LCS，LIS，LPS

const int MAXN = 1e3 + 5;
int dp[MAXN][MAXN];
//HDU ~ 1159 ~ Common Subsequence
//最长公共子序列
int LCS(string a, string b)
{
memset(dp, 0, sizeof(dp));
int lena = a.size(), lenb = b.size();
for (int i = 1; i <= lena; i++)
{
for (int j = 1; j <= lenb; j++)
{
if (a[i-1] == b[j-1])
dp[i][j] = dp[i-1][j-1] + 1;
else
dp[i][j] = max(dp[i-1][j], dp[i][j-1]);
}
}
return dp[lena][lenb];
}
//最长公共子串
int LCS2(string a, string b)
{
memset(dp, 0, sizeof(dp));
int lena = a.size(), lenb = b.size(), ans = -1;
for (int i = 1; i <= lena; i++)
{
for (int j = 1; j <= lenb; j++)
{
if (a[i-1] == b[j-1])
{
dp[i][j] = dp[i-1][j-1] + 1;
ans = max(ans, dp[i][j]);
}
else dp[i][j] = 0;
}
}
return ans;
}
//最长单调递增子序列
//NYOJ ~ 17 ~ 最长单调递增子序列
int dp2[MAXN*MAXN];
int LIS(string a)
{
dp2[0] = a[0];
int ans = 1, len = a.size();
for(int i = 1; i < len; i++)
{
int pos = lower_bound(dp2, dp2 + ans, a[i]) - dp2;
if(pos < len) dp2[pos] = a[i];
else dp2[len++] = a[i];
}
return ans;
}
//最长回文子序列
//HDU ~ 4745 ~ Two Rabbits
int LPS(string a)
{
int len = a.size();
memset(dp, 0, sizeof(dp));
for (int i = len - 1; i >= 0; i--)
{
dp[i][i] = 1;
for (int j = i+1; j < len; j++)
{
if (a[i] == a[j])
dp[i][j] = dp[i+1][j-1]+2;
else
dp[i][j] = max(dp[i+1][j], dp[i][j-1]);
}
}
return dp[0][len - 1];
}

LCS打印路径：
51nod ~ 1006 ~ 最长公共子序列#include<bits/stdc++.h>
using namespace std;
const int MAXN = 1e3 + 5;
string a, b;
int lena, lenb, dp[MAXN][MAXN], path[MAXN][MAXN];
void dfs(int x, int y)
{
if (path[x][y] == 1)
{
dfs(x-1, y-1);
printf("%c", a[x-1]);
}
if (path[x][y] == 2)
dfs(x-1, y);
if (path[x][y] == 3)
dfs(x, y-1);
}
int LCS()
{
for (int i = 1; i <= lena; i++)
{
for (int j = 1; j <= lenb; j++)
{
if (a[i-1] == b[j-1])
{
dp[i][j] = dp[i-1][j-1] + 1;
path[i][j] = 1;
}
else
{
if (dp[i-1][j] > dp[i][j-1])
{
dp[i][j] = dp[i-1][j];
path[i][j] = 2;

4000
}
else
{
dp[i][j] = dp[i][j-1];
path[i][j] = 3;
}
}
}
}
return dp[lena][lenb];
}
int main()
{
ios::sync_with_stdio(false);
while (cin >> a >> b)
{
memset(dp, 0, sizeof(dp));
memset(path, 0, sizeof(path));
lena = a.size(), lenb = b.size();
int len = LCS();
dfs(lena, lenb);
cout << endl;
}
return 0;
}
/*
abcicba
abdkscab
acca
cbbc
*/