invariant

LeetCode SubCategorizer, Part 1: Data

2023-10-28T00:00:00+00:00

1. Idea of the product & problem statement</a></h2>
Most of the time, people who wants to crack the coding interview, starts to do practice on platforms like LeetCode. And most of the MAANG companies asks from broad range of data structure & algorithms problems. If you don’t have a guide OR “curated list of problems”, you are going to be lost in the ocean of problems. Real case:</p>

The Skyline Problem

2023-10-28T00:00:00+00:00

The Skyline (2D Interval merging)</a></h2>
Question is:</strong> A city’s skyline is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. Given the locations and heights of all the buildings, return the skyline formed by these buildings collectively. The geometric information of each building is given in the array buildings where buildings[i] = [lefti, righti, heighti]: lefti is the x coordinate of the left edge of the ith building. righti is the x coordinate of the right edge of the ith building. heighti is the height of the ith building. You may assume all buildings are perfect rectangles grounded on an absolutely flat surface at height 0. The skyline should be represented as a list of “key points” sorted by their x-coordinate in the form [[x1,y1],[x2,y2],…]. Each key point is the left endpoint of some horizontal segment in the skyline except the last point in the list, which always has a y-coordinate 0 and is used to mark the skyline’s termination where the rightmost building ends. Any ground between the leftmost and rightmost buildings should be part of the skyline’s contour.</p>

Largest Rectangle in a Histogram

2022-06-27T00:00:00+00:00

How to start to solve & approach this problem with ZERO knowledge?</a></h2>
Question is: find largest rectangular area? These techniques will enrich your algorithmic arsenal.</p>

Permutation Sequence

2022-06-23T00:00:00+00:00

question </div> Problem</strong></span> </div>
The set [1, 2, 3, …, n] contains a total of n! unique permutations. Given n and k, return the kth permutation sequence.</p> </div> </div>

Jump Game

2022-06-18T00:00:00+00:00

question </div> Problem</strong></span> </div>
Given an array of non-negative integers nums, you are initially positioned at the first index of the array. Each element in the array represents your maximum jump length at that position. Your goal is to reach the last index in the minimum number of jumps. You can assume that you can always reach the last index.</p> </div> </div>

Manacher's Algorithm

2022-06-13T00:00:00+00:00

There are multiple different ways of implementation for this problem, like DP(lcs, etc), expanding from center. But the most optimal approach is Manacher’s Algorithm, time complexity: O(n). It’s core idea is calculating current palindrome information based on previous calculated palindrome information. Let’s draw it and see some formulas and implications.</p>

ZigZag Conversion

2022-06-09T00:00:00+00:00

question </div> Problem</strong></span> </div>
Print the string “SALAM” in a zigzag pattern on a given number of rows.</p> </div> </div>

Median of Two Sorted Arrays

2022-06-05T00:00:00+00:00

question </div> Problem</strong></span> </div>
Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)).</p> </div> </div>

Floyd–Warshall

2022-05-28T00:00:00+00:00

When I saw this algorithm for a first time, It reminded me the Matrix Chain Multiplication</strong>, so therefore didn’t think about that much “how does it work?”, “why does it work?”. Because, MCM problem seems much more interval DP(anyway, it’s acyclic DAG) because of it’s vibe of linearity. Let’s think the problem gradually from simpler to harder, 1. graph is completely linear OR topologically sorted, 2. graph nodes have all the connections pairwise. For simplicity, let’s look at linear graph model.</p>

Optimal Game Strategy

2022-02-17T00:00:00+00:00

Some of the well-known CS problems, such as the choosing of an optimal game strategy, may appear to be mentally exhausting at first glance. However, like with other problems, it necessitates a certain point of view from which we must examine it. First and foremost, let us define the problem:</p>

This is a game for two players. There are an even amount of coins placed in a row, hence the row is even. There will be alternating turns. Each round, a player has the option of selecting either the first coin in the row or the last coin in the row and keeping it in his possession. If a player moves first, the goal of the issue is to figure out how much money he or she can earn with certainty up to the greatest amount conceivable.</p> </blockquote>

