d, Y + d);
		
		for ( int i = 1; i < (int)pt.size(); i++ ){
			auto [x, y, d] = pt[i];
			
			t = t.f(square(x - d, x + d, y - d, y + d));
		}  
		
		if ( t.x1 > t.x2 || t.y1 > t.y2 ){ // area 0
			return false;
		}
		
		bool flag = false;
		
		int l = n, r = n - 1;
		
		set <i64> st;
		
		for ( int i = 0; i < n; i++ ){
			while ( l > 0 && t.x1 - x[i] <= x[l - 1] ){
				st.insert(x[--l]);
			}
			
			while ( r >= 0 && t.x2 - x[i] < x[r] ){
				st.erase(x[r--]);
			}
			
			i64 p = -t.y2 + x[i], q = -t.y1 + x[i];
		
			if ( l <= i && r >= i ) st.erase(x[i]);
			
			if ( st.lower_bound(p) != st.upper_bound(q) ){
				flag = true;
			}
			
			if ( l <= i && r >= i ) st.insert(x[i]);
		}
		
		//~ for ( int i = 0; i < n; i++ ){
			//~ for ( int j = i + 1; j < n; j++ ){
				//~ flag |= t.check(x[i] + x[j], x[i] - x[j]);
			//~ }
		//~ }
		
		return flag;
	};
	
	i64 l = 0, r = 1e15;
	
	while ( l < r ){
		i64 m = (l + r) / 2;
		
		if ( ok(m) ){
			
			r = m;
		} else l = m + 1;
	}
	
	return l;
}

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