Implement a Python function that finds the longest common subsequence between two strings.
def longest_common_subsequence(s1, s2):
    m = len(s1)
    n = len(s2)

    # Create a table to store lengths of the longest common subsequences
    dp = [[0] * (n + 1) for _ in range(m + 1)]

    # Fill the table from bottom up manner
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if s1[i - 1] == s2[j - 1]:
                dp[i][j] = dp[i - 1][j - 1] + 1
            else:
                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])

    # Reconstruct the longest common subsequence
    lcs = []
    i, j = m, n
    while i > 0 and j > 0:
        if s1[i - 1] == s2[j - 1]:
            lcs.append(s1[i - 1])
            i -= 1
            j -= 1
        elif dp[i - 1][j] > dp[i][j - 1]:
            i -= 1
        else:
            j -= 1

    return ''.join(reversed(lcs))


# Test example
s1 = "ABCDGH"
s2 = "AEDFHR"
print(longest_common_subsequence(s1, s2))  # Output: "ADH"