LCS最长公共子序列问题

用递归求解，复杂度为O(2^n)，相当高 

#include <iostream>
#include <algorithm>
#include <iterator>
#include <vector>

using namespace std;

char array1[] = {'B', 'D', 'C', 'A', 'B', 'A'};
const int size1 = sizeof array1 / sizeof *array1;
char array2[] = {'A', 'B', 'C', 'B', 'D', 'A', 'B'};
const int size2 = sizeof array2 / sizeof *array2;

vector<char> cvec;
vector<char> cvec2;
int infor[size1][size2];

int findLongest(char (&array1)[size1], int pos1, char (&array2)[size2], int pos2)
{
	if(pos1 < 0 || pos2 < 0) {
		if(cvec2.size() < cvec.size()) {
			cvec2 = cvec;
		}
		cvec.clear();
		return cvec2.size();
	}
	int len1, len2;

	if(array1[pos1] == array2[pos2]) {
		cvec.push_back(array1[pos1]);
		pos1 -= 1;
		pos2 -= 1;
		
		return findLongest(array1, pos1, array2, pos2);
	} else {
		len1 = findLongest(array1, pos1 - 1, array2, pos2);
		len2 = findLongest(array1, pos1, array2, pos2 - 1);

		return max(len1, len2);
	}
}

void main()
{
	int result = findLongest(array1, size1 - 1, array2, size2 - 1);
	cout << "len: " << result << endl;	
	copy(cvec2.rbegin(), cvec2.rend(), ostream_iterator<char>(cout, " "));
}

利用动态规划法，以空间换取时间

#include <iostream>
#include <algorithm>
#include <iterator>
#include <vector>

using namespace std;

char array1[] = {'A', 'B', 'C', 'B', 'D', 'A', 'B'};
const int size1 = sizeof array1 / sizeof *array1;
char array2[] = {'B', 'D', 'C', 'A', 'B', 'A'};
const int size2 = sizeof array2 / sizeof *array2;

int info[size1 + 1][size2 + 1];

void printMatrix()
{
	if (info == NULL)
		return;

	for (int i = 0; i <= size1; i++)
	{
		for (int j = 0; j <= size2; j++)
		{
			cout << info[i][j] << " ";
		}
		cout << endl;
	}
}

int findLongestLcs(char *array1, int size1, char *array2, int size2)
{
	if (array1 == NULL || array2 == NULL || size1 <= 0 || size2 <= 0)
		return -1;

	for (int i = 0; i <= size1; i++)
		info[i][0] = 0;
	for (int i = 0; i <= size2; i++)
		info[0][i] = 0;

	for (int i = 0; i < size1; i++)
	{
		for (int j = 0; j < size2; j++)
		{
			if (array1[i] == array2[j])
				info[i + 1][j + 1] = info[i][j] + 1;
			else
				info[i + 1][j + 1] = max(info[i + 1][j], info[i][j + 1]);
		}
	}

	printMatrix();

	vector<char> result;
	for (int i = size1, j = size2; i > 0 && j > 0;)
	{
		if (info[i][j] == info[i - 1][j] + 1 && info[i][j] == info[i][j - 1] + 1 && info[i][j] == info[i - 1][j - 1] + 1)
		{
			result.push_back(array1[i - 1]);
			i--;
			j--;
		}
		else if (info[i][j] == info[i - 1][j])
			i--;
		else
			j--;
	}

	copy(result.rbegin(), result.rend(), ostream_iterator<char>(cout, " "));
	return result.size();
}

void main()
{
	int result = findLongestLcs(array1, size1, array2, size2);
	cout << "len: " << result << endl;	
}