Morgan Stanley
200+ Kissht Finance Interview Questions and Answers
Q1. What was the journal entry for prepaid rent which has paid at beginning of the month for the whole year and entry at the end of month ?? Which is entry affects the networth??
Journal entry for prepaid rent paid at beginning and end of month affecting net worth.
Debit prepaid rent account for the full amount paid at the beginning of the month
Credit cash account for the same amount
At the end of the month, debit rent expense account for the portion of rent used during the month
Credit prepaid rent account for the same amount
The entry at the end of the month affects the net worth as it reduces the prepaid rent asset and increases the rent expense
Example...read more
Mary is a party-loving girl of the 21st Generation. She loves to attend parties and events with her family and friends. But she is terrible at remembering the dates of these events.
Mary has ...read more
Q3. What is the entry for share purchased today which will be credited into demat on T+2?
The entry for share purchased today credited into demat on T+2 is a debit to the cash account and a credit to the demat account.
Debit cash account
Credit demat account
Occurs on T+2
Reflects purchase of shares
You have been given an array/list ‘A’ consisting of ‘N’ integers all of which are ‘0’ initially. You are given an array/list ‘ARR’ consisting of ‘M’...read more
You have been given a Binary Search Tree and a target value. You need to find out whether there exists a pair of node values in the BST, such that their sum is equal to the target value.
A binar...read more
You are given an array ‘ARR’ of size ‘N’ and an integer ‘K’. Your task is to find the total number of distinct elements present in every ‘K’ sized window of the arr...read more
Q7. What impact do share price have on issue of dividend ? And what was the reason behind it?
The share price has an impact on the issue of dividends as it affects the dividend yield and the amount of cash paid out to shareholders.
Share price affects the dividend yield, which is calculated by dividing the annual dividend per share by the share price.
A higher share price reduces the dividend yield, making the stock less attractive to income-seeking investors.
Share price also affects the amount of cash paid out as dividends. A higher share price may result in a lower di...read more
Q8. Given a web portal that is running slow, how would you debug the solution for that? Answer stepwise.
Debugging steps for a slow web portal
Check server load and resource usage
Analyze network traffic and latency
Review code for inefficiencies and optimize
Use profiling tools to identify bottlenecks
Consider caching and content delivery networks
Test and monitor performance after changes
You are given an integer array 'ARR' of size 'N' and an integer 'S'. Your task is to return the list of all pairs of elements such that each sum of elements of each pair equals 'S'.
Note:
Each pair shou...read more
You are given a number N that can be broken into three parts N / 2, N / 3, and N / 4 (considering only integer parts). Each number obtained in this process can be divided further recursively....read more
You have been given an integer array/list(ARR) of size N that contains only integers, 0 and 1. Write a function to sort this array/list. Think of a solution which scans the array/list only once and don'...read more
You are given a tree with 'N' nodes with 'N' - 1 distinct edge. You are also given two nodes 'N1' and 'N2'. You have to find and print the shortest path between 'N1' and 'N2'.
A tree data structure is ...read more
Given a directed acyclic graph having ‘N’ nodes. A matrix ‘edges’ of size M x 2 is given which represents the ‘M’ edges such that there is an edge directed from node...read more
You are given string S of length N, and an integer K. Your task is to find the length of the longest substring that contains at most K distinct characters.
I...read more
You have been given an integer array/list(ARR) of size N which contains numbers from 0 to (N - 2). Each number is present at least once. That is, if N = 5, the array/list constitutes values rangin...read more
You are given an array ‘ARR’ of size ‘N’ containing each number between 1 and ‘N’ - 1 at least once. There is a single integer value that is present in the array twice. Your task is to find th...read more
Q17. Can you explain dcf to me? Can dcf be applied to equity?
DCF is a valuation method used to estimate the value of an investment based on its future cash flows.
DCF involves projecting future cash flows and discounting them back to their present value.
It can be applied to equity by estimating the future cash flows of a company and discounting them back to their present value to determine the company's intrinsic value.
DCF is commonly used in investment banking and finance to value companies and assets.
It is important to use realistic a...read more
You are the owner of a Shipment company. You use conveyor belts to ship packages from one port to another. The packages must be shipped within 'D' days.
The weights of the...read more
You have been given two arrays, 'AT' and 'DT', representing the arrival and departure times of all trains that reach a railway station.
