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#The Best Way to Rake Leaves

code-challenge optimization

[This is just a little problem I thought up while doing yard work today. It is not fully specified and I may not finish it if some simple optimal solution is found.]

Suppose some 2D grid represents the area of a lawn. A number of leaves are strewn over the lawn and they are modeled as single grid points. You have a rake that is modeled as a line segment of length L.

To start you can rotate the rake in any way and put it anywhere on the grid.

When the rake is moved some distance d along its perpendicular, all the leaves in its path are caught in it. They stay on the rake line until the rake stops (as with normal raking).

You repeat this process (moving the rake different distances every time) until all the leaves all lie on one singular point.

The question is: what is the minimum distance the rake has to move to make this happen?
(i.e. what is the minimum sum of the d's from each move?)

#Challenge Spec (details incomplete)

Write a program that takes in a list of (x, y) leaf points and the length L of the rake (all floats).

The program should output a sequence of rake moves in the form of ((x1, y1), (x2, y2)) line segments that the rake travels perpendicularly down the center of. This sequence must bring all the leaves to the same exact point when they are "moved" by the rake

The challenge is to make an algorithm that does this with the least possible sum of sqrt((x1-x2)^2 + (y1-y2)^2) over all points.

[At this point several test cases would be given, with different L values and different leaf distributions. The submission that minimizes the total distance wins (assuming they do not hard code the answer).]

[This optimization problem does not seem to have any trivial solutions or even a clear optimal solution. Can anyone else poke holes in it?]

This message is open for anyone to adopt and post to main. For more details, see the chat room or meta post.

The Best Way to Rake Leaves

code-challenge optimization

[This is just a little problem I thought up while doing yard work today. It is not fully specified and I may not finish it if some simple optimal solution is found.]

Suppose some 2D grid represents the area of a lawn. A number of leaves are strewn over the lawn and they are modeled as single grid points. You have a rake that is modeled as a line segment of length L.

To start you can rotate the rake in any way and put it anywhere on the grid.

When the rake is moved some distance d along its perpendicular, all the leaves in its path are caught in it. They stay on the rake line until the rake stops (as with normal raking).

You repeat this process (moving the rake different distances every time) until all the leaves all lie on one singular point.

The question is: what is the minimum distance the rake has to move to make this happen?
(i.e. what is the minimum sum of the d's from each move?)

Challenge Spec (details incomplete)

Write a program that takes in a list of (x, y) leaf points and the length L of the rake (all floats).

The program should output a sequence of rake moves in the form of ((x1, y1), (x2, y2)) line segments that the rake travels perpendicularly down the center of. This sequence must bring all the leaves to the same exact point when they are "moved" by the rake

The challenge is to make an algorithm that does this with the least possible sum of sqrt((x1-x2)^2 + (y1-y2)^2) over all points.

[At this point several test cases would be given, with different L values and different leaf distributions. The submission that minimizes the total distance wins (assuming they do not hard code the answer).]

[This optimization problem does not seem to have any trivial solutions or even a clear optimal solution. Can anyone else poke holes in it?]

#The Best Way to Rake Leaves

code-challenge optimization

[This is just a little problem I thought up while doing yard work today. It is not fully specified and I may not finish it if some simple optimal solution is found.]

Suppose some 2D grid represents the area of a lawn. A number of leaves are strewn over the lawn and they are modeled as single grid points. You have a rake that is modeled as a line segment of length L.

To start you can rotate the rake in any way and put it anywhere on the grid.

When the rake is moved some distance d along its perpendicular, all the leaves in its path are caught in it. They stay on the rake line until the rake stops (as with normal raking).

You repeat this process (moving the rake different distances every time) until all the leaves all lie on one singular point.

The question is: what is the minimum distance the rake has to move to make this happen?
(i.e. what is the minimum sum of the d's from each move?)

#Challenge Spec (details incomplete)

Write a program that takes in a list of (x, y) leaf points and the length L of the rake (all floats).

The program should output a sequence of rake moves in the form of ((x1, y1), (x2, y2)) line segments that the rake travels perpendicularly down the center of. This sequence must bring all the leaves to the same exact point when they are "moved" by the rake

The challenge is to make an algorithm that does this with the least possible sum of sqrt((x1-x2)^2 + (y1-y2)^2) over all points.

[At this point several test cases would be given, with different L values and different leaf distributions. The submission that minimizes the total distance wins (assuming they do not hard code the answer).]

[This optimization problem does not seem to have any trivial solutions or even a clear optimal solution. Can anyone else poke holes in it?]

This message is open for anyone to adopt and post to main. For more details, see the chat room or meta post.

#The Best Way to Rake Leaves

code-challenge optimization

[This is just a little problem I thought up while doing yard work today. It is not fully specified and I may not finish it if some simple optimal solution is found.]

Suppose some 2D grid represents the area of a lawn. A number of leaves are strewn over the lawn and they are modeled as single grid points. You have a rake that is modeled as a line segment of length L.

To start you can rotate the rake in any way and put it anywhere on the grid.

When the rake is moved some distance d along its perpendicular, all the leaves in its path are caught in it. They stay on the rake line until the rake stops (as with normal raking).

You repeat this process (moving the rake different distances every time) until all the leaves all lie on one singular point.

The question is: what is the minimum distance the rake has to move to make this happen?
(i.e. what is the minimum sum of the d's from each move?)

#Challenge Spec (details incomplete)

Write a program that takes in a list of (x, y) leaf points and the length L of the rake (all floats).

The program should output a sequence of rake moves in the form of ((x1, y1), (x2, y2)) line segments that the rake travels perpendicularly down the center of. This sequence must bring all the leaves to the same exact point when they are "moved" by the rake

The challenge is to make an algorithm that does this with the least possible sum of sqrt((x1-x2)^2 + (y1-y2)^2) over all points.

[At this point several test cases would be given, with different L values and different leaf distributions. The submission that minimizes the total distance wins (assuming they do not hard code the answer).]

[This optimization problem does not seem to have any trivial solutions or even a clear optimal solution. Can anyone else poke holes in it?]