已知模式串t=‘abcaabbabcab’编程写出完整的KMP算法、并输出每个字符对应的next函数值和nextval函数值。

KMP算法（Knuth-Morris-Pratt 算法），是一种用于字符串匹配的高效算法，通过预处理模式串，避免了不必要的字符串搜索。在Python中，我们可以编写如下的KMP函数，并计算每个字符对应的next函数值（即nextval函数）：

首先，我们需要定义两个辅助函数：
1. `build_next_table(pattern)`：生成next表
2. `kmp_search(text, pattern)`：实际的KMP搜索

下面是完整的代码：

def build_next_table(pattern):
    next_val = [0] * (len(pattern) + 1)
    j = 0
    for i in range(1, len(pattern)):
        while j > 0 and pattern[j] != pattern[i]:
            j = next_val[j - 1]
        if pattern[j] == pattern[i]:
            j += 1
        next_val[i] = j
    return next_val

def kmp_search(text, pattern):
    text_len = len(text)
    pattern_len = len(pattern)
    next_val = build_next_table(pattern)
    i, j = 0, 0

    while i < text_len:
        if text[i] == pattern[j]:
            i += 1
            j += 1
        elif j > 0:
            j = next_val[j - 1]
        else:
            i += 1
    return i - j == -pattern_len or i == text_len

# 示例
pattern = 'abcaabbabcab'
text = 'abcaabbabcabcb'
next_val = build_next_table(pattern)

print("Next function values:")
for index, val in enumerate(next_val[:-1]):
    print(f"At position {index}: {val}")

# 输出 nextval
for char, val in zip(pattern, next_val[:-1]):
    print(f"Character '{char}': Next value is {val}")