DP Optimization

Everything about DP Optimization

1. Article · Java

   Maximize Sum of Adjacent Differences with 1 Replacement

   Given an integer array, you can replace any number of elements with 1. The goal is to maximize the sum of absolute differences between consecutive elements. This article explains how to solve the problem efficiently using a two-state Dynamic Programming approach in O(n) time and O(1) auxiliary space. It includes the intuition, DP states, transitions, Java implementation, and a step-by-step dry run.

   Sandhiya PriyaSep 33,0401,000
2. Article · Data Structures and Algorithms (DSA)

   Count Subsequences Divisible by N Using Dynamic Programming in Java

   Count Subsequences Divisible by N is a Dynamic Programming problem where we need to count the number of non-empty subsequences of a numeric string whose numeric value is divisible by a given integer n. The solution uses remainder-based DP to efficiently track subsequences for each possible remainder instead of generating all subsequences. The approach runs in O(|s| × n) time and O(n) space and handles large inputs efficiently.

   Sandhiya PriyaSep 24,2491,000
3. Article · Data Structures and Algorithms (DSA)

   Count Prefix-Balanced Binary Strings - Java Explanation

   Count the number of prefix-balanced binary strings of length 2 * n containing exactly n ones and n zeros, where every prefix has at least as many ones as zeros. This article explains the Dynamic Programming approach in Java, including the DP transition, base case, dry run, Catalan number connection, and time and space complexity.

   Sandhiya PriyaAug 242,1981,000