[leetcode]Longest Increasing Subsequence

总体思想就是：

For example, if

nums = [5,6,7,1,2,8,3,4,0,5,9]

then after we prcoess the 7:

S = [5,6,7]

after w process the 2:

S = [1,2,7]

after we process the 8:

S = [1,2,7,8]

Then we process the 3:

S = [1,2,3,8]

We process the 4:

S = [1,2,3,4]

and now the next three lements:

S = [0,2,3,4,5,9]

如果不想使用另外一个数组，则可以使用给定数组的前n个位置。

public class Solution {
    public int lengthOfLIS(int[] nums) {
        int len=nums.length,pos=0;
        if(nums == null || nums.length==0){
            return 0;
        }
        int[] ret = new int[len];
        ret[0] = nums[0];
        pos++;
        for(int i=1;i<len;i++){
            if(nums[i]>ret[pos-1] ){
                ret[pos++]=nums[i];
            }else if(nums[i]<ret[0] ){
                ret[0]=nums[i];
            }else{
                int des=binarySearch(ret,pos,nums[i] );
                ret[des]=nums[i];
            }
        }
        return pos;
    }
    
    private int binarySearch(int[] num,int len,int target){
        int low=0,high=len-1;
        while(low<=high){
            int mid=low+(high-low)/2;
            if(num[mid] ==  target){
                return mid;
            }else if(num[mid] < target ){
                low=mid+1;
            }else{
                high=mid-1;
            }
        }
        return low;
    }
}

参考网址：https://leetcode.com/discuss/89066/short-c-stl-based-solution-o-log-time-space-with-explanation