Optimize Space Complexity for Dynamic Programming
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Introduction
Space compression is not difficult and is mainly used to optimize the space complexity of some dynamic programming problems. However, in general written exams, the space requirements are not very high, and you can pass even without using this optimization technique. Therefore, I personally believe that state compression is not a must-have skill. Interested readers can study and understand it in detail.
We have written more than a dozen articles on dynamic programming in our account. It can be said that dynamic programming techniques significantly improve algorithm efficiency. Generally, they can optimize algorithms with exponential and factorial time complexity to O(N^2), which is like a two-dimensional箔 in the algorithm world, turning all kinds of ghosts and goblins into two-dimensional beings.
However, during the process of solving dynamic programming problems, stage-by-stage optimizations can also be applied. If you carefully observe the state transition equations of some dynamic programming problems, you can further reduce their space complexity from O(N^2) to O(N).