I’ve been learning the Introduction to Algorithms on MIT Open Course, and I got confused about the code of merge sort. Does it not seem to have added the L[i] or the R[j] into the set A?
Here’s the code.

def merge_sort(A, a = 0, b = None):             # T(b - a = n)
    '''Sort A[a:b]'''
    if b is None: b = len(A)                    # O(1)
        if 1 < b - a:                           # O(1)
            c = (a + b + 1) // 2                # O(1)
            merge_sort(A, a, c)                 # T(n / 2)
            merge_sort(A, c, b)                 # T(n / 2)
            L, R = A[a:c], A[c:b]               # O(n)
            merge(L, R, A, len(L), len(R), a, b)# S(n)

def merge(L, R, A, i, j, a, b):                 # S(b - a = n)
'''Merge sorted L[:i] and R[:j] into A[a:b]'''
    if a < b:                                   # O(1)
        if (j <= 0) or (i > 0 and L[i - 1] > R[j - 1]): # O(1)
            A[b - 1] = L[i - 1]                 # O(1)
            i = i - 1                           # O(1)
        else:                                   # O(1)
            A[b - 1] = R[j - 1]                 # O(1)
            j = j - 1                           # O(1)
            merge(L, R, A, i, j, a, b - 1)      # S(n - 1)

I tried to analyze the code, including the recursion part. I thought it only made the A[b-1] = L[j-1] or R[j-1], and recursively assign every element in A[:b-1], but there’s no statement to assign L[i] or R[j] to the A[b], maybe it’s my wrong view. I would be grateful if someone can help me about this problem.