The code snippet has a quadratic time complexity, O(N²), because the total number of operations is based on an arithmetic series that sums up to (N^2 + N)/2, which is dominated by the N^2 term.
To determine the time complexity of the provided code snippet, we need to analyze the number of operations it would perform in terms of the input size, N. The outer loop runs N times, and for each iteration of the outer loop, the inner loop runs a number of times equal to the current value of i, which increments with each run of the outer loop.
The inner loop starts from 0 and goes until it is equal to i. So, during the course of the outer loop's execution, the inner loop will run 1 + 2 + 3 + ... + N times. This series is an arithmetic series that can be summed up as N(N+1)/2, which simplifies to (N^2 + N)/2. This means the complexity is dominated by N^2, giving us a quadratic time complexity, which is represented by O(N²).