in java  Calculate the sum of an array of n integers Compute the sum of all elements of an array 1. Describe the definition of recursive function     Base case(s)    Recursive case(s) 2. Write the code.

ASSIGNMENT: Write a program to use the capability of Recursion to calculate factorials. For example, 5 factorial is normally written as 5! 5! = 5*4*3*2*1 5! = 120 Use recursive function calling to multiply. 5*4*3*2*1 And then print the result. 120 Your output should resemble the image below. >sh -c jav d. -type f > java -cla 5 4 2 5! = 120 } Note: 5! is use in this example but your program should calculate the factorial for any number entered.

Write a recursive function that displays the number of even and odd digits in an integer using the following header: void evenAndOddCount(int value) Write a test program that prompts the user to enter an integer and displays the number of even and odd digits in it.

Calculating the Minimum Sum Path in a Triangle (LeetCode Problem)Given a triangle array, return the minimum path sum from top to bottom. For each step, you may move toan adjacent number of the row below. More formally, if you are on index i on the current row, you maymove to either index i or index i + 1 on the next row.   public static int minSumPathMemo(int[][] triangle)This method will calculate the minimum sum path in the triangle using the top down strategy. Note thismethod MUST BE recursive and you will need to create a recursive helper method. public static int minSumPathBottomUp(int[][] triangle)This method will calculate the minimum sum path in the triangle using the bottom up strategy. Note thismethod CANNOT be recursive and you should not create any additional helper functions.   Extra Challenge: Could you do this using only O(n) extra space where n is the total number of rows in thetriangle?  This is method signature class below: package dynamic; public class MinSumPath {…