Optimize Space Complexity for Dynamic Programming
The main forms of dynamic programming algorithms are recursive solutions with memoization and iterative solutions using state transition. These two approaches are essentially the same and have similar efficiency.
This article will introduce one advantage of the iterative approach in dynamic programming: the ability to optimize the space usage of the dp array (commonly known as the rolling array technique), reducing space complexity.
Simply put, in some cases, if the state transition equation only depends on adjacent states, there is no need to maintain the entire dp array. You only need to keep the necessary states, which can reduce space complexity.
In my opinion, mastering the space optimization technique is not mandatory, for the following reasons:
In most coding tests, space constraints are not very strict. Usually, you can pass all test cases even without this optimization.
Using space optimization can make the code less readable, making it harder to understand and debug.
Therefore, this article is for those who are interested in further study. Feel free to learn and understand it in depth.