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    <p>Well, I get little bit bored so play around with Java to have some experience, can be poorly coded and without tuning, as I am trying to increase my coding skill, comments are welcome. My computer able to answer me for small arrays:)</p> <p>Output looks like:</p> <pre><code>Largest rectangle range is ; 48 ------------------------------------------------- input values; [ 4,2,4,4,6,8,9 ] ------------------------------------------------- Array details of the rectangle: A1: [ 6 ] B1: [ 8 ] A2: [ 2,4 ] B2: [ 4,4 ] </code></pre> <p>combination.class using Kenneth algorithm;</p> <p>import java.math.BigInteger;</p> <pre><code>public class Combination { /** * Burak */ private int[] a; private int n; private int r; private BigInteger numLeft; private BigInteger total; public Combination (int n, int r) { if (r &gt; n) { throw new IllegalArgumentException (); } if (n &lt; 1) { throw new IllegalArgumentException (); } this.n = n; this.r = r; a = new int[r]; BigInteger nFact = getFactorial (n); BigInteger rFact = getFactorial (r); BigInteger nminusrFact = getFactorial (n - r); total = nFact.divide (rFact.multiply (nminusrFact)); reset (); } //------ // Reset //------ public void reset () { for (int i = 0; i &lt; a.length; i++) { a[i] = i; } numLeft = new BigInteger (total.toString ()); } //------------------------------------------------ // Return number of combinations not yet generated //------------------------------------------------ public BigInteger getNumLeft () { return numLeft; } //----------------------------- // Are there more combinations? //----------------------------- public boolean hasMore () { return numLeft.compareTo (BigInteger.ZERO) == 1; } //------------------------------------ // Return total number of combinations //------------------------------------ public BigInteger getTotal () { return total; } //------------------ // Compute factorial //------------------ private static BigInteger getFactorial (int n) { BigInteger fact = BigInteger.ONE; for (int i = n; i &gt; 1; i--) { fact = fact.multiply (new BigInteger (Integer.toString (i))); } return fact; } //-------------------------------------------------------- // Generate next combination (algorithm from Rosen p. 286) //-------------------------------------------------------- public int[] getNext () { if (numLeft.equals (total)) { numLeft = numLeft.subtract (BigInteger.ONE); return a; } int i = r - 1; while (a[i] == n - r + i) { i--; } a[i] = a[i] + 1; for (int j = i + 1; j &lt; r; j++) { a[j] = a[i] + j - i; } numLeft = numLeft.subtract (BigInteger.ONE); return a; } } </code></pre> <p>And main Combinator.class;</p> <p>import java.util.*;</p> <p>public class Combinator {</p> <pre><code>/** * @param args */ private static int[] ad; private static int[] bd; private static String a1; private static String a2; private static String b1; private static String b2; private static int bestTotal =0; public static void main(String[] args) { int[] array={4,2,4,4,6,8,9}; getBestCombination(array, 1); if(bestTotal &lt;= 0){ System.out.println("System couldnt create any rectangle."); }else{ System.out.println("Largest rectangle range is ; " + bestTotal); System.out.println("-------------------------------------------------"); System.out.println("input values; " + parseArrayToString(array)); System.out.println("-------------------------------------------------"); System.out.println("Array details of the rectangle:"); System.out.println("A1: " + a1); System.out.println("B1: " + b1); System.out.println("A2: " + a2); System.out.println("B2: " + b2); } } private static void getBestCombination(int[] array, int level){ int[] a; int[] b; int bestPerimeter = getTotal(array,true); Vector&lt;Vector&lt;Integer&gt;&gt; results = null; for(int o=array.length-1;o&gt;=1;o--){ for(int u=bestPerimeter;u&gt;=1;u--){ results = Combinator.compute (array, o, u); if(results.size() &gt; 0){ for(int i=0;i&lt;results.size();i++){ a = new int[results.elementAt(i).size()]; for(int j = 0;j&lt;results.elementAt(i).size();j++){ a[j] = results.elementAt(i).elementAt(j); } b = removeItems(array, results.elementAt(i)); if(level == 1){ getBestCombination(a,2); getBestCombination(b,3); }else if(level == 2){ ad = a; bd = b; }else{ getBestCombination(a,4); getBestCombination(b,4); if(getTotal(ad, false) == getTotal(a, false) &amp;&amp; getTotal(bd, false) == getTotal(b, false)){ if(bestTotal&lt;(getTotal(ad, false)*getTotal(bd, false))){ bestTotal = getTotal(ad, false)*getTotal(bd, false); a1 = parseArrayToString(ad); a2 = parseArrayToString(a); b1 = parseArrayToString(bd); b2 = parseArrayToString(b); } }else if(getTotal(ad, false) == getTotal(b, false) &amp;&amp; getTotal(bd, false) == getTotal(a, false)){ if(bestTotal&lt;(getTotal(ad, false)*getTotal(bd, false))){ bestTotal = getTotal(ad, false)*getTotal(bd, false); a1 = parseArrayToString(ad); a2 = parseArrayToString(b); b1 = parseArrayToString(bd); b2 = parseArrayToString(a); } } } } } } } } private static String parseArrayToString(int[] items){ String s = "[ "; for(int i=0;i&lt;items.length;i++){ if(i!=items.length-1){ s = s + items[i] + ","; }else{ s = s + items[i]; } } s = s + " ]"; return s; } @SuppressWarnings("rawtypes") private static int[] removeItems(int[] array, Vector items){ ArrayList&lt;Integer&gt; res = new ArrayList&lt;Integer&gt;(); for(int i=0;i&lt;array.length;i++){ res.add(array[i]); } for(int u = 0;u&lt;items.size();u++){ res.remove(items.elementAt(u)); } int[] results = new int[res.size()]; for(int o=0;o&lt;res.size();o++){ results[o] = res.get(o); } return results; } private static int getTotal(int[] array,boolean bestPerimeter){ int sum = 0; for (int i = 0; i &lt; array.length; i++) { sum += array[i]; } if(bestPerimeter == true){ if(sum%2!=0){ sum = sum -1; } sum = sum/2; } //System.out.println(sum); return sum; } @SuppressWarnings("rawtypes") private static int getSum (Vector v) { int sum = 0; Integer n; for (int i = 0; i &lt; v.size (); i++) { n = (Integer) v.elementAt(i); sum += n.intValue (); } return sum; } @SuppressWarnings({ "rawtypes", "unchecked" }) public static Vector&lt;Vector&lt;Integer&gt;&gt; compute (int[] array, int atATime, int desiredTotal) { int[] indices; Combination gen = new Combination (array.length, atATime); Vector results = new Vector (); Vector combination; int sum; Integer intObj; while (gen.hasMore ()) { combination = new Vector (); indices = gen.getNext (); for (int i = 0; i &lt; indices.length; i++) { intObj = new Integer (array[indices[i]]); combination.addElement (intObj); } sum = getSum (combination); if (sum == desiredTotal) { Collections.sort (combination); if (!results.contains (combination)) { results.addElement (combination); } } } return results; } </code></pre> <p>}</p>
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    1. POConstruct the largest possible rectangle out of line segments of given lengths
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