Introduction
If you are looking for a job in the field of algorithms, you must have heard about dynamic programming coding questions. It is one of the most popular interview questions in today's corporate world. Dynamic programming is a subfield of optimization which involves finding an optimal solution to a problem by means of an iterative procedure.
Why Use Dynamic Programming?
In Dynamic Programming, we take advantage of the fact that each intermediate result can be used as input for another iteration. This is known as backtracking: instead of starting from scratch and solving the entire problem from scratch, we can use any previous results as new starting points for further computations
This process continues until we reach an acceptable solution or run out of memory space to store all intermediate solutions (or both).
It is a technique used to solve a problem by breaking it down into smaller subproblems, solving them recursively, and storing their solutions. It can be used in many areas of computer science, such as Bioinformatics, Computer Graphics, and Artificial Intelligence. The general idea behind dynamic programming is to decompose the original problem into smaller ones that can be solved separately by using dynamic programming techniques (DynProg).
The best way to prepare for dynamic programming questions is to do practice problems and see how your answers come out.
Now let us look at some common dynamic programming questions and their answers:
Generate all binary strings of length n with k bits set.
You are given an array of integers and a k-bit string. The goal is to find all binary strings of length n with k bits set such that the sum of their corresponding numbers is at most k.
For example, if you have an array {1, 2}, then the first element in your output should be 1; the second should be 2; and so on. If you want to generate all binary strings with length 5 (that is five bits), then you will need one array for each bit position in this string: {0 through 4} = 0101010...; {5} = 1100110...; etc., until finally having only one element left over after finding all possible combinations for each bit position!
Find a subset that has a maximum sum but less than k.
Write a function to find a subset of an array A whose sum is closest to a given k, but which has the maximum sum.
The solution is to use Dynamic Programming. We can use a recurrence relation with m = n + 1, p = max(a[i]), q = min(a[i]). The time complexity of this solution would be O (n2), and the space complexity would be O (n).
Count ways to reach the n’th stair using steps 1, 2 or 3
In this question, you are given an array of non-negative numbers. You must find the maximum sum of a contiguous subarray (containing at least one number) that has the largest sum and is contiguous within the array.
The recursive formula for calculating the number of ways to reach the n’th stair from a given step is:
Where p(i+1) for i = 1..n is equal to p(i), where i denotes that we have reached this particular step in our sequence. We use an empty stack as our queue since it will contain all possible steps until we get back on track with regards to figuring out how many ways there are overall!
Find three elements from different three arrays such that that a + b + c is closest to a given number.
In this question, you are given three arrays and asked to find the sum of each subarray.
The first array is [1, 2, 3]
The second array is [2, 1].
The third array is [3].
Find the sum of each subarray: 1 + 2 = 3 * Find the maximum sum of all three subarrays: 4 + 2 - 3 = 9 (The maximum possible value for any integer)
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