Your task is to find the minimum number of plat...read more
You have been given a long type array/list 'ARR' of size 'N'. It represents an elevation map wherein 'ARR[i]' denotes the elevation of the 'ith' bar. Print the total amount of rainwater that c...read more
You have been given a binary tree of integers. Your task is to print the boundary nodes of this binary tree in Anti-Clockwise direction starting from the root node.
NOTE:
The boundary nodes of...read more
Prateek is a kindergarten teacher. He wants to give some candies to the children in his class. All the children stand in a line and each of them has a grade according to his or her performance in the cla...read more
You are given a linked list containing N nodes, where every node in the linked list contains two pointers, first one is ‘NEXT’ which points to the next node in the list and the second one i...read more
Q24. What is the technical term we use for the bond interest
The technical term for bond interest is coupon rate.
Coupon rate is the fixed annual interest rate paid on a bond.
It is expressed as a percentage of the bond's face value.
For example, a bond with a face value of $1000 and a coupon rate of 5% will pay $50 in interest annually.
Coupon payments are usually made semi-annually or quarterly.
You are given a string ‘str’ of ‘N’ lowercase alphabets. Your task is to check whether it is possible to split the given string into three non-empty substrings such that one of them is a substri...read more
You have been given an array/list 'ARR' of integers. Your task is to find the second largest element present in the 'ARR'.
Note:
a) Duplicate elements may be present. b) If no...read more
You are given an infinite supply of coins of each of denominations D = {D0, D1, D2, D3, ...... Dn-1}. You need to figure out the total number of ways W, in which you can make a change fo...read more
You are given a string S which represents a number. You have to find the smallest number strictly greater than the given number which contains the same set of digits as of the original number...read more
Bubble Sort is one of the sorting algorithms that works by repeatedly swapping the adjacent elements of the array if they are not in sorted order.
You are given an unsorted array consisting of N non-...read more
You're given a sorted array that has now been rotated 'K' times, which is unknown to you. Rotation here means that every element is shifted from its position to right in each rotation and the last ...read more
Q31. In how many ways can i permute n numbers 1 2 3...n so that all the no.s between u and i+1 are less than i (for all i in the permutation)?
Counting permutations where numbers between u and i+1 are less than i for all i in the permutation.
The first number in the permutation must be 1.
For each i in the permutation, all numbers between u and i+1 must be less than i.
Use dynamic programming to count the number of valid permutations.
The answer is (n-1)th Catalan number.
Example: for n=4, the answer is 5.
Q32. How would you find whether a number is even or odd without using any conditions?
Using bitwise operator to check the last bit of the number.
Use bitwise AND operator with 1 to check the last bit of the number.
If the result is 0, the number is even. If the result is 1, the number is odd.
Example: 6 & 1 = 0 (even), 7 & 1 = 1 (odd)
Q33. Given an array with length n , find highest value which occurs same number of times within the array. [3,8,3,2,1,3,2] 3 occurs 3 times output=3. [4,6,7,6,7,5,4,2,4,9,4,1,9] 4 occurs 3 times output=4
Find the highest value that occurs the same number of times within an array.
Iterate through the array and count the occurrences of each value.
Store the counts in a dictionary or hash map.
Find the maximum count and check which value(s) have that count.
Return the highest value among those with the maximum count.
Q34. In a unit circle, p is chosen uniformly on the circle and q inside the circle, what is the prob. that the rectangle is inside the circle?
Probability of a rectangle being inside a unit circle with p chosen uniformly on the circle and q inside the circle.
The probability can be found by calculating the ratio of the area of the rectangle to the area of the circle.
The area of the circle is pi and the area of the rectangle can be found using the distance between p and q.
The probability is 1/4.
Example: If the distance between p and q is 0.5, then the area of the rectangle is 0.25 and the probability is 0.25/pi.
Given a binary tree with N number of nodes, check if that input tree is BST (Binary Search Tree) or not. If yes, return true, return false otherwise.
A binary search tree (BST) is a binary tree data...read more
You are given a directed acyclic graph. Your task is to find any topological sorting of the graph.
A directed acyclic graph is a directed graph with no directed cycles.
Topological sorting for D...read more
You have been given a singly linked list in which nodes are present in increasing order. Your task is to construct a Balanced Binary Search Tree with the same data elements as ...read more
You have given a Singly Linked List of integers, determine if it forms a cycle or not.
