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Posts tagged as “triangle”

花花酱 LeetCode 1739. Building Boxes

By zxi on January 23, 2021

You have a cubic storeroom where the width, length, and height of the room are all equal to n units. You are asked to place n boxes in this room where each box is a cube of unit side length. There are however some rules to placing the boxes:

  • You can place the boxes anywhere on the floor.
  • If box x is placed on top of the box y, then each side of the four vertical sides of the box y must either be adjacent to another box or to a wall.

Given an integer n, return the minimum possible number of boxes touching the floor.

Example 1:

Input: n = 3
Output: 3
Explanation: The figure above is for the placement of the three boxes.
These boxes are placed in the corner of the room, where the corner is on the left side.

Example 2:

Input: n = 4
Output: 3
Explanation: The figure above is for the placement of the four boxes.
These boxes are placed in the corner of the room, where the corner is on the left side.

Example 3:

Input: n = 10
Output: 6
Explanation: The figure above is for the placement of the ten boxes.
These boxes are placed in the corner of the room, where the corner is on the back side.

Constraints:

  • 1 <= n <= 109

Solution: Geometry

Step 1: Build a largest pyramid that has less then n cubes, whose base area is d*(d+1) / 2
Step 2: Build a largest triangle with cubes left, whose base area is l, l*(l + 1) / 2 >= left

Time complexity: O(n^(1/3))
Space complexity: O(1)

C++

花花酱 LeetCode 976. Largest Perimeter Triangle

By zxi on January 14, 2019

Given an array A of positive lengths, return the largest perimeter of a triangle with non-zero area, formed from 3 of these lengths.

If it is impossible to form any triangle of non-zero area, return 0.

Example 1:

Input: [2,1,2]
Output: 5

Example 2:

Input: [1,2,1]
Output: 0

Example 3:

Input: [3,2,3,4]
Output: 10

Example 4:

Input: [3,6,2,3]
Output: 8

Note:

  1. 3 <= A.length <= 10000
  2. 1 <= A[i] <= 10^6

Solution: Greedy

Answer must be 3 consecutive numbers in the sorted array
if A[i] >= A[i+1] + A[i+2], then A[i] >= A[i+j] + A[i+k], 1 < j < k
if A[i] < A[i+1] + A[i+2], then A[i] + A[i+1] + A[i+2] is the answer

C++

花花酱 LeetCode 812. Largest Triangle Area

By zxi on April 8, 2018

Problem

题目大意：给你一些点，求用这些点能够成的最大的三角形面积是多少？

https://leetcode.com/problems/largest-triangle-area/description/

You have a list of points in the plane. Return the area of the largest triangle that can be formed by any 3 of the points.

Example:
Input: points = [[0,0],[0,1],[1,0],[0,2],[2,0]]
Output: 2
Explanation: 
The five points are show in the figure below. The red triangle is the largest.

Notes:

  • 3 <= points.length <= 50.
  • No points will be duplicated.
  •  -50 <= points[i][j] <= 50.
  • Answers within 10^-6 of the true value will be accepted as correct.

Solution: Brute Force

Time complexity: O(n^3)

Space complexity: O(1)