I&#x27;m pretty sure there is an additional (unstated) assumption that each element of each subarray is less than all elements of subsequent subarrays. Otherwise you could just take the largest sqrt(n) elements, sort them, and then randomly assign the other elements of the collection to their heaps and it would still meet the criteria he&#x27;s laid out, but the search algorithm he&#x27;s proposed wouldn&#x27;t work.<p>In fact, there&#x27;s an error in the search algorithm as well:<p>&gt; <i>Whenever the maximum element (first element in the subarray) is smaller than the searched value, we skip over that entire heap and go to the next one. In the worst case we&#x27;ll skip O(sqrt n) heaps.</i> When the max value in a heap is less than the searched element, <i>we found the heap and we run a linear search among O(sqrt n) elements.</i><p>For the unitalicized portion above, he means to say &quot;When the max value in a heap is greater than the searched element&quot;.