A cycle occurs when a node's next points back to a previous node in the list. The li...read more
You are given a set of ‘n’ types of rectangular 3-D boxes. The height, width, and length of each type of box are given by arrays, ‘height’, ‘width’, and ‘length’ respectively, each consisting of ‘n’...read more
You are given an arbitrary binary tree consisting of N nodes where each node is associated with a certain integer value from 1 to 9. Consider each root to leaf path as a number.
For example:
1 ...read more
You have been given a Binary Tree of distinct integers and two nodes ‘X’ and ‘Y’. You are supposed to return the LCA (Lowest Common Ancestor) of ‘X’ and ‘Y’.
The LCA of ‘X’ and ‘Y’ in the bina...read more
A noticeable aspect in this puzzles is the fact that there’s a circular misplacement, which implies if apple is wrongly labelled as Apple, Apple can’t be labelled as Orange, i.e., it has to be labeled as ...read more
Q43. Why RBI increase Repo rate to control inflation ?
RBI increases Repo rate to control inflation by reducing money supply and increasing cost of borrowing.
Repo rate is the rate at which RBI lends money to commercial banks.
When RBI increases Repo rate, it becomes expensive for banks to borrow money from RBI.
Banks then increase their lending rates to customers, which reduces borrowing and spending.
This reduces money supply in the economy, which helps in controlling inflation.
For example, if inflation is high, RBI may increase Re...read more
Q44. What was difference between options and future?
Options give the right but not the obligation to buy or sell an asset at a predetermined price, while futures require the buyer or seller to fulfill the contract at a specific date and price.
Options provide flexibility to the buyer as they can choose whether or not to exercise the option, while futures require the buyer or seller to fulfill the contract.
Options have a premium that the buyer pays to the seller for the right to buy or sell the asset, while futures do not have a...read more
Ninja is given a binary string ‘S’ of size ‘N’ by his friend, the task is to check if the binary string ‘S’ can be sorted in decreasing order by removing any number of the non-adjacent ch...read more
Ninja is given an integer ‘N’. One day Ninja decides to do the sum of all digits and replace the ‘N’ with the sum of digits until it becomes less than 10. Ninja wants to find what will be the value...read more
Q47. x, y are random variables with probability distribution ke^(-kx) and ue^(-ux). What is the dist. for min(x,y)
Finding the probability distribution for the minimum of two random variables with given distributions.
Use the formula P(min(x,y)>z) = P(x>z)P(y>z)
Integrate over the range of z to get the distribution of min(x,y)
Final distribution is 2ke^(-kx)ue^(-ux)exp(-uz)
The city of Ninjaland is analogous to the unweighted graph. The city has ‘N’ houses numbered from 1 to ‘N’ respectively and are connected by M bidirectional roads. If a road ...read more
Q49. Minimize the cost of the pen, what innovations can you do with it?
Innovations to minimize cost of pen
Use recycled materials for pen body and ink
Simplify design to reduce production costs
Implement refillable ink cartridges to reduce waste and cost
Partner with companies for bulk purchasing of materials
Automate production process to reduce labor costs
You are given an array 'ARR' of integers of length N. Your task is to find the first missing positive integer in linear time and constant space. In other words, find the lowest positive in...read more
Q51. An organism dies out with prob. p and spawns into 2 with prob (1-p). what is the prob. that starting from 1,the organism will die out?
Given prob. p of dying out and prob. (1-p) of spawning into 2, find prob. of dying out starting from 1 organism.
Use probability tree to visualize outcomes
Probability of dying out starting from 1 is p + (1-p) * (probability of dying out starting from 2)^2
Solve recursively to get final answer
You have been given an array/list ‘TREE’ having ‘N’ unique integers. You need to make a maximum binary tree recursively from ‘TREE’ using the following conditions:
1. Create a root of the ma...read more
Q53. Given a class @Data class Account{String name; String acctBalance;}. Write logic to get Map using Stream API which shows the balance of each person i,e, key will be the name of the account holder and value will...
read moreLogic to get Map using Stream API to show balance of each person
Use Stream API to group accounts by name
Use map() to get the sum of balances for each group
Collect the results into a Map
This puzzle usually seems like a tough one to answer, but solving it once makes one realize that the procedure was actually simple. If the candidate pulls out 2 red balls, he replaces them with a b...read more
Q55. What is market cap and how would you explain in Lehman terms?
Market cap is the total value of a company's outstanding shares. It's calculated by multiplying the current stock price by the number of shares outstanding.
Market cap is short for market capitalization.
It's a measure of a company's size and value.
It's calculated by multiplying the current stock price by the number of shares outstanding.
For example, if a company has 1 million shares outstanding and the current stock price is $50, the market cap would be $50 million.
Market cap ...read more
I was asked to design a parking lot in which there were 3 vehicles of small, medium, and large size. There were 3 types of slots for the vehicles small, medium, and large size. The small-sized vehi...read more
Ninja is given a task to implement a priority queue using Heap data structure. The Ninja is busying preparing for the tournament., So he asked for your help.
Your task is to use the cl...read more
Q58. A is a matrix vi's are n linear vectors s.t. Avi= Vj a<=j<=n, what are the possible values of |A|?
Possible values of determinant of matrix A given Avi=Vj for n linear vectors
The possible values of |A| are non-zero as the given vectors are linearly independent
The value of |A| can be calculated using the formula |A| = (-1)^n * det(A)
If the given vectors are orthogonal, then |A| is the product of the magnitudes of the vectors
Q59. Puzzle: There are 5 switches in a room and there are 5 bulbs (not in that room but on different floors). Find the minimum number of trips you will make to find which switch is associated to which bulb
Q60. A and B play a game with unfair count with P[Heads]= p. they count # of heads and tails .if # of heads > #tails +1 at any point, A wins.Find the prob. that A wins
A and B play a game with unfair coin. A wins if # of heads > #tails +1 at any point. Find prob. of A winning.
The game is played with an unfair coin with P[Heads]=p
A wins if # of heads > #tails +1 at any point
Find the probability of A winning
Q61. What is weak reference? garbage collection in case of such references?
Weak reference is a reference that does not prevent the object from being garbage collected.
Weak references are used to refer to objects that can be garbage collected if there are no strong references to them.
They are typically used in scenarios where you want to hold a reference to an object, but don't want to prevent it from being collected.
Weak references are implemented using weak reference queues, which allow you to perform actions when weakly referenced objects are abou...read more
Q62. If the price of a security is showing an upward trend, who would gain - a put option holder or a call option holder?
Call option holder would gain.
A call option gives the holder the right to buy the security at a predetermined price, known as the strike price.
If the price of the security is showing an upward trend, the call option holder can exercise their option and buy the security at the lower strike price, then sell it at the higher market price for a profit.
On the other hand, a put option gives the holder the right to sell the security at a predetermined price.
If the price of the secur...read more
Q63. What is the prob. that element at 20th position lands up at 31st position after the first iteration?
The probability of element at 20th position landing up at 31st position after the first iteration.
The probability depends on the size of the dataset and the algorithm used for iteration.
If the algorithm involves swapping adjacent elements, the probability is higher.
If the dataset is sorted in a way that the element at 20th position is adjacent to the element at 31st position, the probability is 1.
The probability can be calculated using combinatorics and probability theory.
Q64. Find number of occurrences of a character in string. Provide multiple approaches for the solution and choose the best why? For "string aabcadd output=a3b1c1d2
Count occurrences of a character in a string and output in a specific format.
Use a hash table to store the count of each character.
Loop through the string and update the count in the hash table.
Create the output string using the hash table.
Build a system where people subscribe to a particular topic . And if any message is posted regarding the particular topic then the people who have subscribed to that system must get the me...read more
Q66. Find f(n) : pdt F(x) cdf. the value of k> 0 a constant -inf S +inf f(x)*F(kx) dx x follows normal standard distribution?
Finding f(n) for a normal standard distribution with a given constant k.
Calculate the product of probability density function and cumulative distribution function.
Integrate the product of f(x) and F(kx) from -inf to +inf.
The value of k is a constant greater than 0.
Q67. Internal implementation of HashSet? Which scenario will generate same hashcode for a HashMap?
HashSet is implemented using a HashMap internally. Same hashcode is generated when two objects have the same value for hashCode() and equals() methods.
HashSet internally uses a HashMap to store its elements.
The hashcode of an object is generated using the hashCode() method.
If two objects have the same value for hashCode() and equals() methods, they will generate the same hashcode.
For example, if two String objects have the same content, they will generate the same hashcode.
Why do we need to override equals and hashcode methods in Java?
Q69. What is enterprise value and how is it calculated?
Enterprise value is the total value of a company, including debt and equity.
