算法导论_动态规划_最长回文子序列

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

#define MAX 100

int f[MAX][MAX] = { 0 };
int b[MAX][MAX] = { 0 };
int flag = 0;


void Lps_length(string &str)
{
	int len = str.length();

	for (int i = len - 1; i >= 0; --i)
	{
		f[i][i] = 1;
		for (int j = i+1; j < len; ++j)
		{
			if (str[i] == str[j])
			{
				f[i][j] = f[i + 1][j - 1] + 2;
				b[i][j] = 0;
			}   
			
			else if (f[i + 1][j] >= f[i][j - 1])
			{
				f[i][j] = f[i + 1][j];
				if(f[i + 1][j] == f[i][j - 1])
					b[i][j] = 2;
				else
				   b[i][j] = -1;
			}
				
			else
			{
                f[i][j] = f[i][j - 1];
			    b[i][j] = 1;
			}
			
		
		}
	}
	
}

void printf_Lps(int b[MAX][MAX],int i,int j,const string &str)
{
	if (i < 0 || j < 0)
	{
		return;
	}
	
	if (b[i][j] == 0)
	{
		if (j >= 0 && j <= str.length() - 1)
		{
		cout << str[j];
		}
		
		if (i == j)
		{
			flag = 1;
		}

		if(flag == 0)
		    printf_Lps(b, i + 1, j - 1,str);
		else
			printf_Lps(b, i - 1, j + 1, str);
		
		
	}

	else if (b[i][j] == 2 || b[i][j] == 1)
	{
		if (flag == 0)
		    printf_Lps(b, i, j - 1,str);
		else
			printf_Lps(b, i, j + 1, str);
	}

	else if(b[i][j] == -1)
	{
		if (flag == 0)
		    printf_Lps(b, i + 1, j,str);
		else
			printf_Lps(b, i - 1, j, str);
	}
}


int main()
{

	string str = "GTJYTTHA";


	Lps_length(str);

	for (int i = 0; i <= str.length ()-1; ++i)
	{
		for (int j = 0; j <= str.length() - 1; ++j)
		{
			cout << b[i][j] << "\t";
		}
		cout << endl;
	}

	cout << f[0][str.length() - 1] << endl;

	printf_Lps(b, 0, str.length() - 1,str);

	cout << endl;
	return 0;
}