제출 #1088765

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1088765		alexz1205	Aliens (IOI16_aliens)	C++14	100 / 100	701 ms	22284 KiB

aliens

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

typedef long long int lint;
typedef __int128 llint;
typedef long double ldoub;

const int N = 1e5;
llint PREC = 1e3;

array<llint, 2> ransDat[N];
array<llint, 2> rans[N];
int sizeR = 0;

llint dp[N+1];
int dp2[N+1];

inline llint slope(llint a, llint b, llint c, llint d){
	return a*d - b*c;
	/*
	for (int x = 0; x < 200; x ++){
		llint k1 = a / b;
		llint k2 = c / d;
		if (k1 != k2){
			return k1 - k2;
		}
		a %= b;
		c %= d;
		a <<= 1;
		c <<= 1;
	}
	return 0;
	*/
}

void calc(llint adjust){
	vector<array<llint, 3>> hull;
	hull.push_back({rans[0][0], -rans[0][0] * rans[0][0], 0});
	for (int x = 0; x < sizeR; x ++){
		llint s = -2 * rans[x][1];
		llint B = rans[x][1] * rans[x][1];
		int a = 1, b = hull.size()-1;
		while (a <= b){
			int mid = (b-a+1)/2 + a;
			llint slp1 = (hull[mid][1] - hull[mid-1][1]);
			llint slp2 = (hull[mid][0] - hull[mid-1][0]);
			if (slope(slp1, slp2, s, (llint)1) < 0){
				b = mid-1;
			}else {
				a = mid+1;
			}
		}
		int r = a-1;

		dp[x] = -hull[r][1] + B + hull[r][0] * s + adjust;
		dp2[x] = hull[r][2] + 1;

		if (x == sizeR-1) continue;

		llint right = min(rans[x][1], rans[x+1][0]);
		array<llint, 3> p = {rans[x+1][0], -dp[x] + (rans[x][1] - right) * (rans[x][1] - right) - rans[x+1][0] * rans[x+1][0], dp2[x]};

		while (hull.size() > 1){
			llint sl1p1 = (p[1] - hull[hull.size()-2][1]);
			llint sl1p2 = (p[0] - hull[hull.size()-2][0]);
			llint sl2p1 = (hull[hull.size()-1][1] - hull[hull.size()-2][1]);
			llint sl2p2 = (hull[hull.size()-1][0] - hull[hull.size()-2][0]);

			if (slope(sl1p1, sl1p2, sl2p1, sl2p2) >= 0){
				hull.pop_back();
			}else {
				break;
			}
		}
		hull.push_back(p);
	}
}

long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
	PREC = 10*m;

	for (int x = 0; x < n; x ++){
		ransDat[x][0] = PREC*min(r[x], c[x]);
		ransDat[x][1] = PREC*(max(r[x], c[x]) + 1);
	}
	sort(ransDat, ransDat+n, [](array<llint, 2> a, array<llint, 2> b){return (a[0] == b[0] ? a[1] > b[1] : a[0] < b[0]);});
	{
	llint ma = 0;
	for (int x = 0; x < n; x ++){
		if (ma >= ransDat[x][1]){
			continue;
		}
		ma = ransDat[x][1];
		rans[sizeR++] = ransDat[x];
	}
	}

	k = min(k, (int)sizeR);

	llint a = -(llint)1e12 * PREC * PREC, b = (llint)1e12 * PREC * PREC;
	pair<llint, int> up = {1e12 * PREC*PREC, -1};
	pair<llint, int> low = {1e12 * PREC*PREC, -1};
	while (a <= b){
		llint mid = (b-a+1)/2 + a;
		llint v = mid;
		calc(v);

		if (dp2[sizeR-1] == k){
			llint val = dp[sizeR-1];
			val -= k*v;
			val /= PREC;
			val /= PREC;
			return (lint)val;
		}
		if (dp2[sizeR-1] < k){
			llint val = dp[sizeR-1];
			val -= dp2[sizeR-1]*v;
			val /= PREC;
			val /= PREC;
			up = {val, dp2[sizeR-1]};
			b = mid-1;
		}else {
			llint val = dp[sizeR-1];
			val -= dp2[sizeR-1]*v;
			val /= PREC;
			val /= PREC;
			low = {val, dp2[sizeR-1]};
			a = mid+1;
		}
	}
	llint best = ((up.first-low.first) * (k-low.second))/(up.second - low.second) + low.first;
	return best;
}

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 19 / 19
• Subtask 6: 40 / 40