Enterprise value is calculated by adding market capitalization, debt, and minority interest, and then subtracting cash and cash equivalents.
It represents the total value of a company that an acquirer would have to pay to take over the company.
Enterprise value is a more accurate representation of a company's value than market capitalization alone.
For example, if a company has a market capitalization of...read more
Q70. Implementation of singleton pattern and ways of breaking it? singleton pattern implementation in a multithreaded environment?
Singleton pattern ensures a class has only one instance, while allowing global access to it.
Implement a private constructor to prevent direct instantiation.
Create a static method to provide a single point of access to the instance.
Use lazy initialization to create the instance only when needed.
Ensure thread safety in a multithreaded environment using synchronization or double-checked locking.
Breaking the singleton pattern can be done by using reflection, serialization, or clo...read more
Q71. Given a binary tree and a number n, find the root to leaf branch whose sum equals to n. Now find maximum length branch whose sum equals to n (that means of course now there are more than 1 branch whose sum equa...
read moreQ72. Find a local minima of an array in o(log n)? In a functional program
Find local minima of an array in o(log n) in functional programming.
Use binary search to find the local minima.
Check if the mid element is a local minima, if not, move towards the lower side.
If the mid element is greater than its left element, move towards the left side, else move towards the right side.
Repeat until a local minima is found.
Example: [5, 3, 2, 4, 6, 8, 9] -> local minima is 2.
Q73. Given a sorted array find two element (i,j) s.t. i+j =x in O(n) time?
Find two elements in a sorted array that add up to a given sum in linear time.
Use two pointers, one at the beginning and one at the end of the array.
If the sum of the two pointers is greater than the target, move the right pointer to the left.
If the sum of the two pointers is less than the target, move the left pointer to the right.
Repeat until the sum is found or the pointers meet.
Example: Given [1, 2, 3, 4, 5] and target 7, return (2, 5).
Q74. When would a put option holder exercise the option?
A put option holder would exercise the option when the underlying asset's price is below the strike price.
Put option holders exercise when the market price of the underlying asset is lower than the strike price.
They exercise to sell the asset at a higher price than the market price.
Put options are often exercised before the expiration date if the market conditions are favorable.
Exercising a put option allows the holder to profit from a decline in the price of the underlying a...read more
Q75. What is the difference between package and package-lock.json?
package.json lists dependencies and package-lock.json ensures consistent installs.
package.json lists all the dependencies required for the project
package-lock.json ensures that the same versions of dependencies are installed across all environments
package.json is manually edited while package-lock.json is generated automatically
package-lock.json is used for reproducible builds
Basic Questions on Scheduling Algorithms
Difference between Processes and Thread
Disk Scheduling Algorithms-I was asked to explain the difference between the algorithms
LRU Page replacement and the dif...read more
I was asked to explain the basic oops concepts. I did that using real-life examples.
Difference between abstraction and interface.
Virtual Functions
Method Overloading and overriding
Here, they gave us some wooden blocks and crayons and asked us to make a logo for Morgan Stanley and prepare a slogan individually which shows the technological development of MS with collaboratio...read more
Q79. Types of valuation and reason for using each one of them
Valuation methods include market, income, and asset-based approaches, each used for different purposes.
Market approach: based on comparable sales of similar assets in the market
Income approach: based on the present value of expected future income generated by the asset
Asset-based approach: based on the value of the asset's tangible and intangible assets
Market approach is commonly used for real estate, income approach for businesses, and asset-based approach for liquidation or...read more
Q80. What is SQL Cursor? Index? Aggregate Functions examples?
SQL Cursor is a database object used to manipulate data row by row.
Cursor is used to fetch and process data row by row
Index is a database object used to speed up data retrieval
Aggregate functions are used to perform calculations on a set of values
Examples of aggregate functions are SUM, AVG, COUNT, MAX, MIN
Q81. What between Tower and Morgan Stanley?
Tower and Morgan Stanley are both financial services companies.
Tower is a global investment management firm with over $1 trillion in assets under management.
Morgan Stanley is a multinational investment bank and financial services company.
Both companies offer a range of financial services including wealth management, investment banking, and asset management.