Newton–Raphson

2021-12-21T00:00:00+00:00

Using the square-root finding technique as an example, this chapter will examine the Newton-Raphson approach in further detail. The in-depth examination and distinctions between Gradient Descent</strong> and Newton-Raphson</strong> will be the subject of a future season. The Newton-Raphson technique is another numerical method for determining the square root. The root of a nonlinear equation must be bracketed by two estimations using methods like the bisection technique and the false position method. Bracketing approaches are used to accomplish this. Because they reduce the interval between the two estimations in order to zero in on the equation’s root, these approaches are always convergent.</p>

tip </div> Key idea</strong></span> </div>
The root is not bracketed in the Newton-Raphson approach. When it comes to solving an equation, just one initial guess of the root is required to get the iterative process started. As a result, it might be considered an open approach. Open approaches may or may not converge, but if they do, it will be substantially faster than with bracketing.</p> </div> </div>
</th> Bracketing (bisection, false position)</th> Newton-Raphson (open)</th></tr></thead>

Initial guesses</td> two estimations</td> one initial guess</td></tr>
Convergence</td> always convergent</td> may or may not converge</td></tr>
Speed</td> slower</td> substantially faster</td></tr> </tbody></table>

Approximation & Error Analysis

2021-12-20T00:00:00+00:00

While solving a mathematical model using numerical approaches, we can use errors to minimize errors. When doing a numerical analysis, mistakes will inevitably occur. To address the problem of errors, we must first</p>

The Bisection Method

2021-12-08T00:00:00+00:00

Consider the following scenario: we have a nonlinear equation and are attempting to solve it using a computer program. For the nonlinear equation, what strategy can the CPU employ in order to compute a solution? Alternatively, from what point of view would we address that challenge in terms of efficacy?</p>

Why Numerical Methods

2021-12-01T00:00:00+00:00

Have you ever wondered how computer software determines the square root of a given value?</p>

Binary Search: A Survival Guide, Part 2

2021-11-23T00:00:00+00:00

As I have stated in [se1:ch2], [se1:ch5]</strong>, there are different search space reduction scenarios. </p>

Binary Search: A Survival Guide, Part 1

2021-11-22T00:00:00+00:00

From the standpoint of difficulty, binary search is one of the most “deceptive” algorithms available:) At first appearance, it appears to be a simple method to build and an approachable algorithm. However, when you look at the specifics, you will notice that the techniques are counter-intuitive, and this will prove to be intimidating in the long run. But there’s no reason to be concerned when you know where it comes from. Over the course of chapters [1 to 4], we examined the mathematical foundations of the Binary search, including approximation methods, numerical analysis, search space reduction, and so on. There are several terms in computer science for binary search, which is also known as half-interval, logarithmic, or binary chop. Its purpose is to locate the location of an object in an ordered array. An array is compared to its center member when using a binary search. After determining that the target value can’t be found in one half, the remaining half is searched again, selecting a middle element from each half and comparing it to the target value until the target value is discovered. An empty half of the array indicates that your target was not found in the search results. O(logn) comparisons are made in the worst-case scenario when binary search runs in logarithmic time (for sorted array). The number of entries in an array determines how many comparisons are made. Except for tiny arrays, binary search is quicker than linear search. However, in order to use binary search, the array must first be sorted. Specialized data structures like hash tables, which can be searched more quickly than the binary search algorithm, are available. In addition to locating the next-smallest or next-largest element in the array in relation to the target, binary search may also be used to tackle a broader spectrum.</p>

invariant

LeetCode SubCategorizer, Part 1: Data

The Skyline Problem

Largest Rectangle in a Histogram

How to start to solve & approach this problem with ZERO knowledge?</a></h2> Question is: find largest rectangular area? These techniques will enrich your algorithmic arsenal.</p>

Permutation Sequence

Jump Game

Manacher's Algorithm

ZigZag Conversion

Median of Two Sorted Arrays

Floyd–Warshall

Optimal Game Strategy

Newton–Raphson

Approximation & Error Analysis

The Bisection Method

Why Numerical Methods

Binary Search: A Survival Guide, Part 2

Binary Search: A Survival Guide, Part 1

How to start to solve & approach this problem with ZERO knowledge?</a></h2>
Question is: find largest rectangular area? These techniques will enrich your algorithmic arsenal.</p>