最长公共子序列

 

	a	b	c	f	b	c
a	1	1	1	1	1	1
b	1	2	2	2	2	2
f	1	2	2	3	3	3
c	1	2	3	3	3	4
a	1	2	3	3	3	4
b	1	2	3	3	4	4

 

 测试数据：

abfcab
abcfbc

输出结果：

4
a b f c


0 2 2 2 2 2
1 0 2 2 0 2
1 1 1 0 2 2
1 1 0 1 1 0
0 1 1 1 1 1
1 0 1 1 0 1


1 1 1 1 1 1
1 2 2 2 2 2
1 2 2 3 3 3
1 2 3 3 3 4
1 2 3 3 3 4
1 2 3 3 4 4
请按任意键继续. . .

 

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

const int MAXN = 1005;
int dp[MAXN][MAXN];
int flag[MAXN][MAXN];
char dest[MAXN];
char str[MAXN];

int LCS(int x, int y)
{
	for(int i=1;i<=x;i++)
	{
		for(int j=1;j<=y;j++)
		{
			if(dest[i-1] == str[j-1])
			{
				dp[i][j] = dp[i-1][j-1] + 1;
				flag[i][j] = 0;
			}
			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] = 2;
			}
		}
	}
	return dp[x][y];
}

void ShowLCS(int x, int y)
{
	if(x == 0 || y == 0) return;
	if(flag[x][y] == 0)
	{
		ShowLCS(x-1,y-1);
		cout<<dest[x-1]<<" ";//第一行第一列为空数据区
	}
	else if(flag[x][y] == 1)
	{
		ShowLCS(x-1,y);
	}
	else
	{
		ShowLCS(x,y-1);
	}
}

int main()
{
	freopen("in.txt","r",stdin);
	cin>>dest>>str;
	int dest_len = strlen(dest);
	int str_len = strlen(str);
	cout<<LCS(dest_len,str_len)<<endl;
	ShowLCS(dest_len,str_len);
	
	cout<<"\n\n"; 
	for(int i=0;i<=dest_len;i++)
	{
		for(int j=0;j<=str_len;j++)
		{
			cout<<flag[i][j]<<" ";
		}
		cout<<endl;
	}
	cout<<endl;
	for(int i=0;i<=dest_len;i++)
	{
		for(int j=0;j<=str_len;j++)
		{
			cout<<dp[i][j]<<" ";
		}
		cout<<endl;
	}

	return 0;
}