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Both Iteration and Recursion run a part of an algorithm repeatedly. We typically use them when, in a part of an algorithm, we have to do or calculate something (i,e. the logic remains the same though the data changes) for a certain number of times. However,in Recursion, we simply run a loop for a certain number of times in the algorithm, such as printing a statement ten times is recursion. In Iteration, we specifically run a loop, such that, the second run of the loop makes use of the computation/result from the first run, the third run (or iteration) makes use of the result from the second run and so on. Hence, in Iteration, the n th run of the loop makes use of the result from the n-1 th run. Consider the following example for calculating the summation, which we will denote as sum(n), meaning n + n-1 + n-2 + n-3 + ... + 2 + 1 + 0. Hence, sum(5) = 5+4+3+2+1+0 = 15. Now we will write psuedo-code to calculate the sum(n) using Iteration and Recursion. Iterative Version:- ----------------- start sum(n) { i = 0; total = 0; do while i is not greater than n, { total = total + i; i = i + 1; } return total; } Recursive Version:- ----------------- start sum(n) { if n is equal to 0, then return(0); otherwise, return (n + sum(n - 1)); } Notice that the Iterative version calculates the sum by repeatedly accumulating the sum in the variable total. In contrast, the recursive version simply repeatedly calls itself, each time with a decremented value.

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