【雅礼联考DAY01】逃跑

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#include<cstdio>
using namespace std;

const int N = 30000;
const double INF = 1e8;
int n , l , a[N + 5] , b[N + 5] , c[N + 5] , q[N + 5] , head , tail , Mk , Mc;
double ans , f[N + 5] , w[N + 5];
struct tree{double max , tag;}t[(N << 2) + 5];

inline double max(double x , double y) {return x > y ? x : y;}

inline void build(int l , int r , int k)
{
	t[k] = (tree){0 , 0};
	if (l == r) 
	{
		t[k].max = f[l];
		return;
	}
	int mid = (l + r) >> 1;
	if (l <= mid) build(l , mid , k << 1);
	if (r > mid) build(mid + 1 , r , k << 1 | 1);
	t[k].max = max(t[k << 1].max , t[k << 1 | 1].max);
}

inline void pushdown(int k)
{
	if (!t[k].tag) return;
	t[k << 1].max += t[k].tag;
	t[k << 1 | 1].max += t[k].tag;
	t[k << 1].tag += t[k].tag;
	t[k << 1 | 1].tag += t[k].tag;
	t[k].tag = 0;
}

inline void update(int l , int r , int k , int x , double v)
{
	if (l == r && l == x)
	{
		t[k].max = v;
		return;
	}
	int mid = (l + r) >> 1;
	pushdown(k);
	if (x <= mid) update(l , mid , k << 1 , x , v);
	if (x > mid) update(mid + 1 , r , k << 1 | 1 , x , v);
	t[k].max = max(t[k << 1].max , t[k << 1 | 1].max);
}

inline void change(int l , int r , int k , int tl , int tr , double v)
{
	if (l >= tl && r <= tr)
	{
		t[k].tag += v;
		t[k].max += v;
		return;
	}
	int mid = (l + r) >> 1;
	pushdown(k);
	if (tl <= mid) change(l , mid , k << 1 , tl , tr , v);
	if (tr > mid) change(mid + 1 , r , k << 1 | 1 , tl , tr , v);
	t[k].max = max(t[k << 1].max , t[k << 1 | 1].max);
}

inline double query(int l , int r , int k , int tl , int tr)
{
	if (l >= tl && r <= tr) return t[k].max;
	int mid = (l + r) >> 1;
	double res = -INF;
	pushdown(k);
	if (tl <= mid) res = max(res , query(l , mid , k << 1 , tl , tr));
	if (tr > mid) res = max(res , query(mid + 1 , r , k << 1 | 1 , tl , tr));
	return res;
}

inline bool check(double m)
{
	for(register int i = 1; i <= n; i++) w[i] = a[i] - b[i] * m , f[i] = -INF;
	f[0] = 0;
	build(0 , n , 1);
	q[head = tail = 1] = 0;
	for(register int i = 1; i <= n; i++)
	{
		while (head < tail && c[i] >= c[q[tail]])
		{
			change(0 , n , 1 , q[tail - 1] , q[tail] - 1 , -w[q[tail]]);
			tail--;
		}
		q[++tail] = i;	
		change(0 , n , 1 , q[tail - 1] , q[tail] - 1 , w[q[tail]]);
		f[i] = query(0 , n , 1 , i - l > 0 ? i - l : 0 , i - 1);
		update(0 , n , 1 , i , f[i]);
	}
	return f[n] >= 0;
}

int main()
{
//	freopen("逃跑.in" , "r" , stdin);
	scanf("%d%d" , &n , &l);
	for(register int i = 1; i <= n; i++) scanf("%d%d%d" , &a[i] , &b[i] , &c[i]);
	c[0] = INF;
	double l = 0 , r = 1e6 , mid;
	for(register int i = 1; i <= 60; i++)
	{
		mid = (l + r) * 0.5;
		if (check(mid)) l = mid , ans = mid;
		else r = mid;
	}
	
	if (ans == 0) 
	{
		puts("0.000000000e+000");	
		return 0;
	}
	Mk = 0 , Mc;
	if (ans < 1)
	{	
		while (ans < 1) ans *= 10 , Mk++;
		printf("%.9lfe-" , ans);
		if (Mk == 0) Mc = 3;
		else if (Mk < 10) Mc = 2;
		else if (Mk < 100) Mc = 1;
		else Mc = 0;
		while (Mc--) putchar('0');
		if (Mk > 0) printf("%d" , Mk);
		return 0;
	} 
	while (ans >= 10) ans /= 10 , Mk++;
	printf("%.9lfe+" , ans);
	if (Mk == 0) Mc = 3;
	else if (Mk < 10) Mc = 2;
	else if (Mk < 100) Mc = 1;
	else Mc = 0;
	while (Mc--) putchar('0');
	if (Mk > 0) printf("%d" , Mk);
}