what's the Big-Oh complexity for recursive relations T(n)=T(n-1)+n
Question
what's the Big-Oh complexity for recursive relations T(n)=T(n-1)+n
Solution
The Big-Oh complexity for the recursive relation T(n) = T(n-1) + n can be found by solving the recurrence relation.
Step 1: Identify the base case. In this case, it's not explicitly given, but we can assume T(1) = 1 as a reasonable base case.
Step 2: Expand the recurrence relation.
T(n) = T(n-1) + n = T(n-2) + (n-1) + n = T(n-3) + (n-2) + (n-1) + n = ... = T(1) + 2 + 3 + ... + n
Step 3: Recognize the pattern. The right side of the equation is the sum of the first n integers, which is a well-known formula n*(n+1)/2.
Step 4: Substitute the pattern back into the equation.
T(n) = n*(n+1)/2
Step 5: Simplify the equation to find the Big-Oh complexity. The highest power of n in the equation is 2, so the Big-Oh complexity is O(n^2).
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