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Many everyday occurrences can be represented as a binary bit. for example, a door is open or closed, the stove is on or off, and the fog is asleep or awake. could relationships be represented as a binary value? give example.

Describe a data structures that supports the stack push and pop operations and a third operation findmin, which returns the smallest element in the data structure, all in o(1) worst-case time.

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: