Data Structure & Algorithms
  • 🖌️Unlocking the Power of Algorithms with C#
  • Data Structure
    • Data Structure
    • Big O
    • Array
    • Linked Lists
    • Stacks
    • Queues
    • Hash Tables
    • Trees
    • Graphs
    • Heap Sort
    • ParkingLot Algorithm
    • LRU cache
    • Priority Queue
  • Algorithms
    • Algorithm
    • Recursion
    • Sorting
    • Searching
    • Dynamic Programming
  • Problems
    • Array
      • Two Sum
      • Two Sum II - Input Array Is Sorted
      • Contains Duplicate
      • Maximum Subarray
      • House Robber
      • Move Zeroes
      • Rotate Array
      • Plus One
      • Find number of subarrays with even length
      • Find number of subarrays with even sum
      • Find Missing Element
      • Reduce Array Size to The Half
      • Remove Duplicates
      • Merge Sorted Arrays
      • Arrays Intersection
      • 3Sum
      • Trapping Rain Water
      • Maximum sum of a subarray
      • Longest Subarray
      • Subarray Sum Equals K
      • Container With Most Water
      • Missing Number
      • Roman to Integer
      • First Missing Positive
      • Unique Integers That Sum Up To 0
      • Integer to Roman
      • Flatten
    • String
      • Check if two strings are permutation of each other
      • String Compression
      • Palindrome Permutation
      • Determine if a string has all Unique Characters
      • One Away
      • Longest Substring Without Repeating Characters
      • Valid Palindrome
      • Valid Palindrome II
      • Backspace String Compare
      • First Unique Character in a String
      • Is Subsequence
      • URLify a given string
      • String has same characters at same position
      • Number of Ways to Split a String
      • Check whether two Strings are anagram of each other
      • Print last `n` lines of a big file or big string.
      • Multiply Strings
    • Matrix
      • Search a 2D Matrix
      • Search a 2D Matrix II
      • Rotate Matrix
      • Spiral Matrix
      • Set Matrix Zeroes
    • Bit Manipulation
      • Sum of Two Integers
      • Reverse Number
      • Reverse Number II
      • Binary Bits Count
      • Binary Bits Count II
    • Stack
      • Valid Parentheses
      • Balance or not expression
      • Decode String
    • Tree
      • Binary Tree Inorder Traversal
      • Binary Tree Preorder Traversal
      • Binary Tree Postorder Traversal
      • Binary Tree Level Order Traversal
      • Binary Tree Return All Root-To-Leaf Paths
      • Binary Tree Height-Balanced
      • Valid Binary Search Tree
      • Binary Tree Sum of all left leaves.
    • Linked List
      • Linked List Delete Middle Node
      • Merge Sorted Linked List
      • Reverse Linked List
      • Remove Duplicates from Sorted List
      • Remove Duplicates from Unsorted List
      • Linked List Cycle
    • Graph
      • The Number Of Islands
      • Number of Closed Islands
      • Max Area of Island
      • Rotting Oranges
      • Number of Provinces
      • Course Schedule
      • Surrounded Regions
      • Snakes and Ladders
      • Widest Path Without Trees
      • Knight Probability in Chessboard
      • Possible moves of knight
      • Check Knight Tour Configuration
      • Steps by Knight
      • Network Delay Time
    • Greedy
      • Best Time to Buy and Sell Stock
      • Best Time to Buy and Sell Stock II
      • Smallest Subset Array
      • Jump Game
    • Backtracking
      • Towers of Hanoi
      • Subsets
      • Combination Sum
      • Sudoku Solver
      • Word Search
    • Heap
      • Kth Largest Element in an Array
      • Top K Frequent Elements
    • Sorting
      • Order Colors String
    • Recursion
      • Number To Text
      • Divide Number
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  1. Algorithms

Dynamic Programming

Dynamic Programming is nothing just memorized or cached response.

Dynamic Programming (DP) is an algorithm design technique used for optimization. It is mainly used to optimize recursive algorithms that have repeated calls for the same inputs. The idea is to store the results of subproblems, so we do not have to re-compute them when needed later. This simple optimization reduces time complexities from exponential to polynomial. DP is used in various fields, including computer science, mathematics, economics, and aerospace engineering¹. It is particularly useful in solving optimization problems.

Common Applications:

  • Fibonacci Sequence: Calculating the nth Fibonacci number efficiently.

  • Longest Common Subsequence (LCS): Finding the longest common subsequence between two strings or sequences.

  • Knapsack Problem: Optimizing the value of items that can be fit into a knapsack with a given capacity.

  • Bellman-Ford Algorithm: Finding shortest paths in graphs with negative edge weights.

  • Edit Distance: Calculating the minimum number of edits required to transform one string into another.

  • Matrix Chain Multiplication: Optimizing the order of matrix multiplications to minimize the number of scalar multiplications.

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Last updated 1 year ago