java算法题————最长非降子序列以及逆序对数

1.最长非降子序列

时间复杂度：O(nlogn)
代码：

public class 最长非降子序列 {
		public static void main(String[] args) {
			int []arr={1,2,5,4,6,4,5};
			int length=lis(arr);
			System.out.println(length);

				
		}
		public static int lis(int[] arr){
			if (arr==null||arr.length==0) {
				return 0;
			}
			int[] temp =new int[arr.length];
			temp[0]=arr[0];
			int len=1;
			for (int i = 1; i < arr.length; i++) { 
				int index=lower_bound(temp,len,arr[i]);
				temp[index]=arr[i];
				if (index==len) {
					len++;
				}
			}
			return len;
		}
		
		//二分查找求下界
		public static int  lower_bound(int []temp,int len,int compare){
			int low=0;
			int high=len-1;
			while (low<=high) {
				int mid=low+(high-low)/2;
				if (compare<=temp[mid]) {
					high=mid-1;
				}else {
					low=mid+1;
				}
				
			}
			return low;
		}
}

2.逆序对数

时间复杂度：O(logn)
代码：

public class 逆序对个数 {
		static int count=0;
		public static void main(String[] args) {
			int []arr={1,2,5,4,6,3,5,5,5};
			mergesort(arr, 0,arr.length);
			System.out.println(count);
		}
		public static void mergesort(int []arr,int l,int r){
			int []c=new int[arr.length];
			int i,j,temp,mid;
			if (r>l+1) {
				mid=l+(r-l)/2;
				mergesort(arr, l, mid);
				mergesort(arr, mid, r);
				temp=l;
				//利用归并排序
				for (i = l,j=mid; i < mid&&j<r;) {
					if (arr[i]>arr[j]) {
						c[temp++]=arr[j++];
						count+=mid-i;
					}else {
						c[temp++]=arr[i++];
					}
				}
				if (j<r) {
					for (; j < r; ++j) {
						c[temp++]=arr[j];
					}
				}else {
					for (; i < mid;++i) {
						c[temp++]=arr[i];
					}
				}
				for (int k = l; k < r; ++k) {
					arr[k]=c[k];
				}
				
				
			}
			
		}
}