最长公共子串（LCS）

(1) 找出两个字符串的最长公共子串

题目：输入两个字符串，找出两个字符串中最长的公共子串。

找两个字符串的最长公共子串，这个子串要求在原字符串中是连续的。

#include<iostream>
#include<string>
using namespace std;
int main()
{
string s1 = "GCCCTAGCCAGDE";
string s2 = "GCGCCAGTGDE ";
int len1 = s1.size();
int len2 = s2.size();
int** c = new int* [len1];
for (int i = 0; i < len1; i++)
{
c[i] = new int[len2];
memset(c[i], 0, sizeof(int)*len2);
}
int start = -1;
int end = -1;
int maxLen = 0;
for (int i = 0; i < len1; i++)
{
for (int j = 0; j < len2; j++)
{
if (s1[i] == s2[j])
{
int indexI = i == 0 ? 0 : (i - 1);
int indexJ = j == 0 ? 0 : (j - 1);
c[i][j] = c[indexI][indexJ] + 1;
if (c[i][j] > maxLen)
{
maxLen = c[i][j];
end = i;
start = i - c[i][j] + 1;
}
}
else
{
c[i][j] = 0;
}
}
}
if (maxLen != 0)
{
string res = s1.substr(start, maxLen);
cout << res << endl;
}
for (int i = 0; i < len1; i++)
{
delete[] c[i];
}
return 0;
}

(2) 找出两个字符串的最长公共子序列

题目：输入两个字符串，求两个字符串的最长公共子序列。

首先，最长公共子序列与最长公共子串不同，子序列不要求其在原字符串是连续的。例如字符串X={A,B,C,B,D,A,B}，Y={B,D,C,A,B,A}，则X与Y的最长公共子序列为Z={B,C,B,A};

#include<iostream>
#include<string>
using namespace std;
string getLongestSequence(string s1, string s2)
{
int len1 = s1.size();
int len2 = s2.size();
int** c = new int* [len1];
for (int i = 0; i < len1; i++)
{
c[i] = new int[len2];
memset(c[i], 0, sizeof(int)*len2);
}
int start = -1;
int end = -1;
int maxLen = 0;
for (int i = 0; i < len1; i++)
{
for (int j = 0; j < len2; j++)
{
if (s1[i] == s2[j])
{
int preMax = (i == 0 || j == 0) ? 0 : c[i - 1][j - 1];
c[i][j] = preMax + 1;
}
else
{
int preMax1 = (i == 0) ? 0 : c[i - 1][j];
int preMax2 = (j == 0) ? 0 : c[i][j - 1];
c[i][j] = max(preMax1, preMax2);
}
if (c[i][j] > maxLen)
{
maxLen = c[i][j];
}
}
}
string res(maxLen, '-');
for (int i = len1 - 1, j = len2 - 1, index = maxLen; i >= 0 && j >= 0;)
{
int preC1 = i == 0 ? -1 : c[i - 1][j];
//说明s1[i]字符不在最大子序列里
if (c[i][j] == preC1)
{
i--;
continue;
}
//说明s1[i]字符在最大子序列里
else
{
//更新结果
res[--index] = s1[i];
//说明s2[j]字符不在最大子序列里
int preC2 = j == 0 ? -1 : c[i][j - 1];
while (c[i][j] == preC2)
{
j--;
}
i--;
j--;
}
}
return res;
for (int i = 0; i < len1; i++)
{
delete[] c[i];
}
}
int main()
{
string s1 = "ABCBDAB";
string s2 = "BDCABA";
string res1 = getLongestSequence(s1, s2);
string res2 = getLongestSequence(s2, s1);
if (strcmp(res1.c_str(), res2.c_str()))
{
cout << res1 << endl;
cout << res2 << endl;
}
else
{
cout << res1 << endl;
}
return 0;
}