1266. Minimum Time Visiting All Points

1266. Minimum Time Visiting All Points #

题目 #

On a plane there are n points with integer coordinates points[i] = [xi, yi]. Your task is to find the minimum time in seconds to visit all points.

You can move according to the next rules:

  • In one second always you can either move vertically, horizontally by one unit or diagonally (it means to move one unit vertically and one unit horizontally in one second).
  • You have to visit the points in the same order as they appear in the array.

Example 1:

https://assets.leetcode.com/uploads/2019/11/14/1626_example_1.PNG

Input: points = [[1,1],[3,4],[-1,0]]
Output: 7
Explanation: One optimal path is [1,1] -> [2,2] -> [3,3] -> [3,4] -> [2,3] -> [1,2] -> [0,1] -> [-1,0]   
Time from [1,1] to [3,4] = 3 seconds 
Time from [3,4] to [-1,0] = 4 seconds
Total time = 7 seconds

Example 2:

Input: points = [[3,2],[-2,2]]
Output: 5

Constraints:

  • points.length == n
  • 1 <= n <= 100
  • points[i].length == 2
  • -1000 <= points[i][0], points[i][1] <= 1000

题目大意 #

平面上有 n 个点,点的位置用整数坐标表示 points[i] = [xi, yi]。请你计算访问所有这些点需要的最小时间(以秒为单位)。你可以按照下面的规则在平面上移动:

  • 每一秒沿水平或者竖直方向移动一个单位长度,或者跨过对角线(可以看作在一秒内向水平和竖直方向各移动一个单位长度)。
  • 必须按照数组中出现的顺序来访问这些点。

提示:

  • points.length == n
  • 1 <= n <= 100
  • points[i].length == 2
  • -1000 <= points[i][0], points[i][1] <= 1000

解题思路 #

  • 在直角坐标系上给出一个数组,数组里面的点是飞机飞行经过的点。飞机飞行只能沿着水平方向、垂直方向、45°方向飞行。问飞机经过所有点的最短时间。
  • 简单的数学问题。依次遍历数组,分别计算 x 轴和 y 轴上的差值,取最大值即是这两点之间飞行的最短时间。最后累加每次计算的最大值就是最短时间。

代码 #


package leetcode

func minTimeToVisitAllPoints(points [][]int) int {
	res := 0
	for i := 1; i < len(points); i++ {
		res += max(abs(points[i][0]-points[i-1][0]), abs(points[i][1]-points[i-1][1]))
	}
	return res
}


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