Longest Increasing Subsequence Recursive version - recursion

Question

Traditional Longest Increasing Subsequence problem.
This is recursion version ( not DP version )
I realized that version1 code had a bug, so I changed it to version2.
I don't clearly understand why version2 works and version1 has a bug for input A0
Please see version 1 and version2 below:
static int lis1(int[] v) {
int maxLen = 1;
for(int i = 1; i < v.length; i++) {
List<Integer> w = new ArrayList<Integer>();
for( int j = 0; j < i; j++) {
if( v[j] < v[i] ) {
w.add(v[j]);
}
}
// it used to be the following one line which has bug for input A0
//cand = lis1(l2a(w)) + 1; // version1
// so I changed it to the following, but can't clearly understand why it works.
// without this part, it has but for input A0
int cand = 1; // version2
if(v[i-1] < v[i])
cand = lis1(l2a(w)) + 1;
else
cand = lis1(l2a(w));
maxLen = Math.max(maxLen, cand);
}
return maxLen;
}
public static void main(String[] args) {
int[] A0 = {3, 2, 5, 6}; // for this input version1 had a bug which printed out 4 ( instead of 3 )
int[] A1 = {1, 2, 3, 3, 2, 4, 6, 7}; // 6
int[] A2 = { 10, 22, 9, 33, 21, 50, 41, 60, 80 }; // 6
int[] A3 = { 5, 0, 4, 2, 3, 7, 1 }; // 4
int[] A4 = { 2, 7, 3, 4, 9, 8, 12 }; // 5
int[] A5 = {3, 4, 2, 5 }; // 3

Answer 1

Actually... neither of your version works. Try putting A0={3,2,7,6}, your v2 returns 2, obviously wrong.
As for v1, for v={3,2} the answer should be 1, right? Let's see what your code does. When index i=1, your w after inner for loop equals {}. Then you made a recursive call to w={}, which should've returned 0, but it returns 1. Why, because of your maxlen variable, which is wrongly initialized with 1. This error propagates to entire {3,2,5,6} and gives wrong answer.
v2 accidentally solves this problem because your if condition then fails (3<2), and it returns the previously returned 1.
Just delete entire version 2, correct maxlen initialization. And start outer loop for(int i = 1; i < v.length; i++) with i=0, else you will get 0 for single-element array.
static int lis1(int[] v) {
int maxLen = 0;
for(int i = 0; i < v.length; i++) {
List<Integer> w = new ArrayList<Integer>();
for( int j = 0; j < i; j++) {
if( v[j] < v[i] ) {
w.add(v[j]);
}
}
cand = lis1(l2a(w)) + 1; // version1
maxLen = Math.max(maxLen, cand);
}
return maxLen;
}