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    <p>I don't know if you have test cases, try the code below. It is a dynamic-programming approach.</p> <pre><code>1] exp: given 1/2^i, find the largest i as exp. Eg. 1/32 returns 5. 2] max: 10^exp where exp=i. 3] create an array of size max+1 to hold all possible sums of the elements of V. Actually the array holds the indexes, since that's what you want. 4] dynamically compute the sums (all invalids remain null) 5] the last while loop finds the nearest correct answer. </code></pre> <p>Here is the code:</p> <pre><code>public class Subset { public static List&lt;Integer&gt; subsetSum(double[] V, double r) { int exp = exponent(V); int max = (int) Math.pow(10, exp); //list to hold all possible sums of the elements in V List&lt;Integer&gt; indexes[] = new ArrayList[max + 1]; indexes[0] = new ArrayList();//base case //dynamically compute the sums for (int x=0; x&lt;V.length; x++) { int u = (int) (max*V[x]); for(int i=max; i&gt;=u; i--) if(null != indexes[i-u]) { List&lt;Integer&gt; tmp = new ArrayList&lt;Integer&gt;(indexes[i - u]); tmp.add(x); indexes[i] = tmp; } } //find the best answer int i = (int)(max*r); int j=i; while(null == indexes[i] &amp;&amp; null == indexes[j]) { i--;j++; } return indexes[i]==null || indexes[i].isEmpty()?indexes[j]:indexes[i]; }// subsetSum private static int exponent(double[] V) { double d = V[V.length-1]; int i = (int) (1/d); String s = Integer.toString(i,2); return s.length()-1; }// summation public static void main(String[] args) { double[] V = {1/2.,1/4.,1/8.,1/16.,1/32.}; double r = 0.6, s=0.3,t=0.256652; System.out.println(subsetSum(V,r));//[0, 3, 4] System.out.println(subsetSum(V,s));//[1, 3] System.out.println(subsetSum(V,t));//[1] } }// class </code></pre> <p>Here are results of running the code:</p> <pre><code>For 0.600000 get 0.593750 =&gt; [0, 3, 4] For 0.300000 get 0.312500 =&gt; [1, 3] For 0.256652 get 0.250000 =&gt; [1] For 0.700000 get 0.687500 =&gt; [0, 2, 3] For 0.710000 get 0.718750 =&gt; [0, 2, 3, 4] </code></pre>
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    1. COInterestingly, we do not find the same answer for `0.3` (I find `{1, 3} = 0.3125 (+0.0125)` you find `{1, 4} = 0.28125 (-0.01875)`). Is this a typo or does your code never approximate from above ?
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    2. COTry running the code. I provide some additional test results.
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    3. COIt was a typo then :) As for running, I don't know which strange language it's written in, but it seems way to verbose for me to bother anyway.
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