Found 546 Articles for Algorithms

Longest Palindromic Subsequence is the subsequence of a given sequence, and the subsequence is a palindrome.In this problem, one sequence of characters is given, we have to find the longest length of a palindromic subsequence.To solve this problem, we can use the recursive formula, If L (0, n-1) is used to store a length of longest palindromic subsequence, thenL (0, n-1) := L (1, n-2) + 2 (When 0'th and (n-1)'th characters are same).Input and OutputInput: A string with different letters or symbols. Say the input is “ABCDEEAB” Output: The longest length of the largest palindromic subsequence. Here it is ... Read More

Longest Increasing Subsequence is a subsequence where one item is greater than its previous item. Here we will try to find Longest Increasing Subsequence length, from a set of integers.Input and OutputInput: A set of integers. {0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15} Output: The length of longest increasing subsequence. Here it is 6. The subsequence is 0, 2, 6, 9, 13, 15.AlgorithmlongestSubSeq(subarray, n)Input − The sub array and the size of sub array.Output − Longest increasing sub sequence length.Begin    define array length of size n    initially set 0 ... Read More

A matrix of different characters is given. Starting from one character we have to find the longest path by traversing all characters which are greater than the current character. The characters are consecutive to each other.To find the longest path, we will use the Depth First Search algorithm. During DFS, some subproblems may arise multiple times. To avoid the computation of that, again and again, we will use a dynamic programming approach.Input and OutputInput: The matrix as shown above. And the starting point. Here the starting point is e. Output: Enter Starting Point (a-i): e Maximum consecutive path: 5AlgorithmfindLongestLen(i, j, ... Read More

A sequence is said to be bitonic if it is first increasing and then decreasing. In this problem, an array of all positive integers is given. We have to find a subsequence which is increasing first and then decreasing.To solve this problem, we will define two subsequences, they are the Longest Increasing Subsequence and the Longest Decreasing Subsequence. The LIS array will hold the length of increasing subsequence ending with array[i]. The LDS array will store the length of decreasing subsequence starting from array[i]. Using these two arrays, we can get the length of longest bitonic subsequence.Input and OutputInput: A ... Read More

The longest common subsequence is a type of subsequence which is present in both of the given sequences or arrays.We can see that there are many subproblems, which are computed again and again to solve this problem. By using the Overlapping Substructure Property of Dynamic programming, we can overcome the computational efforts. Once the result of subproblems is calculated and stored in the table, we can simply calculate the next results by use of the previous results.Input and OutputInput: Two strings with different letters or symbols. string 1: AGGTAB string 2: GXTXAYB Output: The length of the longest common subsequence. ... Read More

An array of integers is given. We have to find the sum of all elements which are contiguous, whose sum is largest, that will be sent as output.Using dynamic programming we will store the maximum sum up to current term. It will help to find the sum for contiguous elements in the array.Input and OutputInput: An array of integers. {-2, -3, 4, -1, -2, 1, 5, -3} Output: Maximum Sum of the Subarray is: 7AlgorithmmaxSum(array, n)Input − The main array, the size of the array.Output − maximum sum.Begin    tempMax := array[0]    currentMax = tempMax    for i := ... Read More

The Independent Set is the subset of all binary tree nodes when there is no edge between any two nodes in that subset. Now from a set of elements, we will find the longest independent set. i.e. If the elements are used to form a binary tree, then all largest subset, where no elements in that subset are connected to each other.Input and OutputInput: A binary tree. Output: Size of the Largest Independent Set is: 5AlgorithmlongSetSize(root)In this algorithm Binary tree will be formed, each node of that tree will hold data and setSize.Input − Root node of the binary tree.Output − ... Read More

Let us consider, we will try to write the letter ‘A’, using the keyboard. Our goal is to use only four keys and try to write maximum ‘A’s on the text field. The keys are ‘A’, ‘C’, ‘V’ and ‘Ctrl’.To write the maximum number of A, we will use Ctrl + A to select All, Ctrl + C to copy and Ctrl + V to paste.Input and OutputInput: Number of keystrokes, say 7 Output: Maximum Number of A's with 7 keystrokes is: 9 Press A three times. Then Ctrl+A, Ctrl+C, Ctrl+V, Ctrl+VAlgorithmkeyNumbers(keyStrokes)Input: number of keystrokes.Output: Maximum number of letters using these ... Read More

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 More

Floyd-Warshall algorithm is used to find all pair shortest path problem from a given weighted graph. As a result of this algorithm, it will generate a matrix, which will represent the minimum distance from any node to all other nodes in the graph.At first, the output matrix is the same as the given cost matrix of the graph. After that, the output matrix will be updated with all vertices k as the intermediate vertex.The time complexity of this algorithm is O(V^3), where V is the number of vertices in the graph.Input and OutputInput: The cost matrix of the graph. 0 ... Read More