动态规划3.2 最长公共子串

问题：

　　最长公共子串是编辑距离的一种，只允许增加、删除字符两种编辑操作，它表征的也是两个字符串之间的相似程度。

代码：

#include <iostream>
#include <string.h>

int max3(int a, int b, int c)
{
    int tmp = a > b ? a : b;
    if(tmp > c)
        return tmp;
    return c;
}

int main()
{
    const char *a = "mitcmu";
    const char *b = "mtacnu";
    
    int lena = strlen(a);
    int lenb = strlen(b);
    
    int **states = new int*[lena];
    for(int i = 0; i < lena; i++)
    {
        states[i] = new int[lenb];
        memset(states[i], 0, sizeof(int) * lenb);
    }
    
    //  初始化第0行
    for(int i = 0; i < lenb; i++)
    {
        if(a[0] == b[i])
        {
            states[0][i] = 1;
        }
        else if(i == 0)
        {
            states[0][i] = 0;
        }
        else
        {
            states[0][i] = states[0][i - 1];
        }
    }
    
    // 初始化第0列
    for(int j = 0; j < lena; j++)
    {
        if(a[j] == b[0])
        {
            states[j][0] = 1;
        }
        else if(j == 0)
        {
            states[j][0] = 0;
        }
        else
        {
            states[j][0] = states[j - 1][0];
        }
    }
        
    for(int i = 1; i < lena; i++)
    {
        for(int j = 1; j < lenb; j++)
        {
            if(a[i] == b[j])
            {
                states[i][j] = max3(states[i-1][j], states[i][j-1], states[i-1][j-1] + 1);
            }
            else
            {
                states[i][j] = max3(states[i-1][j], states[i][j-1], states[i-1][j-1]);
            }
        }
    }
    
    for(int i = 0; i < lena; i++)
        delete states[i];
    
    delete states;
    
    std::cout << "max_lcs : " << states[lena - 1][lenb - 1] << std::endl;
    
    return 0;
}

运行结果：