Consider a modification to the activity-selection problem in which each activity ai has, in addition to a start and finish time, a value vi. the objective is no longer to maximize the number of activities scheduled, but instead to maximize the total value of the activities scheduled. that is, we wish to choose a set a of compatible activities such that summation of their corresponding values is maximized. give a polynomial-time algorithm for this problem.

Acommon algorithm for converting a decimal number to binary is to repeatedly divide the decimal number by 2 and save the remainder. this division is continued until the result is zero. then, each of the remainders that have been saved are used to construct the binary number.write a recursive java method that implements this algorithm.it will accept a value of int and return a string with the appropriate binary character representation of the decimal number.my code: public class lab16{public string converttobinary(int input){int a; if(input > 0){a = input % 2; return (converttobinary(input / 2) + "" +a); } return ""; } }