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    <p>I think the following C# program should work. It uses the <a href="http://en.wikipedia.org/wiki/Branch_and_bound" rel="nofollow noreferrer">branch and bound method</a> and works for arrays of any number of dimensions.</p> <pre><code> using System; using System.Collections.Generic; namespace SO_strides { sealed class Dimension { public int Min { get; private set; } public int Max { get; private set; } public int Stride { get; private set; } private Dimension() { } public Dimension(int max, int stride) { Min = 0; Max = max; Stride = stride; } public Dimension[] Halve() { if (Max == Min) throw new InvalidOperationException(); int split = Min + (Max - Min) / 2; return new Dimension[] { new Dimension { Min = Min, Max = split, Stride = Stride }, new Dimension { Min = split + 1, Max = Max, Stride = Stride } }; } } sealed class ArrayPart { public int BaseAddr { get; private set; } public Dimension[] Dimensions { get; private set; } public int FirstNonconstantIndex { get; private set; } int? min; public int Min { get { if (min == null) { int result = BaseAddr; foreach (Dimension dimension in Dimensions) result += dimension.Min * dimension.Stride; min = result; } return min.Value; } } int? max; public int Max { get { if (max == null) { int result = BaseAddr; foreach (Dimension dimension in Dimensions) result += dimension.Max * dimension.Stride; max = result; } return max.Value; } } public int Size { get { return Max - Min + 1; } } public ArrayPart(int baseAddr, Dimension[] dimensions) : this(baseAddr, dimensions, 0) { Array.Sort(dimensions, (d1, d2) =&gt; d2.Stride - d1.Stride); } private ArrayPart(int baseAddr, Dimension[] dimensions, int fni) { BaseAddr = baseAddr; Dimensions = dimensions; FirstNonconstantIndex = fni; } public bool CanHalve() { while (FirstNonconstantIndex &lt; Dimensions.Length &amp;&amp; Dimensions[FirstNonconstantIndex].Min == Dimensions[FirstNonconstantIndex].Max) FirstNonconstantIndex++; return FirstNonconstantIndex &lt; Dimensions.Length; } public ArrayPart[] Halve() { Dimension[][] result = new Dimension[2][]; Dimension[] halves = Dimensions[FirstNonconstantIndex].Halve(); for (int i = 0; i &lt; 2; i++) { result[i] = (Dimension[])Dimensions.Clone(); result[i][FirstNonconstantIndex] = halves[i]; } return new ArrayPart[] { new ArrayPart(BaseAddr, result[0], FirstNonconstantIndex), new ArrayPart(BaseAddr, result[1], FirstNonconstantIndex) }; } } sealed class CandidateSet { public ArrayPart First { get; private set; } public ArrayPart Second { get; private set; } public CandidateSet(ArrayPart first, ArrayPart second) { First = first; Second = second; } public bool Empty { get { return First.Min &gt; Second.Max || Second.Min &gt; First.Max; } } public CandidateSet[] Halve() { int firstSize = First.Size; int secondSize = Second.Size; CandidateSet[] result; if (firstSize &gt; secondSize &amp;&amp; First.CanHalve()) { ArrayPart[] halves = First.Halve(); result = new CandidateSet[] { new CandidateSet(halves[0], Second), new CandidateSet(halves[1], Second) }; } else if (Second.CanHalve()) { ArrayPart[] halves = Second.Halve(); result = new CandidateSet[] { new CandidateSet(First, halves[0]), new CandidateSet(First, halves[1]) }; } else throw new InvalidOperationException(); return result; } public static bool HasSolution(ArrayPart first, ArrayPart second) { Stack&lt;CandidateSet&gt; stack = new Stack&lt;CandidateSet&gt;(); stack.Push(new CandidateSet(first, second)); bool found = false; while (!found &amp;&amp; stack.Count &gt; 0) { CandidateSet candidate = stack.Pop(); if (candidate.First.Size == 1 &amp;&amp; candidate.Second.Size == 1) found = true; else { foreach (CandidateSet half in candidate.Halve()) if (!half.Empty) stack.Push(half); } } return found; } } static class Program { static void Main() { Console.WriteLine( CandidateSet.HasSolution( new ArrayPart(2, new Dimension[] { new Dimension(1, 1), new Dimension(2, 4) }), new ArrayPart(4, new Dimension[] { new Dimension(1, 1), new Dimension(2, 4) }) ) ); } } } </code></pre>
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    1. COThanks! That seems like a fairly clever general solution indeed. It will perform poorly on some of the cases we care about (see the note I added to the question), but I think we could treat those with some special case tests -- for instance, check if the base values are different modulo the least common denominator of all the strides; and check if the larger strides are the same and if so compare "rows".
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