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Problem solution · Java

CCC 2008 S2 - Pennies in the Ring

CCC 2008 S2 - Pennies in the Ring: a Java solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to CCCSolutions.

Technique
Direct simulation
Source
CCCSolutions
Length
50 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Direct simulation

For CCC 2008 S2 - Pennies in the Ring, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 50 lines of Java from the credited upstream file ccc08s2.java.
  • The implementation visibly relies on sequence storage.
  • 2 loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from CCCSolutions by CCCSolutions contributors · Milliken Mills High School and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeCCC 2008 S2 - Pennies in the Ring · JavaJava
Use this to learn the idea, then write your own version.
// CCC 2008//// S2: Pennies in the Ring//// This is a relatively simple geometry problem.//// Think of the cirles as four quadrants, plus the centre.// Calculate the pennies in the 1st quadrant, then the answer// is 4 times that, plus the central penny on the origin.//// to calculate the pennies in a quadrant I calculate the // pennies above the point x=1, then above x=2, ...// the # pennies is just the integer value of the height // of the circle at that point.// One trick: don't forget to add the penny on the x-axis// (hence the +1 inside the loop)//// I ensure all calculations are done in the double world// and only converted to integers at the last moment.// import java.awt.*;import hsa.*; public class CCC2008S2PenniesInTheRing{    static Console c;     public static void main (String[] args)    { 	int radius, pennies;	double r2;	c = new Console ();	TextInputFile f = new TextInputFile ("s2.5.in"); 	radius = f.readInt ();	while (radius != 0)	{	    pennies = 0;	    r2 = (double) (radius) * radius;	    for (int x = 1 ; x <= radius ; x++)		pennies += (int) Math.sqrt (r2 - (double) x * x) + 1;	    pennies = 4 * pennies + 1;	    c.println (pennies);	    radius = f.readInt ();	}    }}

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