例：计算模式串"abaabcac"的KMP算法中next函数值
由函数定义
n e x t [ j ] = { 0 , j = 1 M a x { k ∣ 1 < k < j 且 " t 1 t 2 ⋅ ⋅ ⋅ t k − 1 " = " t j − k + 1 t j − k + 2 ⋅ ⋅ ⋅ t j − 1 " } 1 , k = 1 next[j]=\left\{ \begin{aligned} 0 , & \ j=1 \\ Max & \{k|1<k<j且"t_1t_2···t_{k-1}"="t_{j-k+1}t_{j-k+2}···t_{j-1}" \} \\ 1 , & \ k=1 \end{aligned} \right. next[j]=⎩ ⎨ ⎧0,Max1, j=1{k∣1<k<j且"t1t2⋅⋅⋅tk−1"="tj−k+1tj−k+2⋅⋅⋅tj−1"} k=1
可得 next[1] = 0，其修正值 nextval[1] = 0
对模式串进行自我匹配的过程如图所示：（主串指针i，子串指针j）
故计算得到的函数值为：
| 模式串 | a | b | a | a | b | c | a | c |
|---|---|---|---|---|---|---|---|---|
j | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
next[j] | 0 | 1 | 1 | 2 | 2 | 3 | 1 | 2 |
nextval[j] | 0 | 1 | 0 | 2 | 0 | 3 | 0 | 2 |
