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In this article, we will be discussing a program to find the minimum vertex cover size of a given graph using binary search.Minimum vertex cover is a set of vertices of the given graph such that every edge in the graph is incident of either of the vertices in that set.For example, take the graph2 ---- 4 ---- 6 | | | | | | 3 ---- 5Here, the minimum vertex cover involves vertices 3 and 4. All the edges of the graphs are incident on either 3 or 4 ... Read More
In this article, we will be discussing a program to find the first digit in the factorial of a given number.The basic approach for this is to find the factorial of the number and then get its first digit. But since factorials can end up being too large, we would make a small tweak.At every point we would check for any trailing zeroes and remove if any exists. Since trailing zeroes isn’t having any effect on the first digit; our result won’t change.Example Live Demo#include using namespace std; int calc_1digit(int n) { long long int fact = 1; ... Read More
In this article, we will be discussing a program to find the first collision point i.e the first point that both of the series have.In this, we would be given with five variables ‘a’, ‘b’, ‘c’, ‘d’ and ‘n’. We have to create two arithmetic progression series from these having n digits eachb, b+a, b+2a, ….b+(n-1)a d, d+c, d+2c, ….. d+(n-1)cAnd then find the first common point that both of the given series has.To solve this, we would create the numbers in the first series. And for each number we would check if it is greater than or equal to ... Read More
In this article, we will be discussing a program to find the cabs near about (less than 50km) using the Great Circle Distance formula.Let us suppose we have been given a JSON file which contains the name and coordinates of the people who need a cab and also the coordinates of the all the cabs available.To solve this, we would convert the GPS coordinates into double. From the double form, we would finally convert them in degrees to radians. Then we can ultimately apply the Great Circle Distance formula to find the cabs available in 50km from the user’s position.Note ... Read More
In this article, we will be discussing a program to find an integer ‘k’, such that its modulus with each element of a given array is the same.For example, let us suppose we have been given with an array, arr = {12, 22, 32}Then we have the output value of k = 1, 2, 5, 10.Take the case of two values in the array ‘x’ and ‘y’ (x>y). Then we have (y+difference)%k = y%k. Solving this we get, difference%k = 0So, we will find all the divisors to the difference of the maximum and minimum element in the array and ... Read More
In this article, we will be discussing a program to execute the Finite Automata algorithm for pattern searching.We are provided with a text[0...n-1] and a pattern[0...m-1]. We have to find all the occurrences of the pattern[] in the text[].For this we would preprocess the text[] and build a 2-d array to represent it. After that we just have to traverse between the elements of the text[] and the different states of the automata.Example Live Demo#include #include #define total_chars 256 int calc_nextstate(char *pat, int M, int state, int x) { if (state < M && x == pat[state]) ... Read More
In this article, we will be discussing a program to check if it is possible to finish all the given tasks on the basis of the given prerequisites.For example, let us say we have been given three tasks and prerequisites are [[1, 0], [2, 1], [3, 2]].( [1, 0] means that to pick up ‘1’ task; the ‘0’ task must be completed first.)Then, in this example since the ‘0’ task doesn’t have any prerequisite it can be completed first. Then the ‘1’ task can be completed, since the ‘0’ task has been completed. Similarly, both ‘2’ and ‘3’ tasks can ... Read More
In this article, we will be discussing a program to find ways an integer (say X) can be expressed as sum of n-th power of unique natural numbers.For example, let X = 100 and n = 2Then there would be 3 ways to express 100 as sum of squares of natural numbers.100 = 102 100 = 62 + 82 100 = 12 + 32 + 42 + 52 + 72This can be done easily by using recursion. We would start from 1 and go till the n-th root of the given number. In every run, we would subtract the n-th ... Read More
In this article, we will be discussing a program to find unique pairs of numbers having elements less than or equal to N and following some certain conditions −The square of difference between the two numbers must be equal to the LCM of those two numbers.The HCF of those two numbers can be represented as a product of any two consecutive numbers.The best approach to solve this problem would be to take two consecutive numbers (starting from 1) and finding the multiples of product of those numbers. Then among the multiples, to specify to one pair of numbers we need ... Read More
In this article, we will be discussing a program to find the union and intersection of two given unsorted arrays.Let us denote the two arrays with ‘A’ and ‘B’. Then union of those arrays is denoted by A ∪ B which is basically an array of all the elements in both the given arrays; provided that each element repeats only once.To find this, we will create a separate array and copy down all the elements from the first array. Then we will traverse through the elements of the second array and check if it is already present in the union ... Read More