Editing Simulation

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.

== Example ==
=== Problem ===
Given M trees and the number of days each tree takes to grow a fruit, compute the total number of fruits after <math>N</math> days.
=== Solution ===
For each tree <math>i</math>, keep a variable <math>K_i</math> indicating the number of days it takes for the next fruit to grow. Simulate the situation day by day. On each day, decrease <math>K_i</math> by 1 and increase the fruit count by the number of <math>K_i</math>'s that equal zero, and reset these <math>K_i</math>'s. Output the total sum at the end.
=== Analysis ===
This solution gives the correct answer, in <math>\mathcal{O}(MN)</math> time. This is fine if <math>MN</math> is small, but a better technique is required if <math>MN</math> is large.

== Characteristics ==
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.