最长公共子序列（LCS）的C++实现

首先有如下递归式

绘制图表如下

首先我们实现最长公共子序列长度的输出，代码如下：

#include<iostream>#include<vector>#include<algorithm>#include<string>using namespace std;int table[100][100] = { 0 };int main(){string a, b;cin >> a >> b;int m = a.length();int n = b.length();for (int i = 1; i <= m; i++){for (int j = 1; j <= n; j++){if (a[i-1] == b[j-1]){table[i][j] = table[i - 1][j - 1] + 1;}else{table[i][j] = max(table[i - 1][j], table[i][j - 1]);}}}cout << table[m][n] << endl;system("pause");}

只需做一点小改动，假如一个判断数组和一个输出函数，用到递归，代码如下：

#include<iostream>#include<vector>#include<algorithm>#include<string>using namespace std;int table[100][100] = { 0 };int judge[100][100] = { 0 };int print_LCS(int judge[][100], string x,int,int);int main(){string a, b;cin >> a >> b;int m = a.length();int n = b.length();for (int i = 1; i <= m; i++){for (int j = 1; j <= n; j++){if (a[i-1] == b[j-1]){table[i][j] = table[i - 1][j - 1] + 1;judge[i][j] = 1;}else if(table[i - 1][j] >= table[i][j - 1]){table[i][j] = table[i - 1][j];judge[i][j] = 2;}else{table[i][j] = table[i][j - 1];judge[i][j] = 3;}}}cout << table[m][n] << endl;print_LCS(judge, a, m, n);cout << endl;system("pause");}int print_LCS(int judge[][100],string a,int x,int y)//x,y,分别为两段长度{if (x == 0 || y == 0){return 0;}if (judge[x][y] == 1){print_LCS(judge, a, x-1, y-1);cout << a[x-1];}if (judge[x][y] == 2){print_LCS(judge, a, x - 1, y);}if (judge[x][y] == 3){print_LCS(judge, a, x, y - 1);}}