Programming Articles - Page 1749 of 3366

We are given a number N. The goal is to count the number of steps required to reduce the number to 1 by following rules −If the number is power of 2, reduce it to its half.Else reduce it to the N-(nearest power of 2 which is less than N).For step 1, we will check if N is power of 2, by checking if ceil(log2(N)), floor(log2(N)) return the same result. If yes then N=N/3, increment count of operation.If the result of step 1 is false then we will perform step 2 and subtract the nearest power of 2 less than ... Read More

We are given with integers x and p. The goal is to find the number of solutions of the equation −x2=1 ( mod p ) such that x lies in range [1, N].We will do this by traversing from 1 to N and take each number as x check if (x*x)%p==1. If yes then increment the count.Let’s understand with examples.Input − n=5, p=2Output − Number of Solutions − 3Explanation − Between the range 1 to 5.12=1%2=1, count=1 22=4%2=0, count=1 32=9%2=1, count=2 42=16%2=0, count=2 52=25%2=1, count=3 Total number of solutions=3.Input − n=3, p=4Output − Number of Solutions − 2Explanation − Between ... Read More

We are given a perimeter P of a triangle. Perimeter is the sum of all sides of the triangle. The goal is to find the number of right triangles that can be made which have the same perimeter.If the sides of the triangle are a, b and c. Then a + b + c = P and a2 + b2 = c2 ( pythagoras theorem for any combination of a, b, and c )We will check this by taking a from 1 to p/2 and b from a+1 to p/3. Then c = p-a-b (a+b+c=p)For all right triangles, apply Pythagoras ... Read More

We are given with a rectangle of length L and breadth B, such that L>=B. The goal is to find the number of squares that a rectangle of size LXB can accommodate.Above figure shows a rectangle of size 3 X 2. It has 2, 2X2 squares and 6, 1X1 squares in it.Total squares= 6+2=8.Every rectangle of size LXB has L*B number of 1X1 squares.Biggest squares are of size BXB.For L=B=1, squares = 1.For L=B=2, squares = 1 + 4 = 5. ( 1 of 2X2, 4 of 1X1 )For L=B=3, squares = 1 + 4 + 9 = 14. ( ... Read More

We are given an array of integers of size N. Variables L and R define a range between 1 and N. The goal is to find the number of smallest elements that lie in range L and R such that L>=1 and R

We are given with an array of numbers. The goal is to find the count of prime numbers in that array.A prime number is the one which is divisible by 1 and the number itself. It has only two factors. We will check if the number is prime starting from the first element till the last and increase the count of prime numbers found so far.To check if the number N is prime, check if numbers between the range [2 to N/2], fully divides N. If yes then it is non-prime. Else it is prime.Let’s understand with examples.Input − arr[]= ... Read More

We are given with five integers N, A, B, X and Y. The goal is to maximize the profit by checking that between numbers in range [ 1 to N ] , ifA number is divisible by A, then profit increases by X.A number is divisible by B then profit increases by Y.A profit can be added once only, for a particular number in range.Let’s understand with examples.Input − N=4, A=2, B=3, X=2, Y=3Output − Maximized profit is − 7Explanation −2, 4 are divisible by A ( 2 ). Profit increases from 0 to 2, then 2 to 4 ( ... Read More

We are given with an array of N numbers with elements lying in range 0 and N-1. The elements are unsorted. The goal is to find the maximum number of partitions of the array which can be sorted individually and then can be concatenated to make a whole sorted array of length N.Each partition is chosen such that elements in it are unsorted. For N numbers ranging between 0 and N-1, sorted elements are at index equal to the value. Arr[i] = i.We will solve this by comparing each element by maximum value found so far on its left. When ... Read More

A matrix can have one or more than one minimum and maximum values. Also, the size of the matrix can be just one column and multiple rows or thousands of columns and thousands of rows. The row number and column number for the minimum and maximum values in a matrix can be found by using the following syntax −For Maximumwhich(“Matrix_Name”==min(“Matrix_Name”),arr.ind=TRUE)For Minimum>which(“Matrix_Name”==max(“Matrix_Name”),arr.ind=TRUE)Example M1

The pairwise maximum refer to the values that are largest between the vectors. For example, if we have a vector that contains 1, 2, 3 and a second vector contains 2, 1, 4 then the pairwise maximum will be 2, 2, 4 because the maximum between 1 and 2 is 2, the maximum between 2 and 1 is 2, and the maximum between 3 and 4 is 4. In R, we can find these maximum values for many vectors using pmax function.Example> x1 y1 pmax(x1, y1) [1] 27 28 65 25 17 21 29 > x2 x2 [1] 7 ... Read More