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    <p>The wording is a little confusing, but I think you mean the maximum of</p> <ul> <li>the maximum length of a path that starts at any node and then only goes to the left, or</li> <li>the maximum length of a path that starts at any node and then only goes to the right.</li> </ul> <p>You do this in two passes, one to find the max left path and one to find the max right path (and then take the max of those two). Or you can do it in a single pass that does both at once.</p> <p>For every node, you want to know three values:</p> <ol> <li>the length of the left path starting at that node,</li> <li>the length of the right path starting at that node, and</li> <li>the length of the longest path starting at that node or one of its descendants.</li> </ol> <p>If you are doing this recursively, this means the recursion should return these three values, probably as a small array or as a simple three-field object.</p> <p>This would look something like</p> <pre><code>Results calculate(Tree node) { if (node == null) return new Results(0,0,0); else { Results leftResults = calculate(node.left); Results rightResults = calculate(node.right); int leftLength = 1 + leftResults.leftLength; int rightLength = 1 + rightResults.rightLength; int maxLength = Math.max(Math.max(leftLength, rightLength), Math.max(leftResults.maxLength, rightResults.maxLength)); return new Results(leftLength, rightLength, maxLength); } } </code></pre> <p>and the overall result would just be <code>calculate(root).maxLength</code>.</p>
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    1. POmaximum length of a descending path in a tree which always goes left|right
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    1. USChris Okasaki
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    1. POmaximum length of a descending path in a tree which always goes left|right
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    1. COI had no clue that the OP meant this, but reading your answer, it makes a lot of sense! +1 Btw, it's quite useless to drag `Results.maxLength` all around your tree, while you're only interested in the maximum of left and right on the root.
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      1. USVincent van der Weele
    2. COrecursion is allowed
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