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    <p>So here is the algorithm I thought it would work:</p> <ol> <li>Sort the volumes from largest to smallest.</li> <li>Divide the largest cake to 1...k people, i.e., target = volume[0]/i, where i = 1,2,3,4,...,k</li> <li>If target would lead to total number of pieces greater than k, decrease the number i and try again.</li> <li>Find the first number <strong>i</strong> that will result in total number of pieces greater than or equal to K but <strong>(i-1)</strong> will lead to a total number of cakes less than k. Record this volume as baseVolume.</li> <li>For each remaining cake, find the smallest fraction of remaining volume divide by number of people, i.e., division = (V_cake - (baseVolume*(Math.floor(V_cake/baseVolume)) ) / Math.floor(V_cake/baseVolume)</li> <li>Add this amount to the baseVolume(baseVolume += division) and recalculate the total pieces all volumes could divide. If the new volume result in less pieces, return previous value, otherwise, repeat step 6.</li> </ol> <p>Here are the java codes:</p> <pre><code>public static int getKonLagestCake(Integer[] sortedVolumesList, int k) { int result = 0; for (int i = k; i &gt;= 1; i--) { double volumeDividedByLargestCake = (double) sortedVolumesList[0] / i; int totalNumber = totalNumberofCakeWithGivenVolumn( sortedVolumesList, volumeDividedByLargestCake); if (totalNumber &lt; k) { result = i + 1; break; } } return result; } public static int totalNumberofCakeWithGivenVolumn( Integer[] sortedVolumnsList, double givenVolumn) { int totalNumber = 0; for (int volume : sortedVolumnsList) { totalNumber += (int) (volume / givenVolumn); } return totalNumber; } public static double getMaxVolume(int[] volumesList, int k) { List&lt;Integer&gt; list = new ArrayList&lt;Integer&gt;(); for (int i : volumesList) { list.add(i); } Collections.sort(list, Collections.reverseOrder()); Integer[] sortedVolumesList = new Integer[list.size()]; list.toArray(sortedVolumesList); int previousValidK = getKonLagestCake(sortedVolumesList, k); double baseVolume = (double) sortedVolumesList[0] / (double) previousValidK; int totalNumberofCakeAvailable = totalNumberofCakeWithGivenVolumn(sortedVolumesList, baseVolume); if (totalNumberofCakeAvailable == k) { return baseVolume; } else { do { double minimumAmountAdded = minimumAmountAdded(sortedVolumesList, baseVolume); if(minimumAmountAdded == 0) { return baseVolume; }else { baseVolume += minimumAmountAdded; int newTotalNumber = totalNumberofCakeWithGivenVolumn(sortedVolumesList, baseVolume); if(newTotalNumber == k) { return baseVolume; }else if (newTotalNumber &lt; k) { return (baseVolume - minimumAmountAdded); }else { continue; } } }while(true); } } public static double minimumAmountAdded(Integer[] sortedVolumesList, double volume) { double mimumAdded = Double.MAX_VALUE; for(Integer i:sortedVolumesList) { int assignedPeople = (int)(i/volume); if (assignedPeople == 0) { continue; } double leftPiece = (double)i - assignedPeople*volume; if(leftPiece == 0) { continue; } double division = leftPiece / (double)assignedPeople; if (division &lt; mimumAdded) { mimumAdded = division; } } if (mimumAdded == Double.MAX_VALUE) { return 0; }else { return mimumAdded; } } </code></pre> <p>Any Comments would be appreciated. Thanks</p>
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