Final answer:
To sum elements in an n×n array using recursion, a recursive function is defined to iterate through each element, adding its value to the sum. The running time of this recursive algorithm is O(n^2), as each of the n² elements is visited once.
Step-by-step explanation:
Recursion to Compute Sum of Two-Dimensional Array
To compute the sum of all elements in an n×n two-dimensional array of integers using recursion, you can define a recursive function that takes the array, its size, and position indices as parameters. The base case of the recursion could be when the function reaches the last element of the array. For each recursive call, you can add the value of the current element to the sum obtained from the recursive call of the next element (either in the current row or the new row). Here's a step-by-step process:
Define the recursive function with parameters for the array, current row, current column, and the size of the array.If the current row or column is equal to the array size, return 0 - the base case.Add the current element to the result of the recursive call on the next element.For each row, once the last column is reached, recursively call the function for the first column of the next row.
The running time of this algorithm is O(n^2), since each element of the array is accessed exactly once in a single recursive call, and there are a total of n² elements in the array.