Depth-First-Search(DFS) vs Dynamic Programming(DP)

DFS is a searching algorithm that would go as far as possible before backtracking, and Dynamic Programming, referring to GeeksforGeeks, is an algorithmic paradigm that solves a given complex problem by breaking it into subproblems and stores the results of subproblems to avoid computing the same results again. What are connections do they share? Let me uncover this by a Leetcode problem: 494. Target Sum.

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[Leetcode Problems]240. Search a 2D Matrix II

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Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties: Integers in each row are sorted in ascending from left to right. Integers in each column are sorted in ascending from top to bottom.

Example:
Consider the following matrix:
[ [1, 4, 7, 11, 15], 
  [2, 5, 8, 12, 19], 
  [3, 6, 9, 16, 22], 
  [10, 13, 14, 17, 24], 
  [18, 21, 23, 26, 30] ]
Given target = 5, return true.
Given target = 20, return false.
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Visualized! Intro to 7 Sorting Algorithms and their complexity analysis

After we introduced Graph Algorithm: Topological Sort, let’s now take a time to learn some more general and commonly used sorting algorithms! Actually, if you take a look at Introduction to Algorithms, you will find that sorting is the first algorithm you will learn! Time complexities of them will be appended at the end.

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[Leetcode for Interviews]DFS, BFS, and Backtracking II – How to backtrack? Detailed Explanations with Examples

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Backtracking is a general algorithm … that incrementally builds candidates to the solutions, and abandons a candidate (“backtracks”) as soon as it determines that the candidate cannot possibly be completed to a valid solution.

https://en.wikipedia.org/wiki/Backtracking

Note: This is the second part for BFS, DFS and Backtracking. The first part is here: [Leetcode for Interview]DFS, BFS, and Backtracking I.

What is backtracking?

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Intro to Graph Algorithms – BFS & DFS

Graphs are a pervasive data structure in computer science, and algorithms for working with them are fundamental to the field.

Cormen, Thomas H., et al. Introduction to algorithms. MIT press, 2009.

Given a graph defined as G=(V,E) which is a set of vertices and edges, we’d be curious about how to represent it and how to search it systematically so as to visit the vertices following the edges. This blog will briefly introduce two ways of representations of a graph, and then will dive deep into two graph search algorithms: Breadth-First-Search (BFS) and Depth-First-Search (DFS).

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