LCIS类模板

最新推荐文章于 2018-08-02 22:38:50 发布

原创最新推荐文章于 2018-08-02 22:38:50 发布 · 432 阅读

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本文介绍了一个模板类LCIS，用于求解两个序列的最长递增公共子序列（Longest Common Increasing Subsequence, LCIS）。该算法通过动态规划方法实现了对两个序列的比较，并记录了形成LCIS的路径。

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template<class T>
class LCIS
{
private:
	static const short maxLength = 501;				//序列的最大长度
	unsigned short length1,length2;					//分别表示seq1,seq2的长度
	T seq1[maxLength],seq2[maxLength];				//源序列
	unsigned short dp[maxLength][maxLength];		//dp[i][j]表示子串seq1[1,2,...i]和以seq2[j]结尾的子串seq2[1,2,...j]的LCIS
	unsigned short lastindex;						//LCIS的seq2的结尾下标，即若最后的LCIS串为seq = {s1,s2,...st}，那么seq[st] = seq2[lastindex]
	short path[maxLength][maxLength];				//路径记录，path[i][j] = y表示(i - 1,y) -> (i,y)

	void copyArray(T num1[],int& l1,T num2[],int l2);

public:
	LCIS(){};
	LCIS(T num1[],int l1,T num2[],int l2);
	void init(T num1[],int l1,T num2[],int l2);
	int getLCIS();									//计算LCIS，path并返回LCSI的值
	int getLastindex();								//返回组成LCIS串的seq2串的结尾下标
	void printPath(int x,int y);					//打印路径，注意，入口处的参数y必须是LCIS的相应结尾lastindex
};

template<class T>
void LCIS<T>::copyArray(T num1[],int& l1,T num2[],int l2)
{
	l1 = l2;
	for(int i = 1;i <= l1;i++)
		num1[i] = num2[i];
}

template<class T>
LCIS<T>::LCIS(T num1[],int l1,T num2[],int l2)
{
	init(num1,l1,num2,l2);
}

template<class T>
void LCIS<T>::init(T num1[],int l1,T num2[],int l2)
{
	copyArray(seq1,length1,num1,l1);
	copyArray(seq2,length2,num2,l2);
	memset(dp,0,sizeof(dp));
	memset(path,0,sizeof(path));
}

template<class T>
int LCIS<T>::getLCIS()
{
	for(int i = 1;i <= length1;i++)
	{
		int maxj = 0;
		for(int j = 1;j <= length2;j++)
		{
			if(seq1[i] > seq2[j] && dp[i - 1][maxj] < dp[i - 1][j])
				maxj = j;
			if(seq1[i] != seq2[j])
			{
				dp[i][j] = dp[i - 1][j];
				path[i][j] = j;
			}
			else if(seq1[i] == seq2[j])
			{
				dp[i][j] = dp[i - 1][maxj] + 1;
				path[i][j] = maxj;
			}
		}
	}
	lastindex = 1;
	for(int i = 1;i <= length2;i++)
		if(dp[length1][lastindex] < dp[length1][i])
			lastindex = i;
	return dp[length1][lastindex];
}

template<class T>
int LCIS<T>::getLastindex()
{
	return lastindex;
}

template<class T>
void LCIS<T>::printPath(int x,int y)
{
	if(x < 1 || y < 1)
		return;
	while(x >= 1 && path[x][y] == y)
		x--;
	if(x >= 1)
	{
		printPath(x,path[x][y]);
		if(!path[x][y])
			printf("%d",seq2[y]);
		else
			printf(" %d",seq2[y]);
	}
}