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Write a program that performs a simple n-body simulation, called "jumping leprechauns." this simulation involves n leprechauns, numberd 1 to n. it maintains a gold value g_i for each leprechaun i, which begins with each leprechaun starting out with a million dollars worth of gold, that is, g_i = 1000000 for each i = 1,. in addition, the simulation also maintains, for each leprachaun,i, a place on the horizon, which is represented as a double-precision floating point number, x_i. in each iteration of the simulation, the simulation processes the leprachauns in order. processing a leprachaun i during its iteration begins by computing a new place on the horizon for i, which is determined by the assignment:

When analyzing data sets, such as data for human heights or for human weights, a common step is to adjust the data. this can be done by normalizing to values between 0 and 1, or throwing away outliers. for this program, adjust the values by subtracting the smallest value from all the values. the input begins with an integer indicating the number of integers that follow. ex: if the input is 5 30 50 10 70 65, the output is: 20 40 0 60 55

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 ""; } }