Learn how to solve the minimum unused elements problem using dynamic programming by splitting an array into strictly increasing and decreasing subsequences.
Learn how to find the K-th element of two sorted arrays in Java using binary search with O(log(min(n, m))) time and efficient partition-based searching.
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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.
Learn how to solve the cafe computer allocation problem in Java using a three-state tracking approach to correctly count customers rejected when no computer is available.
Learn how to count palindromic strings of length up to n using the first k lowercase English letters, where no character appears more than twice. This article explains the key palindrome observations, separates even and odd-length cases, derives the permutation formulas, and provides an efficient Java solution using modular arithmetic. The solution achieves O(k) time complexity and O(1) auxiliary space.
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.
Learn how to solve the Minimum Cost Selection problem using Dynamic Programming in Java. Understand the recurrence, dry run, optimal substructure, and O(n) time with O(1) auxiliary space.
Learn how to find the maximum all-1s rectangle in a binary matrix when columns can be swapped, using histogram heights, column rearrangement, counting sort, and an O(n × (n + m)) Java solution.
Learn how to detect negative weight cycles in a directed graph using the Bellman-Ford algorithm in Java, including relaxation, disconnected graphs, complexity, and examples.
Learn how to solve the minimum moves array sorting problem in Java using a position array and the longest consecutive increasing sequence with O(n) time complexity.
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.
Learn how to solve the Transform String problem in Java using a greedy approach. This article explains how to check character frequencies, compare both strings from right to left, and calculate the minimum number of operations required to transform one string into another. The solution runs in O(n) time and O(1) auxiliary space.
Find the maximum difference between an ancestor node and its descendant node in a binary tree using DFS and recursion. This article explains the approach, Java solution, dry run, time complexity, and space complexity.
Learn how to solve the "Triplets with Sum in Range" problem in Java with an optimal $O(n^2)$ time complexity and $O(1)$ auxiliary space using sorting and the two-pointer technique.
Learn how to solve the Secret Cipher problem efficiently using the KMP (Knuth-Morris-Pratt) prefix function / LPS array in Java. This article explains how repeated prefixes can be identified and compressed using *, how the algorithm constructs the lexicographically smallest encrypted string, and how to achieve O(n) time complexity for strings up to 105 characters.
The Snake and Ladder Problem is a classic shortest-path problem that can be efficiently solved using Breadth-First Search (BFS). The board is represented as a graph where each cell is a node, and each dice throw creates edges to the next 1–6 possible cells. Snakes and ladders act as immediate jumps between cells. The goal is to find the minimum number of dice throws required to reach the final cell. This article explains the BFS approach, Java implementation, step-by-step logic, and complexity analysis.
Subset Sum on Generated Sequence is a Greedy Algorithm problem where a sequence is dynamically generated from an initial value s and the given array arr[]. Each new value is calculated using the sum of all previously generated values plus the current array element. The generated sequence has a special property where each new value is greater than the sum of all previous values. This property allows us to determine whether a target x can be formed efficiently by processing the sequence from largest to smallest and greedily selecting suitable values. The solution runs in O(n) time and uses O(n) auxiliary space.
Learn how to find the Longest Path in a Directed Acyclic Graph (DAG) using Java. This solution uses Topological Sorting and Dynamic Programming to calculate the maximum distance from a given source vertex to every other vertex. The article explains adjacency lists, DFS-based topological sorting, distance initialization, edge relaxation using Math.max(), handling unreachable vertices with Integer.MIN_VALUE, and the overall time and space complexity
Solve maze pathfinding with dynamic programming in Java. Calculate total paths (mod 10^9+7) and max adventure sum.
Efficiently find the largest odd-sized square with at most k ones in a binary matrix using 2D prefix sums and binary search.
Master dynamic programming to maximize tasks! Learn the optimal strategy for high vs. low effort tasks with O(n) time and O(1) space.
Solve the Friends Pairing Problem with dynamic programming in Java. Learn the recurrence relation and O(1) space optimization.
Find the minimum operations (increment by 1 or double all) to convert an all-zero array to a target array. Reverse thinking reveals the solution.
Learn how to count contiguous subarrays with sums in a given range using a sliding window for positive integer arrays in O(n) time.
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