Solving 0/1 Knapsack problem using Recursion

Introduction A knapsack is a bag with straps, usually carried by soldiers to help them take their valuables or things which they might need during their journey. The 0/1 knapsack problem is a very famous interview problem. The problem statement is as follows: Given a set of items, each of which is associated with some weight and value. Find the subset of items which can be carried in a knapsack of capacity W (where W is the weight). It is required that the cumulative value of the items in the knapsack is maximum value possible. In simple words, it asks you to pick certain items from the...
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Find Interleaving Strings using Dynamic Programming

Introduction This problem is already discussed in the post here. This post attempts to solve the same using the dynamic programming approach. Here is a brief description of the problem. Given three strings A, B and C such that A is "ab", B is "ade" and C is "adabe" find if C is an interleaving of A and B or not. Interleaving means constructing the third string C using the characters of A and B such that the characters in A and B preserve their relative ordering in C. In the above example C is an interleaving of A and B. Approach to Find Interleaving Strings using Dynamic Programming How ...
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Build Balanced Binary Search Tree from Array

Introduction This post describes the algorithm to build binary search tree from array of sorted elements. However, this technique can be used to build balanced binary search tree from array. A balanced binary tree is a binary tree which has minimum height. To know more about various aspects of a binary search tree, please visit my previous posts. What does balanced means? In this post as we are trying to build a BST, we will assume the input to be a sorted array. In case, we are just building a binary tree, we can take any array as an input. Let me explain the process with the help of a ...
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Solving Sudoku using Backtracking

Introduction This post is the continuation of the backtracking series. Sudoku can be solved using multiple algorithms based on Neural Networks and Genetic Algorithms by doing exhaustive searches in the solution space. However, here we are focusing on solving Sudoku using backtracking algorithm. For people who are unaware of the Sudoku puzzle, please check out Wikipedia for details. For a brief description read below: A Sudoku puzzle is a 9 * 9 grid. Few cells in the grid contain random numbers between 1 and 9 (both inclusive) A fully solved Sudoku must contain numbers through 1-...
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Print all paths of robot through the grid

Introduction This is a supplement to the previous post where we were interested in just one path of a robot from top left corner to the bottom right corner. In this post we will print all paths of robot moving through a given grid containing few blocked cells. The algorithm for this solution remains the same, we just need few tricks to get that right. Here, I will explain the idea behind printing all paths of robot through the grid. Approach Here, let us discuss what different we need to do to print all the paths. As we can recall from the previous post, the moment we reached the destina...
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Find Path through grid – constrained motion

Introduction This is another addition to the backtracking series of problems. The problem is asked in many interviews in many different forms. Here are few of them: Given a grid where few of the cells are blocked. You have a robot placed at the top left corner of the grid. Find path through grid such that the robot starts from the top left corner and moves to the bottom right corner. Another form just asks for all possible paths from one cell to another into a grid. Of course there are constraints on the movement of the robot, else you would end up going in circles and the paths wo...
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Knight’s Tour Problem Simply Explained

Introduction This post is a continuation of the back tracking series. You can refer to other similar posts here. In this post we will be discussing the Knight's Tour Problem. The problem states that, given a N * M chessboard, a Knight's Tour is defined as the sequence of moves of a Knight, such that the Knight visits every square only once. Does this sound similar? Yes it is similar to finding the Hamiltonian Path as defined in this post. Approach for solving the Knight's Tour problem Here I define the backtracking approach to solve this problem. Let the Knight start from any location...
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