算法导论中LCS的C++实现程序

        LCS即最长公共子序列，输入为两个串X、Y，输出为X与Y的最长公共子序列。其求解方法是动态规划，即原序列的最长公共子序列依赖于前缀的最长公共子序列。具体的实现原理参考算法导论（第三版）222页-226页，本文给出它的C++实现程序：

#include<iostream>
#include<string>
#define NUM 20
using namespace std;
int c[NUM][NUM];
char b[NUM][NUM];
void LCS_LENGTH(string X, string Y){
int m = X.length();
int n = Y.length();
for (int i = 1; i <= m; i++)
c[i][0] = 0;
for (int j = 0; j <= n; j++)
c[0][j] = 0;
for (int i = 1; i <= m; i++){
for (int j = 1; j <= n; j++){
if (X[i - 1] == Y[j - 1]){
c[i][j] = c[i - 1][j - 1] + 1;
b[i][j] = 'a';
}
else if (c[i - 1][j] >= c[i][j - 1]){
c[i][j] = c[i - 1][j];
b[i][j] = 'b';
}
else{
c[i][j] = c[i][j - 1];
b[i][j] = 'c';
}
}
}
}

void PRINT_LCS(string X,int m, int n)
{
if (m == 0 || n == 0)
return;
if (b[m]
== 'a'){
PRINT_LCS(X,m - 1, n - 1);
cout << X[m-1];
}
else if (b[m]
== 'b'){
PRINT_LCS(X, m - 1, n);
}
else
PRINT_LCS(X, m, n - 1);
}
void main()
{
string X, Y;
cin >> X >> Y;
LCS_LENGTH(X, Y);
PRINT_LCS(X,X.length(), Y.length());
}