By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a minute to sign up. Can you point me towards the solution? I've been trying for a few days now, and I'm no closer to an algorithm than I was few days ago. Use dynamic programming. This is a straightforward application of dynamic programming.

This is a very nice exercise, so I'll let you do the exercise yourself and won't spoil it for you -- but since you only wanted a hint, my hint is "use dynamic programming" that's a huge, enormous hint that should be enough for you to work out the rest of the details.

I faced a similar question in an algorithm exam. If we get partitions less than the required number then we can choose a required number of partitions whose sum is less than the bound and split it such that both have individual sums less than the bound. Invariance condition meted. Runtime analysis : 3b. So the worst case runtime will be of the order O nk. For my particular question I just need to have one more pass over the array and find the max sum which may be less than the bound I set.

This is the game of inserting the biggest currently available number into the sub array with the smallest sum. So it is best done by sorting the main array first.

There has been a solution in StackOverflow. It uses Backtracking algorithm like 8-queen problem. But this solution is brute-forcing with additional improvement. Sign up to join this community. The best answers are voted up and rise to the top. Partition array into K subsets, each with balanced sum Ask Question. Asked 6 years, 9 months ago. Active 1 year, 7 months ago. Viewed 8k times. AI course? Algorithms course?

What was the topic? Active Oldest Votes. I believe that you gave him some new information only in complexity that you mentioned, as the headline of the exercise probably was something like "dynamic programming". I missed that detail!Given an integer array of N elements, the task is to divide this array into K non-empty subsets such that the sum of elements in every subset is same.

All elements of this array should be part of exactly one partition. We can solve this problem recursively, we keep an array for sum of each partition and a boolean array to check whether an element is already taken into some partition or not.

First we need to check some base cases, If K is 1, then we already have our answer, complete array is only subset with same sum. If sum of array is not divisible by K, then it is not possible to divide the array. We will proceed only if k divides sum. If sum of this subset reaches required sum, we iterate for next part recursively, otherwise we backtrack for different set of elements. If number of subsets whose sum reaches the required sum is K-1we flag that it is possible to partition array into K parts with equal sum, because remaining elements already have a sum equal to required sum.

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Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. Attention reader! Writing code in comment? Please use ide. Write a program to print all permutations of a given string Given an array A[] and a number x, check for pair in A[] with sum as x.

Python3 program to check whether an array can be. Recursive Utility method to check K equal sum. Method returns True if arr can be. If K is 1. If total number of partitions are more than N.

Initialize sum of each subset from 0. K-substitution condition. WriteLine "Partitions into equal sum is possible. WriteLine "Partitions into equal sum is not possible. Load Comments. We use cookies to ensure you have the best browsing experience on our website.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Here maximum sum subset is one of k subsets that give maximum sum e. Assume you know the answer is x which means sum of the maximum subset is equal to x. You can verify this assumption by a greedy algorithm O n.

Traverse the array from left to right and pick items until the sum of that subset is lower than x. Now you can binary search on x and find the minimum value for x.

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The complexity of this algorithm is O nlogn. Lets start with an example. We can observe that if k was equal to 1, then sum of maximum partition would be sum all array elements i. Now, we can observe that as k increases, sum of maximum partition's minimum value decreases. Our algorithm will take the help of binary search in doing so.

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But how to do it????? We are going to do exactly the same stuff but will take the help of a function in doing so. Look at the code and answer from here, parallelly. The helper function will find the value of K when the minimum sum of maximum partition is provided. So,our code will execute on our example in following way To get a better solution, you can use the binary search method as suggested by others.

Lets define first DP[n,m] to be the optimal solution for dividing the subarray C[ Where each part has at least one element. Explanation: DP[n,1] - Base case, when the number of partitions is 1 there is only one way - all elements left from 1 to n. DP[n,n] - Whenever the number of partitions are equal to the number of elements left in the array there is only one legal way to divide it - each element in a different partition, so the partition with the maximum sum is the maximum element in the array.

DP[n,m] - This is the main solution. We don't know exactly how many elements will be our next partition, so we need to go over all options and get the minimum from it. The division is just a brute force problem.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Computer Science Stack Exchange is a question and answer site for students, researchers and practitioners of computer science. It only takes a minute to sign up.

Sign up to join this community. The best answers are voted up and rise to the top. Partition array into k subsets Ask Question. Asked 1 year, 6 months ago. Active 1 year, 6 months ago. Viewed 1k times. Partition array into K subsets such that let MaxSum be the maximum sum of among subsets.

Manoharsinh Rana Manoharsinh Rana 2 2 silver badges 14 14 bronze badges. It's not clear what the summation means. Please spend some effort to formulate your question more precisely.

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Do the subsets have to be contiguous? What's the context where you encountered this problem? Can you credit the original source? We discourage posts that simply state a problem out of context, and expect the community to solve it. What did you try? Where did you get stuck? We're happy to help you understand the concepts but just solving exercises for you is unlikely to achieve that.

Did you try a greedy algorithm? Dynamic programming?

### Count number of ways to partition a set into k subsets

Learn more. Partition a set into K subsets with equal sum Ask Question. Asked 2 years, 10 months ago. Active 1 year, 2 months ago. Viewed 2k times. I'm going through an exercise to partition a set into K subsets with equal sum. It doesn't gets the partition and finally solves it to [[4,1], [4,1], [3,2], [3,2]]. I am not sure how does this algorithm finds the alternative?

I'm not able to follow up with the recursion. What are the ways to solve it? Is the backtracking the only way? You do realize this problem is NP hard. Partitioning into 2 has a simple pseudo polynomial time algorithm in dynamic programming haven't thought about k. What does "doesn't gets the partition" mean? I still don't really understand what you mean Is [[2,2,1], [4,1]] its first attempt? It's not surprising that this first attempt is not a valid solution; the whole design of backtracking algorithms like this one is to keep trying solutions until a valid one is found.

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Equal Sum Subsets Partition - Recursive - Subset Sum Problem - Backtracking in JAVA

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