Tower is known for its focus on sustainable investing, while Morgan Stanley has a strong presence in mergers and acquisit...read more
Q82. Implement a dynamic 2D excel sheet using DS (underwent various levels of improvisations)
Implement a dynamic 2D excel sheet using DS
Use a 2D array to store the data
Implement functions to add, delete, and modify data
Use data structures like linked lists or hash tables for efficient searching and sorting
Implement dynamic resizing to handle large amounts of data
Use GUI libraries like Tkinter or PyQt for user interface
Q83. Tell me about Yourself. What excel functions are you aware of?
I am a detail-oriented analyst with knowledge of various Excel functions.
I am proficient in basic functions such as SUM, AVERAGE, MAX, MIN, COUNT, etc.
I am also familiar with more advanced functions such as VLOOKUP, HLOOKUP, INDEX, MATCH, IF, AND, OR, etc.
I have experience using PivotTables, PivotCharts, and creating macros to automate tasks.
I am constantly learning and exploring new functions to improve my skills.
Q84. A build up that resulted in the concept of using joins in DBMS
Joining tables in DBMS evolved as a solution to handle complex data relationships.
Joins allow combining data from multiple tables based on a common column.
The concept of joins originated from the need to handle complex data relationships.
Joins can be inner, outer, left, right, or cross depending on the type of data required.
Joins can improve query performance by reducing the number of queries needed to retrieve data.
Joins can also help in data normalization by reducing data r...read more
Print even and odd numbers in increasing order using two threads in Java
Q86. Build a system where people subscribe to a particular topic . And if any message is posted regarding the particular topic then the people who have subscribed to that system must get the message...
read moreBuild a system where people can subscribe to a topic and receive messages related to that topic.
Create a subscription system where users can choose topics of interest
Implement a messaging system to post messages related to topics
Store user subscriptions and messages in a database
Send notifications to subscribed users when a message is posted for their subscribed topic
Q87. Find an even length palindrome in a string in o(n)?
To find an even length palindrome in a string in O(n), we can use the two-pointer approach.
Initialize two pointers at the center of the string.
Expand the pointers outwards while checking if the characters at both pointers are equal.
If they are not equal, return the previous substring as the even length palindrome.
If the pointers reach the end of the string, return the entire string as the even length palindrome.
Q88. Design the database for an online shopping website like flipkart. Now how will you modify your database if you want to give some discount on those product which are going to expire after 6 months
Q89. A puzzle: two dice are given. each has six face. Change the numbering on one dice only so that the probability of occurrence of sum (of the numbers appearing in a throw of two dice) from 1 to 12, are all equal....
read moreQ90. Is virtual constructors available ? what about Virtual destructors ? Why it is used ???
Q91. Write a code to sort a list without pipes?
Code to sort a list without pipes
Use a sorting algorithm like bubble sort, insertion sort, or selection sort
Implement the algorithm in the programming language of your choice
Test the code with different input sizes and types
Q92. What is the difference between hash map and hash set . Explain time complexity in each ??
A hash map is a data structure that stores key-value pairs, while a hash set is a data structure that stores unique elements.
Hash map allows for efficient retrieval of values based on keys.
Hash set only stores unique elements and does not allow duplicates.
Time complexity for hash map and hash set operations is generally O(1) on average, but can be O(n) in worst case scenarios.
Examples of hash map operations include inserting a key-value pair, retrieving a value based on a key...read more
Internal working of hash map in Java
How is memory allocation done in recursion?
Q95. What data structure will you use to find the unique words and the number of times the word appear in a novel
Internal working of CopyOnWrite ArrayList ?
Q97. What are Hedge Funds? Components of Financial Statements
Hedge funds are alternative investment vehicles that use pooled funds to employ various strategies to generate high returns.
Hedge funds are privately owned and managed investment funds
They use a variety of investment strategies such as long-short equity, global macro, and event-driven
They are typically only available to accredited investors due to their high-risk nature
Components of financial statements include balance sheet, income statement, and cash flow statement
Q98. How can we make sure that package versions are taken from package-lock.json and not package.json
To ensure package versions are taken from package-lock.json, use npm ci instead of npm install.
npm ci installs packages based on package-lock.json
npm install may update package versions in package.json
Always commit package-lock.json to version control
Q99. Prove that for N>= a, N> N^.5 + N^(1/3)+N^(1/4)
Prove N>=N^.5+N^(1/3)+N^(1/4) for N>=a
Use AM-GM inequality
Substitute N with a and prove the inequality holds
Use calculus to find the minimum value of the expression
Why is the time complexity of Binary Search O(Logn)?
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