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Articles by Chandu yadav
Page 49 of 81
Reservoir Sampling
The Reservoir sampling is a randomized algorithm. In this algorithm, k items are chosen from a list with n different items.We can solve it by creating an array as a reservoir of size k. Then randomly pick one element from the main list and placed that item in the reservoir list. When one item is selected once, it will not be selected for next time. But his approach is not effective, we can increase the complexity by this method.In the reservoir list, copy first k items from the list, now one by one from the (k+1)th number in the list, ...
Read MorePossible walks from a source to a destination with exactly k edges
A directed graph is given. Another two vertices u and v are also given, u is the starting vertex, and v is the ending vertex. Our task is to find a number of walks from vertex u to v with exactly k edges. The value of k is also provided in the algorithm.By using dynamic programming, we need to create a 3D table, Where the row will point the values of u, columns will point the values v and depth will be used to track the number of edges from start to end.Input and OutputInput: The adjacency matrix of the ...
Read MoreBabylonian method to find the square root
The Babylonian method to find square root is based on one of the numerical method, which is based on the Newton- Raphson method for solving non-linear equations.The idea is simple, starting from an arbitrary value of x, and y as 1, we can simply get next approximation of root by finding the average of x and y. Then the y value will be updated with number / x.Input and OutputInput: A number: 65 Output: The square root of 65 is: 8.06226AlgorithmsqRoot(number)Input: The number in real.Output: Square root of given number.Begin x := number y := 1 precision ...
Read MoreSecant method to solve non-linear equatio
Secant method is also used to solve non-linear equations. This method is similar to the Newton-Raphson method, but here we do not need to find the differentiation of the function f(x). Only using f(x), we can find f’(x) numerically by using Newton’s Divide difference formula. From the Newton-Raphson formula, we know that, Now, using divide difference formula, we get, By replacing the f’(x) of Newton-Raphson formula by the new f’(x), we can find the secant formula to solve non-linear equations.Note: For this method, we need any two initial guess to start finding the root of non-linear equations.Input and OutputInput: The ...
Read MoreShortest Common Super Sequence
Shortest common super-sequence is a sequence where each element of both of the given sequences is present. In other words, we can say that the given two strings, both are sub-sequence of Shortest Common Super-Sequence.When there are no common characters in two strings, then we can simply concatenate them to get Super-sequence. But when they have some common characters, then firstly we have to find the longest string, then add extra characters of the other string.Input and OutputInput: Two strings. “ABCDEF” and “XYDEF” Output: The length of the shortest common super-sequence. Here the super-sequence is “ABCDEFXY”. So the length is ...
Read MoreMaximum profit by buying and selling a share at most twice
In a trading, one buyer buys and sells the shares, at morning and the evening respectively. If at most two transactions are allowed in a day. The second transaction can only start after the first one is completed. If stock prices are given, then find the maximum profit that the buyer can make.Input and OutputInput: A list of stock prices. {2, 30, 15, 10, 8, 25, 80} Output: Here the total profit is 100. As buying at price 2 and selling at price 30. so profit 28. Then buy at price 8 and sell it again at price 80. So ...
Read MoreMin Cost Path
A matrix of the different cost is given. Also, the destination cell is provided. We have to find minimum cost path to reach the destination cell from the starting cell (0, 0).Each cell of the matrix represents the cost to traverse through that cell. From a cell, we cannot move anywhere, we can move either to the right or to the bottom or to the lower right diagonal cell, to reach the destination.Input and OutputInput: The cost matrix. And the destination point. In this case the destination point is (2, 2). 1 2 3 4 8 2 1 5 3 ...
Read MoreGenerate Fibonacci Series
The Fibonacci sequence is like this, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ……In this sequence, the nth term is the sum of (n-1)'th and (n-2)'th terms.To generate we can use the recursive approach, but in dynamic programming, the procedure is simpler. It can store all Fibonacci numbers in a table, by using that table it can easily generate the next terms in this sequence.Input and OutputInput: Take the term number as an input. Say it is 10 Output: Enter number of terms: 10 10th fibinacci Terms: 55AlgorithmgenFiboSeries(n)Input: max number of terms.Output − The nth Fibonacci ...
Read MoreFleury's Algorithm
Fleury’s Algorithm is used to display the Euler path or Euler circuit from a given graph. In this algorithm, starting from one edge, it tries to move other adjacent vertices by removing the previous vertices. Using this trick, the graph becomes simpler in each step to find the Euler path or circuit.We have to check some rules to get the path or circuit −The graph must be a Euler Graph.When there are two edges, one is bridge, another one is non-bridge, we have to choose non-bridge at first.Choosing of starting vertex is also tricky, we cannot use any vertex as ...
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