제출 #1085884

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1085884		alexz1205	Aliens (IOI16_aliens)	C++14	0 / 100	1 ms	448 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;
const llint PREC = 1e12;

array<llint, 2> rans[N];

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

int n, m;
int term;

void print(__int128 x) {
    if (x < 0) {
        putchar('-');
        x = -x;
    }
    if (x > 9) print(x / 10);
    putchar(x % 10 + '0');
}

llint slope(llint sl1p1, llint sl1p2, llint sl2p1, llint sl2p2){
	assert(sl2p2 != 0);
	for (int x = 0; x < 200; x ++){
		llint k1 = sl1p1 / sl1p2;
		llint k2 = sl2p1 / sl2p2;
		if (k1 != k2){
			return k1 - k2;
		}
		sl1p1 %= sl1p2;
		sl2p1 %= sl2p2;
		sl1p1 <<= 1;
		sl2p1 <<= 1;
	}
	return 0;
}

void calc(llint c){
	/*
	dp[0] = (rans[0][1] - rans[0][0]) * (rans[0][1] - rans[0][0]);
	dp2[0] = 1;
	deque<array<llint, 3>> hull;
	hull.push_back({rans[0][0], - rans[0][0] * rans[0][0], 0});
	array<llint, 2> ma = {rans[0][1], 1};
	term = 0;
	*/
	dp[0] = 0;
	dp2[0] = 0;
	deque<array<llint, 3>> hull;
	hull.push_back({0, 0, 0});
	array<llint, 2> ma = {0, 0};
	term = 0;
	for (int x = 1; x <= n; x ++){
		if (ma[0] >= rans[x-1][1]){
			continue;
		}
		llint s = -2 * rans[x-1][1];
		llint B = rans[x-1][1] * rans[x-1][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 (slp1 < s * slp2){
			if (slope(slp1, slp2, s, (llint)1) < 0){
				b = mid-1;
			}else {
				a = mid+1;
			}
		}
		int r = a-1;
		//cout << r << endl;
		//cout << (lint)hull[r][0] << " " << (lint)hull[r][1] << " " << (lint)hull[r][2] << endl;

		// (pos_right_j ** 2 - 2 * pos_j * pos_right_j  - dp_j) = pos_i ** 2 - dp_i + (- 2 * pos_j * pos_i)
		// hull[r][1] = B - dp_i + s * hull[0]
		// dp_i = B - hull[r][1] + s * hull[0]

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

		{
		llint l = max(ma[0], rans[x-1][0]);
		llint r = (rans[x-1][1] - rans[x-1][0]) * (rans[x-1][1] - rans[x-1][0]) - (l - rans[x-1][0]) * (l - rans[x-1][0]) + dp[ma[1]] + c;
		if (r < dp[x]){
			dp[x] = r;
			dp2[x] = dp2[ma[1]] + 1;
		}
		}

		/*
		print(dp[x]);
		cout << " " << dp2[x] << endl;;
		*/
		//cout << (lint)dp[x] << " " << dp2[x] << endl;
		//cout << (lint)rans[x-1][0] << " " << (lint)rans[x-1][1] << endl;

		llint right = max(rans[x-1][0], ma[0]);
		array<llint, 3> p = {rans[x-1][0], right * right - 2 * rans[x-1][0] * right - dp[ma[1]], dp2[ma[1]]};
		//cout << (lint)p[0] << " " << (lint)p[1] << " " << (lint)p[2] << endl;

		if (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 (sl1p1*sl2p2 >= sl2p1*sl1p2){
			if (slope(sl1p1, sl1p2, sl2p1, sl2p2) >= 0){
				hull.pop_back();
			}
		}
		hull.push_back(p);
		ma = {rans[x-1][1], x};
		term = x;
	}
}

long long take_photos(int n, int m, int k, std::vector<int> r, std::vector<int> c) {
	// dp_i = (pos_i-pos_j)**2 - (pos_right_j - pos_j)**2 + dp_j
	// (pos_right_j - pos_j) ** 2 - dp_j - pos_j ** 2 = pos_i ** 2 - dp_i - 2 * pos_i * pos_j
	// dp_i = (pos_i - pos_j + pos_right_j - pos_j) * (pos_i - pos_right_j) + dp_j
	// dp_i = pos_i ** 2 - 2 * pos_j * pos_i + 2 * pos_j * pos_right_j - pos_right_j ** 2 + dp_j
	// (pos_right_j ** 2 - 2 * pos_j * pos_right_j  - dp_j) = pos_i ** 2 - dp_i + (- 2 * pos_j * pos_i)
	//
	// subsume all within range
	// transition from possible left endpoints
	::n = n;
	::m = m;

	for (int x = 0; x < n; x ++){
		rans[x][0] = PREC*min(r[x], c[x]);
		rans[x][1] = PREC*(max(r[x], c[x]) + 1);
	}
	sort(rans, rans+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;
	int tot = 0;
	for (int x = 0; x < n; x ++){
		if (rans[x][1] > ma){
			tot ++;
			ma = rans[x][1];
		}
	}
	k = min(tot, k);
	}

	llint a = -(llint)1e12 * PREC * PREC, b = (llint)1e12 * PREC * PREC;
	while (a <= b){
		llint mid = (b-a+1)/2 + a;
		llint v = mid;
		calc(v);
		/*
		print(mid);
		cout << " ";
		print(dp[term]);
		cout << " " << dp2[term] << endl;;
		*/
		if (dp2[term] == k){
			llint val = dp[term];
			val -= k*v;
			val /= PREC;
			val /= PREC;
			return (lint)val;
		}
		if (dp2[term] < k){
			b = mid-1;
		}else {
			a = mid+1;
		}
	}
	throw runtime_error("DID NOT FIND ANSWER\n");
	//exit(-1);
	//return 0;
}

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