Dynamic-Programming

This is a classical problem of Computer Science: it’s used to study both Greedy and Dynamic Programming algorithmic techniques. I hate having my pocket full of copper!!! -_- Definition Given: A set of n Denominations D[0…n-1] in ascending order, representing a Monetary Coin System An money amount A, as input calculate a solution: * <strong><code>S[0...n-1]</code></strong>, with <code>0 &lt;= S[i] &lt;= (A/S[i])</code> and <code>0 &lt; i &lt; n-1</code> where: * <strong><code>A = Sum_{[i=0 -> n-1]} { D[i] * S[i] }</code></strong> * <strong><code>Min{ Sum_{[i=0 -> n-1]} { S[i] } }</code></strong> In other words Find the smallest amount of coins to make the given amount. ...

Another simple-but-yet-interesting problem that I found challenging solving is the to Write a Fibonacci’s numbers calculator. It’s a REALLY SIMPLE problem, but still can demonstrate how superficial thinking in programming can lead to dramatically bad solutions. What’s a Fibonacci’s number A Fibonacci’s number is an integer number generated using the following function: Assumed that: f(0) = 0 f(1) = 1 for a generic “n” Integer: f(n) = f(n-1) + f(n-2) For example, the first 20 Fibonacci’s number are: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 ...