If we replace the body of the while loop of the quick-find algorithm (you can find it in a previous article) with the following code we have a program that meets the same specifications as the quick-find algorithm but performs fewer calculations for the act of union, to the expense of more calculations for act of finding. The ‘for’ loop and the ‘if’ operation that follows in this code determine the necessary and sufficient conditions in the array ‘id’ that p and q be linked. The act of union is implemented by the assignment id[i] = j.

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