Programming Articles - Page 2403 of 3363

In this article, we will be discussing a program to find the vertex, focus and directrix of a parabola when the coefficients of its equation is given.Parabola is a curve whose all points on the curve are equidistant from a single point called focus.As we know the general equation for a parabola isy = ax2 + bx + cFor this equation, the following are defined as :Vertex -(-b/2a, 4ac - b2/4a) Focus - (-b/2a, 4ac - b2+1/4a) Directrix - y = c - (b2 +1)4aExample Live Demo#include using namespace std; void calc_para(float a, float b, float c) {    cout ... Read More

In this article, we will be discussing a program to find the probability of reaching from the initial state to the final state in a given time period in Markov chain.Markov chain is a random process that consists of various states and the associated probabilities of going from one state to another. It takes unit time to move from one state to another.Markov chain can be represented by a directed graph. To solve the problem, we can make a matrix out of the given Markov chain. In that matrix, element at position (a, b) will represent the probability of going ... Read More

In this article, we will be discussing a program to find the parity of a given number N.Parity is defined as the number of set bits (number of ‘1’s) in the binary representation of a number.If the number of ‘1’s in the binary representation are even, the parity is called even parity and if the number of ‘1’s in the binary representation is odd, the parity is called odd parity.If the given number is N, we can perform the following operations.y = N ^ (N >> 1)y = y ^ (y >> 2)y = y ^ (y >> 4)y = ... Read More

In this article, we will be discussing a program to find the number of triangles that can be formed by joining the intersection points of the given horizontal and vertical line segments.For example, let us say we had been given the following line segments. In this we have 3 intersection points. So the number of triangles that can be formed using these points will be 3C2.   | ---|--------|--    |        |    |  --|---|    |        |We will be following the Sweep Line Algorithm. We will be storing all the values of the line ... Read More

In this article, we will be discussing a program to find the first digit in the product of the elements of the given array.For example, let us say we have been given an array.arr = {12, 5, 16}Then the product is of these elements would be 12*5*16 = 960. Therefore, the result i.e the first digit of the product in this case would be 9.Example Live Demo#include using namespace std; int calc_1digit(int arr[], int x) {    long long int prod = 1;    for(int i = 0;i < x; i++) {       prod = prod*arr[i];    } ... Read More

In this article, we will be discussing a program to find the best fit rectangle that covers a given point.In this problem, we are given we the coordinates of a point (x, y) and a ratio of length/breadth = l/b (say). We have to find the coordinates of a rectangle which contains the given point and whose dimensions follow the given ratio. In case of multiple rectangle existing, we have to choose the one having the shortest distance between its euclid’s center and the given point.To solve this, first we would minimize the ratio l/b. After that, we find the ... Read More

In this article, we will be discussing a program to find the sum of digits of a number until the sum itself becomes a single digit and cannot be done summation of further.For example, take the case of a number 14520. Adding the digits of this number we get 1 + 4 + 5 + 2 + 0 = 12. Since this is not a single digit number, we would further add the digits of the number received. Adding them we get, 1 + 2 = 3.Now, 3 is the final answer because it is a single digit number itself ... Read More

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