声明：算法学习来自，7月算法，面试&算法&机器学习&找工作就上七月算法

1. 今天学习的算法是 LCS，最长公共子序列，属于典型的动态规划基础题。

十分钟搞定LCS 学习视频：http://julyedu.com/video/play/id/9

2. 实践代码：

/*
Algorithm LCS
*/
#include 
#include 
#include 
#include 
#include 
using namespace std;

#define MAX 50

// Get LCS
int GetLcs(int dp[][MAX], int path[][MAX], const string& strOne, const string& strTwo) {
	int strOneLength = strOne.length();
	int strTwoLength = strTwo.length();
	for (int i = 0; i < strOneLength; ++i) {
		dp[i][0] = 0;
	}
	for (int i = 0; i < strTwoLength; ++i) {
		dp[0][i] = 0;
	}
	for (int i = 0; i < strOneLength; ++i) {
		for (int j = 0; j < strTwoLength; ++j) {
			if (strOne[i] == strTwo[j]) {
				dp[i+1][j+1] = dp[i][j] + 1;
				path[i+1][j+1] = 0; //leftTop
			}
			else {
				if (dp[i][j+1] > dp[i+1][j]) {
					dp[i+1][j+1] = dp[i][j+1];
					path[i+1][j+1] = -1; //top
				}
				else {
					dp[i+1][j+1] = dp[i+1][j];
					path[i+1][j+1] = 1; //left
				}
			}
		}
	}
	return dp[strOneLength][strTwoLength];
}

// Print LCS string
string PrintLcs(int path[][MAX], const string& strOne, const string& strTwo) {
	stack  stk;
	int i = strOne.length();
	int j = strTwo.length();
	while ((i > 0) && (j > 0)) {
		if (path[i][j] == 0) {
			stk.push(strOne[i-1]);
			--i;
			--j;
		}
		else if (path[i][j] == 1) {
			--j;
		}
		else {
			--i;
		}
	}
	string lcsString = "";
	while (!stk.empty()) {
		lcsString = lcsString + stk.top();
		stk.pop();
	}
	return lcsString;
}

int main(int argc, char **argv) {
	string strOne = "bdcaba";
	string strTwo = "abcbdab";
	int dp[MAX][MAX], path[MAX][MAX];

	cout << GetLcs(dp, path, strOne, strTwo) << endl;
	cout << PrintLcs(path, strOne, strTwo) << endl;

	return 0;
}