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C++ Articles
Page 384 of 597
Number of ways to reach at starting node after travelling through exactly K edges in a complete graph
Introduction The number of ways to reach the beginning hub after traveling through precisely K edges in a total chart can be calculated utilizing different approaches within the C dialect. One approach is to utilize brute constrain recursion, where we investigate all conceivable ways. Another approach includes energetic programming, where we store and reuse halfway comes about to dodge excess computations. Moreover, a numerical equation exists to specifically compute the number of ways based on the number of hubs and edges. These strategies give effective arrangements to decide the check of ways driving back to the beginning hub in a ...
Read MoreFind first undeleted integer from K to N in given unconnected Graph after Performing Q queries
Introduction Finding the primary undeleted integer from a given extend in a detached graph after performing multiple queries may be a challenging issue in graph theory. In this article, we investigate the errand of distinguishing the primary undeleted numbers and give two approaches to fathom it utilizing C++. Each approach offers a diverse point of view and utilizes distinctive calculations and data structures. The problem includes developing a graph, checking certain nodes as deleted, and after that deciding the primary undeleted numbers inside an indicated extend. The graph represents associations between nodes, and the deleted nodes are those that have ...
Read MorePermutations and Combinations (Concept, Examples, C++ Program)
Permutations and Combinations refer to the arrangements of objects in mathematics. Permutation − In permutation, the order matters. Hence, the arrangement of the objects in a particular order is called a permutation. Permutations are of two types − Permutation with repetition Suppose we have to make a three-digit code. Some possible numbers are 123, 897, 557, 333, 000, and 001. So how many numbers can we make like this? Let us look at it this way− In the once place, we have ten options − 0-9 Similarly, at the tenth and the hundredth place also, we have ten options. 0-9. ...
Read MoreHCF of an array of fractions (or rational numbers)
HCF or the Highest common factor of two or more numbers refers to the highest number which divides them. A rational number is the quotient p/q of two numbers such that q is not equal to 0. Problem Statement Given an array with fractional numbers, find the HCF of the numbers. Example 1 Input [{4, 5}, {10, 12}, {24, 16}, {22, 13}] Output {2, 3120} Explanation The fractional numbers given are: 4/5, 10/12, 24/16 and 22/13 2/3120 is the largest number that divides all of them. Example 2 Input [{18, 20}, {15, 12}, {27, 12}, {20, 6}] ...
Read MoreStella Octangula Number
In mathematics, a Stella Octangula number is a figurate number based on the Stella Octangula, of the form n(2n2 − 1). Stella Octangula numbers which are perfect squares are 1 and 9653449. Problem Statement Given a number n, check whether it is the Stella Octangula number or not. The sequence of Stella Octangula numbers is 0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990 Example1 Input x = 14 Output Yes Explanation $$\mathrm{For\: n = 2, expression \:n\lgroup 2n^2 – 1\rgroup is\: 14}$$ Example2 Input n = 22 Output No Explanation $$\mathrm{There \:is\: no\: ...
Read MoreNicomachus’ Theorem
According to Nicomachus’ Theorem, the sum of the cubes of the first n integers is equal to the square of the nth triangular number. Or, we can also say − The sum of cubes of first n natural numbers is equal to square of sum of first natural numbers. Putting it algebraically, $$\mathrm{\displaystyle\sum\limits_{i=0}^n i^3=\lgroup \frac{n^2+n}{2}\rgroup^2}$$ Theorem $$1^3 = 1$$ $$2^3 = 3 + 5$$ $$3^3 = 7 + 9 + 11$$ $$4^3 = 13 + 15 + 17 + 19\vdots$$ Generalizing $$n^3 =\lgroup n^2−n+1\rgroup+\lgroup n^2−n+3\rgroup+⋯+\lgroup n^2+n−1\rgroup$$ Proof By Induction For all n Ε Natural ...
Read MoreEqual sum array partition excluding a given element
Problem Statement For an index and an arr[]. Check if the array[] can be partitioned into two disjoint sets, excluding arr[index] such that the sum of both sets has equal value. Example 1 Input arr[] = {4, 3, 1, 2}, Index = 1 Output No Explanation We have to exclude arr[1] = 3 All possible sets are − Set 1: (4), Set 2: (2, 1), sum = 4≠3 Set 1: (4, 1), Set 2: (2), sum = 5≠2 Set 1: (4, 2), Set 2: (1), sum = 6≠1 No combination satisfies the conditions. Example 2Input arr[] ...
Read MoreSquared Triangular Number (Sum of Cubes)
A square triangular number, also referred to as a triangular square number, is a number that is both a triangular number and a perfect square. Square triangular numbers have an unlimited number of possible values; the first few are − 0, 1, 36, 1225, 41616... A triangular number or triangle number counts objects arranged in an equilateral triangle. The nth triangular number is the number of dots in the triangular arrangement with n dots on each side and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers, ...
Read MoreSum of all prefixes of given numeric string
In this problem, we need to find the sum of all prefixes of the given string. The best solution approach is that traverse through each prefix of the string and add them to get the answer. Problem statement - We have given a string named num_Str containing N digits. We need to find the sum of all prefixes of the given string. Sample examples Input num_str = "1123" Output 1247 Explanation - All prefixes of the given strings are 1, 11, 112, and 1123. The sum of all prefixes is 1247. Input num_str = ...
Read MoreMinimize the cost to convert given string to either type XYXY… or XXYY…
In this problem, we need to convert the given binary string to abababab or aabbaabb format and find the minimum cost for that. Also, we have given the cost to flip any character in the operations array. Problem statement - We have given a bin_str binary string and operations array containing the positive integers. The size of the string and array is the same and even. The task is to find the minimum costs to convert the string in the ababab… or aabbaabb… format. The cost to flip any character in the given string is the value at the ...
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