51nod 最长公共子序列

基本算法

如上

#include <iostream>

using namespace std;
string a,b;
int c[1010][1010] = {0};//记忆化最长度
int step[1010][1010] = {0};//记忆最长来源
int main()
{
	cin>>a>>b;
	a = '1' + a;
	b = '1' + b;
	for(int i = 1; i < b.length() ; i++)
	{
		for(int j = 1; j < a.length(); j++)
		{
			if(b[i] == a[j])
			{
				c[i][j] = c[i - 1][j - 1] + 1;
				step[i][j] = 1;
			}
			else
			{
				if(c[i][j - 1] > c[i - 1][j])
				{
					c[i][j] = c[i][j - 1];
					step[i][j] = 2;//左 
				}
				else
				{
					c[i][j] = c[i - 1][j];
					step[i][j] = 3;//上 
				}
			}
		}
	}
	/*for(int i = 0 ; i < b.length() + 1; i++)
	{
		for(int j = 0; j < a.length() + 1; j++)
		{
			cout<<step[i][j]<<' ';
		}
		cout<<endl<<endl;
	}*/
	int x = b.length() - 1,y = a.length() - 1,flag = 0;
	char ans[1010];
	while(x != 0 && y != 0)
	{
		//cout<<x<<' '<<y<<endl;
		if(step[x][y] == 1)
		{
			ans[flag++] = b[x];
			//cout<<b[x]<<endl;
			x--;
			y--;
		}
		else if( step[x][y] == 2)
		{
			y--;
		}
		else if( step[x][y] == 3)
		{
			x--;
		}
	}
	for(int i = flag - 1; i >= 0; i--)
	{
		cout<<ans[i];
	}
	cout<<endl;
	return 0; 
}