Category: Dynamic Programming

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Collatz Conjecture – Maximum Steps takes to transform (1, N) to 1.

Objective: Given a number N, write an algorithm to find the maximum number of steps it takes to transform (1, N) to 1 using Collatz Conjecture.  The Collatz conjecture is a conjecture in mathematics...

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Minimum No of operations required to convert a given number to 1 – Integer Replacement Problem.

Objective: Given a number N, write an algorithm to convert that number to 1. Below are the allowed operations. If N is even, do N = N/2. If N is odd, either do N...

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Dynamic Programming – Egg Dropping Problem

Objec­tive:  There are n number of eggs and building which has k floors. Write an algorithm to find the minimum number of drops is required to know the floor from which if egg is dropped,...

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Dynamic programming – Printer Problem

Objective:  Given a printer which can perform only 2 operations- Printer can print consecutive identical characters in one go. It can replace consecutive characters by consecutive identical characters at any position. You are given a...

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Dynamic programming – Minimum Jumps to reach to end

Objective:  Given an array of non negative integers, start from the first element and reach the last by jumping. The jump length can be at most the value at the current position in the array....

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Dynamic programming – Remove Boxes Problem

Objec­tive:  Given a number of boxes with different colors represented by different positive numbers. You need to remove all the boxes in several rounds, each time you can choose continuous boxes with the same color (means...

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Stock Single Sell Problem – O(n) Solution

Objec­tive:  Given an array represents cost of a stock on each day. You are allowed to buy and sell the stock only once. Write an algorithm to maximize the profit in single buy and sell....

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Maximum difference between two elements where larger element appears after the smaller element

Objective: Given an array A[], write an algorithm to find Maximum difference between two elements where larger element appears after the smaller element or in other words find A[i] and A[j] such that A[j]-A[i]...

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Find longest Snake sequence in a given matrix

Objective: Given two dimensional matrix, write an algorithm to find out the snake sequence which has the maximum length. There could be many snake sequence in the matrix, you need to return the one...

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Dynamic Programming – Count all paths in 2D Matrix with Obstructions in it

Objective: Given two dimensional matrix, write an algorithm to count all possible paths from top left corner to bottom-right corner. You are allowed to move only in two directions, move right OR move down....

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Dynamic Programming – Count all paths from top left to bottom right of a mXn matrix

Objective: Given two dimensional matrix, write an algorithm to count all possible paths from top left corner to bottom-right corner. You are allowed to move only in two directions, move right OR move down....

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Dynamic Programming – Edit Distance Problem

Objective: Given two strings, s1 and s2 and edit operations (given below). Write an algorithm to find minimum number operations required to convert string s1 into s2. Allowed Operations: Insertion – Insert a new...

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Dynamic Programming – Coin In a Line Game Problem

Objective: In this game, which we will call the coins-in-a-line game, an even number, n, of coins, of various denominations from various countries, are placed in a line. Two players, who we will call...

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Dynamic Programming – Box Stacking Problem

Objective: You are given a set of n types of rectangular 3-D boxes, where the i^th box has height h(i), width w(i) and depth d(i) (all real numbers). You want to create a stack...

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Dynamic Programming – Highway Billboard Problem

Objective:  Suppose you’re managing construction of billboards on the Rocky & Bullwinkle Memorial Highway, a heavily traveled stretch of road that runs west-east for M miles. The possible sites for billboards are given by...

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