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.
Example
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
Approach
- 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.
Conclusion
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.
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