This is a C++ program to implement Modular Exponentiation Algorithm.AlgorithmBegin    function modular():    // Arguments: base, exp, mod.    // Body of the function:       initialize res = 1       while (exp > 0)          if (exp mod 2 == 1)          res= (res * base) % mod          exp = exp left shift 1          base = (base * base) % mod       return res. EndExample#include using namespace std; long long modular(long long base, long long exp, int mod) {    long long res = 1;    while (exp > 0) {       if (exp % 2 == 1)          res= (res * base) % mod;       exp = exp >> 1;       base = (base * base) % mod;    }    return res; } int main() {    long long b, e;    int mod;    coutb;    coute;    coutmod;    cout

The algebraic expression is a combination of numbers, variables (x or y), and arithmetic operators like +, -, *, and /. In this article, we'll write a C++ program to find the maximum value of an expression in the form (x1 + x2 + x3 + . . . + xa) * (y1 + y2 + . . . + yb) where a total of a+b integers are given. Our task is to split these integers into two groups, one with a numbers and the other with b numbers, and calculate the product of their sums. By ... Read More

The algebraic expression is a combination of numbers, variables (x or y), and arithmetic operators like +, -, *, and /. In this article, we'll write a C++ program to find the minimum value of an expression in the form (x1 + x2 + x3 + . . . + xa) * (y1 + y2 + . . . + yb) where a total of a+b integers are given. Our task is to split these integers into two groups, one with a numbers and the other with b numbers, and calculate the product of their sums. By trying ... Read More

This is a C++ program to perform Optimal Paranthesization using Dynamic Programming.AlgorithmBegin    Take the length n and dimension of matrix as input.    MatrixChain() to find out minimum multiplications:    Arguments:       a[i][j]=Minimum number of scalar multiplications needed to          compute the matrix A[i]A[i+1]...A[j] = A[i..j] where dimension of A[i] is p[i-1] x p[i].          a[i][j] means cost is zero when multiplying one matrix.       L is chain length.       m = cost / scalar multiplications.    Body of the function:       for i = ... Read More

This is a C++ Program to optimize Wire Length in Electrical Circuit.AlgorithmBegin    Function optimizeLength() :    1) Declare a array dist[N].    2) sptSet[i] will be true if component i is included in shortest    path tree or shortest distance from src to i is finalized.    3) Initialize all distances as INFINITE and stpSet[] as false    4) Distance of source component from itself will be always 0.    5) Run a for loop cnt = 0 to N-2, Find shortest path for all components.       A) Pick the minimum distance component from the set of ... Read More

This is a C++ program to represent Linear Equations in matrix form.AlgorithmBegin    1) Take the no of variables n and the coefficients of each variable as input.    2) Declare a matrix[n][n] and constant[n][1].    3) Make for loops i = 0 to n-1 and j = 0 to n-1    to take the coefficients of each variable as the elements of the matrix.    4) Display the matrix by using nested for loops. EndExample#include using namespace std; int main(void) {    char variable[] = { 'x', 'y', 'z', 'd' };    cout > n;    cout > matrix[i][j];       }       cin >> constant[i][0];    }    cout

Gauss Seidel method is used to solve linear system of equations in iterative method. This is a C++ Program to Implement Gauss Seidel Method.AlgorithmBegin    Take the dimensions of the matrix p and its elements as input.    Take the initials values of x and no of iteration q as input.    While q>0       Make a for loop i = 0 to p-1          initialize n[i] = (b[i] / a[i][i]).             Make a for loop i = 0 to p-1             If (j == ... Read More

Freivalds' algorithm determines whether the matrices are equal for a chosen k value with a probability of failure less than 2^-k in O(kn^2).It is used to verify matrix multiplication.AlgorithmBegin    Take matrix1(n*n), matrix2(n*n), matrix3(n*n) as input.    // According to the algorithm we have to verify:    // matrix1 × matrix2 = matrix3.    1) Choose vector a[n][1] randomly and uniformly in which component will be 0 or 1.    2) Compute matrix2 * a, matrix3 * a and then matrix1 * (matrix2 * a) for evaluating the expression, matrix1 * (matrix2 * a) - matrix3 * a.    3) ... Read More

Disjoint set is basically as group of sets where no item can be in more than one set. It supports union and find operation on subsets.Find(): It is used to find in which subset a particular element is in and returns the representative of that particular set.Union(): It merges two different subsets into a single subset and representative of one set becomes representative of other.Functions and pseudocodesBegin    Assume k is the element    makeset(k):       k.parent = k.    Find(x):    If k.parent == k       return k.    else    return Find(k.parent)    Union ... Read More

Virtual functions in C++ used to create a list of base class pointers and call methods of any of the derived classes without even knowing kind of derived class object. Virtual functions are resolved late, at runtime.Here is an implementation of virtual function in C++ program −Example#include using namespace std; class B {    public:       virtual void s() { //virtual function          cout