Dynamic programming of five algorithms

Problem: A sequence has N numbers: A[1],A[2],...,A[N], find the length of the longest non-descending subsequence.

Abstract: Find the length of the longest non-decreasing subsequence of these N numbers.

Idea: Using dynamic programming recursion, if d(i) is the length of the longest non-descending subsequence of the first i numbers, then it depends on the length of d(1)...d(i-1), and find Get d(i), and you can find d(i+1)...n later. Its state transition equation is: d(i) = max{1, d(j)+1}, where j=1...i-1, A[j]<=A[i].

code show as below:

package test;
 
/**
 * Dynamic programming to find the longest non-decreasing subsequence problem
 * @author yanghang
 *
 */
public class Dongtaiguihua {
    /**
     * longest increasing subsequence
     * @param a
     * @return
     */
    public static int lis(int[] a) {
        // Count the longest non-descending subsequence of the current stage
        int len ​​= 0;
        // original array length
        int n = a.length;
        // current state
        int[] d = new int[n];
         
        for (int i = 0; i < n; i++) {
            d[i] = 1;
            for (int j = 0; j < i; j++) {
                //implementation of state transition equation
                if (a[j] <= a[i] && d[j] + 1 > d[i]) {
                    d[i] = d[j] + 1;
                }
            }
            if (d[i] > len) {
                len = d [i];
            }
        }
        return len;
    }
 
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        int[] a = { 5, 3, 4, 8, 6, 7 };
        System.out.println(lis(a));
 
    }
 
}