In the box below, write a recursive function that calculates the sum of integers from M to N inclusive. You may assume M is less than or equal to N.
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- (Numerical) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters to 0, and then generate a large number of pseudorandom integers between 0 and 9. Each time a 0 occurs, increment the variable you have designated as the zero counter; when a 1 occurs, increment the counter variable that’s keeping count of the 1s that occur; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of the time they occurred.15. Write a program to implement and test the algorithm that you designed for Exercise 15 of Chapter 1. (You may assume that the value of . In your program, declare a named constant PI to store this value.)(Numerical) Using the srand() and rand() C++ library functions, fill an array of 1000 floating-point numbers with random numbers that have been scaled to the range 1 to 100. Then determine and display the number of random numbers having values between 1 and 50 and the number having values greater than 50. What do you expect the output counts to be?
- 2. Sum: a recursive function that computes the sum of integers 1, 2, 3, …., n for a given number n. So Sum(6) should return 1 + 2 + 3 + 4 + 5 + 6 , i.e. 21.sum(n) = n + sum(n-1)Write a recursive function that converts a decimal number to binary number.int DecToBin(int dec);11.11 LAB: Number pattern Write a recursive function called PrintNumPattern() to output the following number pattern. Given a positive integer as input (Ex: 12), subtract another positive integer (Ex: 3) continually until 0 or a negative value is reached, and then continually add the second integer until the first integer is again reached. For this lab, do not end output with a newline. Ex. If the input is: 12 3 the output is: 12 9 6 3 0 3 6 9 12 main.cpp: #include using namespace std; // TODO: Write recursive PrintNumPattern() function int main(int argc, char* argv[]) { int num1; int num2; cin >> num1; cin >> num2; PrintNumPattern(num1, num2); return 0; }
- //Can you please debug this program. Thank you #include<stdio.h>#include<stdlib.h> //This function takes n and k and computes n using Pascal’s Rule.long choose(int n, int k); //This functions below create a memoization table containing//long values of dimension (n+1)×(k+1) long chooseWithMemoization(int n, int k); //This is a new recursive function that also takes the table as a parameter.//When the function needs to compute (n , k )it checks the table first, and//if the value has already been comput(is not -1) then it returns that value. long chooseWithMemoizationRecursive(int n, int k, long **tableau); int main(int argc, char **argv) {//variable declaration int n; int k; scanf("%d",&n); scanf("%d",&k ); long choice = -1;//printing out the out put choice = chooseWithMemoization(n,k); printf("choose(%d,%d) = %ld\n", n, k, choice); return 0;} /** * This function takes n and k and computes n using Pascal’s Rule.*/long choose(int…Write a recursive function named sumSquares that returns the sum of the squares of the numbers from 0 to num, in which num is a nonnegative int variable. Do not use global variables; use the appropriate parameters. Also write a program to test your function.A,5digit positive integer is entered through the keyboard write a function of digit of the 5 digit number 1 without using recurism 2 using recursion
- Computer scientists and mathematicians often use numbering systems other than base 10. Write a program that allows a user to enter a number and a base and then prints out the digits of the number in the new base. Use a recursive function baseConversion (num, base) to print the digits. Hint: Consider base 10. To get the rightmost digit of a base 10 number, simply look at the remainder after dividing by 10. For example, 153 % 10 is 3. To get the remaining digits, you repeat the process on 15, which is just 153 // 10. This same process works for any base. The only problem is that we get the digits in reverse order (right to left). The base case for the recursion occurs when num is less than base and the output is simply num. In the general case, the function (recursively) prints the digits of num // base and then prints num % base. You should put a space between successive outputs, since bases greater than 10 will print out with multi-character "digits." For example, baseConversion(1234,…c++ Write the function called factorial. The function is passed in an integer. This function should use recursion to solve the problem. Five factorial is 5 * 4 * 3 * 2 * 1 = 120. Example run:Input a number -> 5The factorial of 5 is 120Create a recursive function that multiplies two positive integers without the need of the * (or /) operator. You can utilise addition, subtraction, and bit shifting, but you should keep the amount of operations to a minimum.