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Data Structure Articles
Page 161 of 164
Closest Pair of Points Problem
In this problem, a set of n points are given on the 2D plane. In this problem, we have to find the pair of points, whose distance is minimum.To solve this problem, we have to divide points into two halves, after that smallest distance between two points is calculated in a recursive way. Using distances from the middle line, the points are separated into some strips. We will find the smallest distance from the strip array. At first two lists are created with data points, one list will hold points which are sorted on x values, another will hold data ...
Read MorePeak Element in 2D array
An item is said to be a peak element when it is greater than or equal with all four neighbor of that element. The neighbor elements are the top, bottom, left and right elements. For this problem, we will consider some bounds. The diagonal elements are not checked as neighbor elements. More than one peak element may present in a matrix, and the peak element is not necessarily the largest element in the matrix.Input and OutputInput: A matrix of different numbers. 10 8 10 10 14 13 12 11 15 9 11 11 15 9 11 21 16 17 19 ...
Read MoreCount Inversions in an array
The inversions of an array indicate; how many changes are required to convert the array into its sorted form. When an array is already sorted, it needs 0 inversions, and in another case, the number of inversions will be maximum, if the array is reversed.To solve this problem, we will follow the Merge sort approach to reduce the time complexity, and make it in Divide and Conquer algorithm.Input and OutputInput: A sequence of numbers. (1, 5, 6, 4, 20). Output: The number of inversions required to arrange the numbers into ascending order. Here the number of inversions are 2. First ...
Read MoreMedian of two sorted array
Medians are the middle numbers, in other words, the median value is the middle observation in an ordered list. It corresponds to the cumulative percentage of 50%.The size of two arrays must be same, we will find the median of two separate arrays at first, then compare the separate medians to get an actual median of two lists.Input and OutputInput: Two sorted array are given. Array 1: {1, 2, 3, 6, 7} Array 2: {4, 6, 8, 10, 11} Output: The median from two array. Here the median value is 6. Merge the given lists into one. {1, 2, 3, ...
Read MoreBiconnected Graph
An undirected graph is said to be a biconnected graph, if there are two vertex-disjoint paths between any two vertices are present. In other words, we can say that there is a cycle between any two vertices.We can say that a graph G is a bi-connected graph if it is connected, and there are no articulation points or cut vertex are present in the graph.To solve this problem, we will use the DFS traversal. Using DFS, we will try to find if there is any articulation point is present or not. We also check whether all vertices are visited by ...
Read MoreZ Algorithm
This algorithm is named Z Algorithm because, in this algorithm, we need to create a Z array. The size of the Z array is the same as the text size. This array is used to store the length of longest possible substring starting from the current character of the main string. At first, the pattern and the main text are concatenated with a special symbol which is not present in the text and pattern. If the P is pattern and T is the main text, then after concatenation, it would be P$T (Assuming $ is not present in the P ...
Read MoreRat in a Maze Problem
In this problem, there is a given maze of size N x N. The source and the destination location is top-left cell and bottom right cell respectively. Some cells are valid to move and some cells are blocked. If one rat starts moving from start vertex to destination vertex, we have to find that is there any way to complete the path, if it is possible then mark the correct path for the rat.The maze is given using a binary matrix, where it is marked with 1, it is a valid path, otherwise 0 for a blocked cell.NOTE: The rat can ...
Read MoreSudoku Solving algorithms
In this section, we will try to solve the famous number maze problem called Sudoku. Sudoku is a 9 x 9 number grid, and the whole grid are also divided into 3 x 3 boxes There are some rules to solve the Sudoku.We have to use digits 1 to 9 for solving this problem.One digit cannot be repeated in one row, one column or in one 3 x 3 box.Using the backtracking algorithm, we will try to solve the Sudoku problem. When some cell is filled with a digit, it checks whether it is valid or not. When it is ...
Read MoreSuffix Array
From a given string, we can get all possible suffixes. After sorting the suffixes in lexicographical order, we can get the suffix array. Suffix arrays can also be formed using suffix trees. By using the DFS traversal of suffix trees, we can get suffix arrays. Suffix arrays are helpful to find suffixes in linear time. We can also find substrings using suffix array by using binary search type procedure.The time complexity is O(m log n)Input and OutputInput: Main String: “BANANA”, Pattern: “NAN” Output: Pattern found at position: 2AlgorithmfillSuffixArray (text, suffArray)Input: The main stringOutput: The array of suffixesBegin n := text Length ...
Read MoreTrie of all Suffixes
From the text, we can generate all suffixes to make a tree structure. We know that every pattern that presents in the text, must be a prefix of one of the possible suffix in the text. By building Trie of all suffixes, we can find any substring in linear time. Every suffix is ending with string terminating symbol. From each node if there is any path, it moves forward, otherwise returns that pattern is not found.For this algorithm, the time complexity is O(m+k), where the m is the length of string and k is the frequency of the pattern in ...
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