Monday, November 21, 2022

The Painters Partition Problem


The Painters Partition Problem

There are numerous painters available for painting a board, but you have to make sure that all of them finish painting the board in the minimum time. This is what the painter’s partition problem means. 

There are a lot of programmers who are not able to figure out how they can solve this problem. Even many of them are not able to understand the problem properly because of the lack of proper guides. 

Those who are looking for a guide through which they can take help to solve the painter’s partition problem, then it is the guide that you only need to read. 

What is The Painter's Partition Problem?

The painters partition problem is based on finding the most optimal way where each painter can finish their work in a minimal time. In this problem, the painters will be assigned for colouring the boat. 

You will have to assign them the paint and the length in which they will color. Each painter will take 1 unit of time to paint the board. However, you can make the partition in a way that the painters will be able to completely paint the board in the shortest time. 

For solving the painter’s partition question, you need to properly understand the problem statement with the help of examples. 

Below we have explained an example for you, so do check it to understand the problem properly. 


arr= [10, 20, 30, 40]

Answer: 60

Explanation: You might be thinking that how we have got the 60 as the answer. First of all, we have to make all the possible partitions for it. Once we have made the partition, then we will have to check for the time that we will get through it. Thus, first of all, see the partitions: 

Partition 1: [10],[20,30,40] = 90

Partition 2: [10,20],[30,40] = 70

Partition 3: [10,20,30],[40] = 60

If you see that we have got three partitions from it. Now, we will check for the timing for the highest unit. Therefore, we will start iterating over the array and will store the sum in every iteration. Now, for partition 1, we iterated. The first sum that we stored is 10. Again, we will start our iteration over the next array which is [20,30,40]. On adding them, we will get 90 units of time. 

Thus, we will compare the value of the previously stored unit with the currently stored unit. After comparing, we will store the highest number. Now, we will again do it for the next partitions that we have made.

Once we are done with all, then we will compare the time for each partition. After comparing, we will print the partition which has taken less time. Here we have partition 3 which will take less time, thus we will print its value. 

Now, let's figure out how we are going to solve it. 

How To Solve The painter's partition problem

We hope that you have now understood the problem of the painter’s partition. Now, it's time to know what approach we have to follow and solve the problem. 

Problem Statement

Find the painter’s partition problem.

arr= [10, 30, 40, 50]

Solution: 80


  • First of all, we have to make the different arrays by picking each element in every iteration. 
  • We will do it by first making a partition of the first element of the array. After it, we will do the same thing but this time we will make the partition by increasing the length. 
  • Once we have made all the partitions, then we will have to compare the value of the elements of the arrays with each other. Like if we have 2 partitions for the newly made array, then we will compare the unit of time between both of them. After it, we will store the highest unit of time for that element. 
  • We will do it for each partition. Once we are done with it, then we will compare the unit of time for each partition and after it, we will print the minimum value. 

Dry Run

  • We are starting with our first partition. For the first partition, we are taking one element and making two partitions. In doing it, we will get: [10], [30, 40, 50].
  • Now, we will again start our iteration. This time it will be for Partition 2. Thus, the partition that we will get is [10, 30], [40, 50].
  • Again we will iterate over the array and will make a new iteration which is Partition 3. The partition that we will get is [10, 30, 40], [50]
  • Now, we have got all three partitions. It's time, to sum up, the time that they will take to paint the length. 
  • Partition 1 will take: 120, Partition 2 will take: 90, and the third partition will take 80 units of time. 
  • Thus, we have got all the units of time that will be taken for the completion of the painting. 

Now, you have to code the problem in your preferred language. Once you solve the painter’s partition problem, then you will get to know about the control statements and the right approach properly. You can use them for solving the Mirror Tree Problem

This problem is based on making the binary tree look the same if we place a mirror in front of it. Thus, we have to traverse over the tree to make it a mirror tree. In short, we can say that we have to swap the number.


The painter's partition problem is one of the important problems that programmers should know when they are solving data structures problems. By solving the problem, programmers will be able to improve their coding skills. 

Thus, code the problem by taking the help of the approach and dry run that we have mentioned.

If you are also going to appear for the technical interviews, make sure to use this guide to recall the concept.

Also Read: Websites Accepting Guest Posts For The Write For Us News Category

Accepting Guest Posts

Contact For Health Accepting Guest Posts or Health Blogs Write For Us

We at A Class Blogs accept Guest Posts, Articles, Info-graphics and Creative Video Posts, etc. If you guys have the talent to write for the best categories like Health, Travel, Tech, Technology Business, Home And Improvements, Real Estate, Finance, etc. Then contact us at

A Class Blogs - Health Accepting Guest Posts

We are accepting guest posts on almost every niche like fashion, Health, healthcare, finance, home and improvement, travel, technology niche, etc.

But we have noticed users and SEO's are more likely to find us using Health accepting guest posts or health and wellness guest post using queries.

The most likely queries are listed below:

Health accepting guest posts
“submit guest post” + “health”
health blogs + write for us
health and wellness guest post
Pet Health + "write for us"
write for us health
health + write for us + guest post
health “accepting guest posts”
health care write for us
health blog guest post
medical news write for us
health tips write for us
health and fitness write for us
"health blog" + "write for us"
guest posting sites for health
“submit guest post” + “fitness”

This is how A Class blogs tend to found on number one search engine Google. So you can also Submit blogs and articles on the number one platform in all the categories.

For Write For Us Finance or Tech Submit Guest Post or Write For us Fashion visit the link.