[LintCode] 最长上升子序列

动态规划：

lis[i] = max_{j = 0, 1, ..., i - 1, nums[j] < nums[i]} lis[j] + 1

class Solution {
public:
    /**
     * @param nums: The integer array
     * @return: The length of LIS (longest increasing subsequence)
     */
    int longestIncreasingSubsequence(vector<int> nums) {
        // write your code here
        vector<int> lis(nums.size(), 1);
        int maxlen = 0;
        for (int i = 1; i < (int)nums.size(); i++) {
            for (int j = 0; j < i; j++)
                if (nums[j] <= nums[i] && lis[j] + 1 > lis[i])
                    lis[i] = lis[j] + 1;
            maxlen = max(maxlen, lis[i]);
        }
        return maxlen;
    }
};