Minimum Size Subarray Sum

1. The obvious way

   Try all start/end pairs: O(n²).

2. The key insight

   All numbers are positive, so once the window total reaches the target you can try to make it shorter from the left; removing numbers can only lower the total. Both edges only move forward, so every number enters and leaves once: O(n).

3. The algorithm
   1. Window total = 0, left edge at the start, best = infinity.
   2. Add the next number on the right to the total.
   3. While the total is at least the target: note the window length, drop the left number and move the left edge on.
   4. At the end return best (0 if no window ever reached the target).

Watch it run

best 4

def min_sub_array_len(target, nums):
    left = 0
    total = 0
    best = float("inf")
    for right, number in enumerate(nums):
        total += number
        while total >= target:                       # enough: try a shorter run
            best = min(best, right - left + 1)
            total -= nums[left]
            left += 1
    return 0 if best == float("inf") else best

Now close this and write it again from memory, in the language you will use in the interview. Reattempt after 1 day, 7 days and about 30 days.