I am trying to do the leetcode question
I got the answer and trying to understand a systematical way to come up with the answer using the DP bottom-up approach, and I am having a hard time to understand it, up to m=2.
- What would be the best way to visualized or step by step to come up with this answer??
- What is non-after effect property?
The problem statement:
"Given an array which consists of non-negative integers and an integer m, you can split the array into m non-empty continuous subarrays. Write an algorithm to minimize the largest sum among these m subarrays."
Example to clarify the Question
Given the array [7,2,5,10,8] and split it into 2, there are 4 possible ways to split the array, with a minimum of 1 element in a subarray:
[2,5,10,8] , largestSum 25 = sum(2,5,10,8)
[7,2][5,10,8] , largestSum 23 = sum(5,10,8)
[7,2,5][10,8] , largestSum 18 = sum(10,8)
[7,2,5,10] , largestSum 24 = sum(7,2,5,10)
min(largestSums) = 18
The problem satisfies the non-aftereffect property. We can try to use dynamic programming to solve it.
The non-aftereffect property means, once the state of a certain stage is determined, it is not affected by the state in the future. In this problem, if we get the largest subarray sum for splitting nums[0..i] into j parts, this value will not be affected by how we split the remaining part of nums.
To know more about non-aftereffect property, this link may be helpful : http://www.programering.com/a/MDOzUzMwATM.html
- row is referring to the partition size
- col is referring to the array nums
7, 2, 5,10, 8 0[0, ∞, ∞, ∞, ∞, ∞] 1[∞, ∞, ∞, ∞, ∞, ∞] 2[∞, ∞, ∞, ∞, ∞, ∞] 3[∞, ∞, ∞, ∞, ∞, ∞]
Here is the working code and output