We require the appropriate knowledge to create several unique pairs in an array syntax in C++. In finding the number of unique pairs, we count all unique pairs in a given array, i.e., all possible pairs can be formed where each pair should be unique. For example −Input : array[ ] = { 5, 5, 9 } Output : 4 Explanation : The number of all unique pairs are (5, 5), (5, 9), (9, 5) and (9, 9). Input : array[ ] = { 5, 4, 3, 2, 2 } Output : 16Approach to find The SolutionThere are Two ... Read More

We are given several points present in 3 lines now; we are required to find how many triangles these points can form, for exampleInput: m = 3, n = 4, k = 5 Output: 205 Input: m = 2, n = 2, k = 1 Output: 10We will apply some combinatorics to this question and make up some formulas to solve this problem.Approach to find The SolutionIn this approach, we will devise a formula by applying combinatorics to the current situations, and this formula will give us our results.C++ Code for the Above ApproachHere is the C++ syntax which ... Read More

n the article, first, we have to draw a colored triangle. We need to take an uncolored triangle and divide the triangle into four small equilaterals. Triangles with the same area and keep doing it till the nth step and find the number of equilateral triangles present in the figure.Approach to find The SolutionThere are Two Approaches for this Solution and they are −Brute Force ApproachWe can observe that the number of triangles keeps increasing by some number (increasing by 3*previous_number + 2) after every step. So we can run a loop till n and calculate the number of triangles.Example#include ... Read More

In this article, we will understand the problem of finding trailing zeros of a given number N in the base B representation of its factorial. For examplesInput : N = 7 Base = 2 Output : 4 Explanation : fact(7) = 5040 in base10 and 1001110110000 in base16 having 4 trailing zero. Input : N = 11 Base = 5 Output : 2 Explanation : fact(11) = 39916800 in base10 and 40204314200 in base16 having 2 trailing zeroes.Let's first recap the process of converting any decimal number from one base to another. Let's take an example of converting (5040)10 ... Read More

In this article, we will understand the problem of finding trailing zeros of a given number N in the base 16 representation of its factorial for exampleInput : N = 7 Output : 1 Explanation : fact(7) = 5040 in base10 and 13B0 in base16 having 1 trailing zero. Input : N = 11 Output : 2 Explanation : fact(11) = 39916800 in base10 and 2611500 in base16 having 2 trailing zeroes.Let's first recap the process of converting any decimal number from one base to another; let's take an example of converting (5040)10 to (?)16i.e., dividing the number by ... Read More

In this article, we are given two strings, and we need to find out how many substrings of the 1st string can be found in the 2nd string(the exact substring can occur multiple times). For exampleInput : string1 = “fogl”    string2 = “google” Output : 6 Explanation : substrings of string1 present in string2 are [ “o”, “g”, “l”, “og”, “gl”, “ogl” ]. Input : string1 = “ajva”    string2 = “java” Output : 5 Explanation : substrings of string1 present in string2 are [ “a”, “j”, “v”, “a”, “va” ].Approach to find The SolutionLet's discuss how we ... Read More

In this article, you will learn about the approaches to find the number of substrings (non-empty) that you can form in a given string.Input : string = “moon” Output : 10 Explanation: Substrings are ‘m’, ‘o’, ‘o’, ‘n’, ‘mo’, ‘oo’, ‘on’, ‘moo’, ‘oon’ and ‘moon’. Input : string = “yellow” Output : 21Approach to find The SolutionLet the length of the string be n, so looking at the example above, we understand that to find all possible numbers of substrings, we need to add substrings of length n, (n-1), (n-2), (n-3), (n-4), ......2, 1.Total number of substrings = n ... Read More

To find the probability of numbers’ parity, i.e., is it even or odd, and for the given ranges. For each query, we need to print p and q representing the probability by p / q, for example.Input : N = 5, arr[] = { 6, 5, 2, 1, 7 } query 1: 0 2 2 query 2: 1 2 5 query 3: 0 1 4 Output : 0 3 4 1 2In this problem, we will maintain two arrays containing the number of odd and even numbers present until that index. This simplifies our problems, and now we need ... Read More

In this problem we are given a binary tree and we are required to perform dfs from a particular node in which we assume the given node as the root and perform dfs from it.In the above tree suppose we are required to perform DFS from node FIn this tutorial we are going to apply some unorthodox methods so that it will decrease our time complexity substantially and thus we will be able to run this code for higher constraints also.Approach − In this approach we are not simply going to go the naive way i.e. where we simply apply ... Read More

Given n, r, k, now we have to find how we can select r things from n so that specific k things always occur together, for example.Input : n = 8, r = 5, k = 2 Output : 960 Input : n = 6, r = 2, k = 2 Output : 2We need a little knowledge for this problem because this problem is asking us to find the permutation of n and r such that k things come together.Approach to Find the SolutionWe need to formulate our formula for this question, and that will ... Read More