最长公共子序列问题伪代码输出字符串
时间: 2024-07-20 16:00:38 浏览: 49
最长公共子序列(Longest Common Subsequence, LCS)问题是一个经典的计算机科学问题,用于找到两个或多个字符串中最长的共同子序列,但这些子序列不一定连续。下面是使用动态规划方法求解LCS问题的一种简单伪代码:
```plaintext
function longest_common_subsequence(string1, string2):
m = length of string1
n = length of string2
L = matrix with dimensions (m+1) x (n+1) initialized with zeros
for i from 1 to m:
for j from 1 to n:
if string1[i-1] == string2[j-1]:
L[i][j] = L[i-1][j-1] + 1
else:
L[i][j] = max(L[i-1][j], L[i][j-1])
// The last element of the L matrix contains the length of LCS
lcs_length = L[m][n]
// Build the LCS by backtracking through the matrix
lcs = ""
i = m
j = n
while i > 0 and j > 0:
if string1[i-1] == string2[j-1]:
lcs = string1[i-1] + lcs
i -= 1
j -= 1
elif L[i-1][j] > L[i][j-1]:
i -= 1
else:
j -= 1
return lcs
// 示例:
string1 = "ABCBDAB"
string2 = "BDCAB"
result = longest_common_subsequence(string1, string2)
print("最长公共子序列是:", result)
```
执行这段伪代码后,会输出给定字符串`"ABCBDAB"`和`"BDCAB"`的最长公共子序列。请注意,实际应用中可能需要根据编程语言的具体语法调整。