【算法2】最长公共子序列

https://blog.****.net/someone_and_anyone/article/details/81044153

https://www.cnblogs.com/gispf/p/6733074.html（讲解了最长公共子串、最长公共子序列、字符串相似度）

#define N 1010
int dp[N][N];
char c;
int main()
{
    char a[N];
    char b[N];
    scanf("%s%s",a,b);
    int la=strlen(a);
    int lb=strlen(b);
    memset(dp,0,sizeof(dp));
    for(int i=1; i<=la; i++)
    {
        for(int j=1; j<=lb; j++)
        {
            if(a[i-1]==b[j-1])
                dp[i][j]=dp[i-1][j-1]+1;
            else
                dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
        }
    }//dp[la][lb]即为子序列长度
    int i=la,j=lb;
    stack<char>s;
    while(dp[i][j])
    {
        if(dp[i][j]==dp[i-1][j])///来自于左方向
        {
            i--;
        }
        else if(dp[i][j]==dp[i][j-1])///来自于上方向
        {
            j--;
        }
        else if(dp[i][j]>dp[i-1][j-1])///来自于左上方向
        {
            i--;
            j--;
            s.push(a[i]);
        }
    }
    while(!s.empty())
    {
        c=s.top();
        printf("%c",c);
        s.pop();
    }
    system("pause");
    return 0;
}

//第六十三题  查找两个字符串a,b中的最长公共子串
int main()
{
	string str1, str2;
	while (cin >> str1 >> str2)
	{
		if (str1.size()>str2.size())
			swap(str1, str2);
 
		int len1 = str1.size(), len2 = str2.size(), i, j, start = 0, max = 0;
 
		vector<vector<int>>dp(len1 + 1, vector<int>(len2 + 1, 0));
		for (i = 1; i <= len1; i++)
			for (j = 1; j <= len2; j++)
			{
				if (str1[i - 1] == str2[j - 1])
					dp[i][j] = dp[i - 1][j - 1] + 1;
				if (dp[i][j]>max)
				{
					max = dp[i][j];
					start = i - max;
				}
			}
		cout << str1.substr(start, max) << endl;
	}
	return 0;
}