Consider an array of integers consisting of the numbers: 8 12 19 32 45 55 67 72 89 90 92. Suppose the binary search algorithm is applied to this list to search for the key 56 (not in the list). What is the index of the first element in the array that is compared with 56 and how is this index evaluated?

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: