最长公共子序列

参考博客：

　http://www.cnblogs.com/sasuke-/p/5396843.html

http://www.cnblogs.com/huangxincheng/archive/2012/11/11/2764625.html

理解好这张图。

就是开个数组flag来判断每个点是怎么更新的，因为箭头只有三个方向，输出路径时只需要找斜着的就行了。

输出路径的代码：

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
using namespace std;
const int maxn = 10;
char s[maxn], t[maxn],re[maxn];
int dp[maxn][maxn],flag[maxn][maxn];
int cnt;

void print(int x, int y)
{
    if (x == 0 || y == 0) {

        for (int i = cnt-1; i >= 0; i--)
            cout << re[i];
        cout << endl;
        return;
    }
    if (flag[x][y] == 2) {
        re[cnt++] = s[x];
        print(x - 1, y - 1);
    }if (flag[x][y] == 1) {
        print(x - 1, y);
    }
    else if(flag[x][y]==3)
    {
        print(x, y - 1);
    }
}

int main()
{
    while (scanf("%s%s",s+1,t+1)==2)
    {
        memset(re, '', sizeof(re));
        cnt = 0;
        int lens = strlen(s + 1);
        int lent = strlen(t + 1);

        for (int i = 0; i <= lens; i++) dp[i][0] = 0;
        for (int j = 0; j <= lent; j++) dp[0][j] = 0;
        dp[0][0] = 0;

        for (int i = 1; i <= lens; i++)
        {
            for (int j = 1; j <= lent; j++)
            {
                if (s[i] == t[j]) {
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                    flag[i][j] = 2;
                }
                else if (dp[i - 1][j] >=dp[i][j - 1]) {
                    dp[i][j] = dp[i - 1][j];
                    flag[i][j] = 1;
                }
                else {
                    dp[i][j] = dp[i][j-1];
                    flag[i][j] = 3;
                }
            }
        }
        cout << dp[lens][lent] << endl;
        print(lens, lent);

    }
    return 0;
}