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Simulation is a technique in programming where all events are processed in the order of occurrence. By translating real world logic into programming code, simulation speeds up tasks that may otherwise take a long time for human. Simulation does not provide alternative shortcuts to a solution; it simply speeds up the process.



Given M trees and the number of days each tree takes to grow a fruit, compute the total number of fruits after N days.


For each tree i, keep a variable K_i indicating the number of days it takes for the next fruit to grow. Simulate the situation day by day. On each day, decrease K_i by 1 and increase the fruit count by the number of K_i's that equal zero, and reset these K_i's. Output the total sum at the end.


This solution gives the correct answer, in \mathcal{O}(MN) time. This is fine if MN is small, but a better technique is required if MN is large.


When a problem is logically simple and can be directly done by human, simulation is very likely the solution. When the bounds on variables are small, simulation is a quick, safe, and convincing technique. When run time is a concern, other techniques such as dynamic programming may be required.