kindergarten_adventures.py

# source: https://www.hackerrank.com/challenges/kindergarten-adventures
# video: https://youtu.be/9vcrruySa9s
def sanitize_index(index, n):
    # index already valid
    if 0 <= index and index < n:
        return index
    
    # negative index
    if index < 0:
        return n + index

    # index out of range
    return index % n # CORRECTION. Thanks to Naman Goyal

def solve(t):
    n = len(t)
    running_sum_builder = [0] * n

    for i, value in enumerate(t): # O(n)
        if not value or value == n: # skip 0 and max value (student never finishes)
            continue
        index_to_start_counting = sanitize_index(i - value + 1, n) # add 1 for math
        index_to_stop_counting  = sanitize_index(i + 1, n)
        # if interval contains first index, then we should increment it by 1, since we're
        # starting there (we don't care about ending at )
        if index_to_stop_counting <= index_to_start_counting:
            running_sum_builder[0] += 1

        running_sum_builder[index_to_start_counting] += 1
        running_sum_builder[index_to_stop_counting]  -= 1
    
    min_counter = float("inf")
    best_starting_i = None
    running_sum = 0
    for starting_i, val in enumerate(running_sum_builder): # O(n)
        running_sum += val
        if running_sum < min_counter:
            min_counter = running_sum
            best_starting_i = starting_i
    
    return best_starting_i + 1 # not using zero-indexing
    # Total Time Complexity = O(n)

Thanks, minor error in Line 12-13

# index out of range
    return n % index

Should be

# index out of range
    return index % n

Thanks! I've made this correction.