Passing the Google interview is a dream for many. This interview is a test of your technical valor and requires hard work and preparation, not luck or shortcuts. Fortunately, Google is very transparent about its expectations for applicants. Data science experts suggest the more you know about Google’s process and company culture, the more likely you are to be successful. Most of the interviews for technical roles in Google and similar companies are focused on measuring the Algorithms knowledge of the candidates. So today, to show you how to crack the interview, we’ll take a deep dive into some dynamic programming algorithms that you must know.
Table of contents
- Overview of dynamic programming
- Frequently Asked Algorithms
- Commonly Asked Questions
- EndNote
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Overview of dynamic programming
Dynamic programming is an algorithmic paradigm that, by breaking it into subproblems, solves a given complex problem and stores the outcomes of subproblems to prevent the same results from being computed again. It is mainly an optimization over direct recursion. Wherever we see a recursive solution with repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to store the results of subproblems so that we do not have to re-compute them when needed later. This simple optimization reduces time complexities from exponential to polynomial. For example, suppose we write a simple recursive solution for Fibonacci Numbers. In that case, we get exponential time complexity, and if we optimize it by storing solutions of subproblems, time complexity reduces to linear.
Frequently Asked Algorithms
Dynamic programming is used for solving problems with the following properties:
- An instance is solved using the solutions for smaller instances.
- The solution for a smaller instance might be needed multiple times.
- The solutions to smaller instances are stored in a table to solve each smaller instance only once.
- Additional space is used to save time.
The problem of climbing steps perfectly fit those four properties. Therefore, it can be solved by using dynamic programming.
Fibonacci sequence
Applying dynamic programming in the calculation of the nth member of the Fibonacci sequence improves its performance significantly.
Dijkstra’s algorithm for the shortest path problem
From a dynamic programming perspective, the Dijkstra’s algorithm for the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation by the Reaching method for the shortest path problem. In the shortest path problem, Dijkstra’s explanation of the logic behind the algorithm paraphrases Bellman’s famous Optimality Principle.
A type of balanced 0–1 matrix
A memoized recursive function that resolves the dynamic programming algorithm uses a more flexible subproblem:
The function requires a number of k rows to be filled and the number of 1s to be placed in those k rows for each column. The number of possible assignments of 1s in the block of k rows must be returned in such a manner that every row contains n/2 1s, and each column contains the correct number of 1s in the argument.
Checkerboard
In a checkerboard pattern, the 1s and 0s are written into alternate memory locations of the cell array. The algorithm divides the cells into two alternate groups so that each adjacent cell is in a different group. The checkerboard pattern is mainly used for activating failures resulting from leakage, cell-to-cell shorts, and SAF.
Sequence alignment
Sequence alignment is a crucial application in genetics, where dynamic programming is essential. The problem typically involves turning one sequence into another using editing operations that replace, insert, or remove an element. There is an associated cost for each operation, and the aim is to find the sequence of edits with the lowest total cost.
Tower of Hanoi puzzle
A mathematical game or puzzle is the Tower of Hanoi or the Towers of Hanoi. It consists of three rods that can slide onto any rod and several discs of different sizes. The puzzle begins with the discs on one rod in a neat stack in ascending order of size, the tiniest at the top, making a conical shape.
Egg dropping puzzle
Egg dropping is a class of problems in which it is essential to find the correct response without exceeding a (low) number of individual failure states.
Matrix chain multiplication
Multiplication of the matrix chain is a problem of optimization that can be solved with dynamic programming. The objective is to find the most effective way to multiply these matrices, given a sequence of matrices.
Commonly Asked Questions
Here is a list of commonly asked problems in interviews to help you ace any interview you go for!
Smallest Change
Write a function to calculate the minimum number of coins needed to make that amount of change, given the input amount of change x.
Longest Common Substring
Given two strings, formulate a function that returns the longest common substring.
Fibonacci Number
Given an integer n, write a function to calculate the nth Fibonacci number.
Square Submatrix
Given a 2D array of 1s and 0s, obtain the largest square subarray of all 1s.
Matrix Product
Given a matrix, moving only down and right, find the path from top left to bottom right with the greatest product.
0-1 Knapsack
Given a list of items with weights and values and max weight, find the maximum value you can create from items where the weights’ sum is less than the max.
EndNote
A lot of programmers dread dynamic programming questions in their coding interviews. It’s easy to understand why. They’re hard! For one, dynamic programming algorithms aren’t an easy concept to wrap your head around. Any data science developer will tell you that Dynamic Programming mastery involves lots of practice. Above, we discussed some dynamic programming algorithms you be asked about in a coding interview.