luogu#P4876. [USACO14MAR] The Lazy Cow G

[USACO14MAR] The Lazy Cow G

题目描述

It's a hot summer day, and Bessie the cow is feeling quite lazy. She wants to locate herself at a position in her field so that she can reach as much delicious grass as possible within only a short distance.

There are NN patches of grass (1<=N<=100,000)(1 <= N <= 100,000) in Bessie's field. The ithith such patch contains gig_i units of grass (1<=gi<=10,000)(1 <= g_i <= 10,000) and is located at a distinct point (xi,yi)(x_i, y_i) in the field (0<=xi,(0 <= x_i, yi<=y_i <= 1,000,000)1,000,000). Bessie would like to choose a point in the field as her initial location (possibly the same point as a patch of grass, and possibly even a point with non-integer coordinates) so that a maximum amount of grass is within a distance of KK steps from this location (1<=K<=2,000,000)(1 <= K <= 2,000,000).

When Bessie takes a step, she moves 1 unit north, south, east, or west of her current position. For example, to move from (0,0)(0,0) to (3,2)(3,2), this requires 5 total steps. Bessie does not need to take integer-sized steps -- for example, 1 total step could be divided up as half a unit north and half a unit east.

Please help Bessie determine the maximum amount of grass she can reach, if she chooses the best possible initial location.

输入格式

  • Line 1: The integers NN and KK.

  • Lines 2..1+N: Line i+1i+1 describes the ithith patch of grass using 3 integers: gi,xi,yi.g_i, x_i, y_i.

输出格式

  • Line 1: The maximum amount of grass Bessie can reach within KK steps, if she locates herself at the best possible initial position.

题目大意

  Bessie的田里有N(1<=N<=100,000)块草地,每块草地的坐标是 (xi, yi) (0<=xi,yi<=1,000,000),上面长着gi(1<=gi<=10,000)个单位的牧草。 
  Bessie可以向东南西北方向走,一次走一步(一个单位长度)。如她从(0,0)走到(3,2)需要5步。她最多可以一次走k (1<=k<=2,000,000) 步。
  现在她想找一个位置,使她从该位置出发可以得到最多单位的牧草(她可以走多次,但每次都从该位置出发)。 
  输入格式: 
  第1行:两个整数N和K 
  第2~N+1行:三个整数gi,xi,yi 
  输出格式: 
  第1行:Bessie所能获得的最多单位牧草数
4 3
7 8 6
3 0 0
4 6 0
1 4 2
8

提示

INPUT DETAILS:

Bessie is willing to take at most 3 steps from her initial position. There are 4 patches of grass. The first contains 7 units of grass and is located at position (8,6)(8,6), and so on.

OUTPUT DETAILS:

By locating herself at (3,0)(3,0), the grass at positions (0,0)(0,0), (6,0)(6,0), and (4,2)(4,2) is all within KK units of distance.