LeetCode 673 Number of Longest Increasing Subsequences - Dual State

You need two arrays: $length[i]$ = length of LIS ending at $i$ $count[i]$ = number of LIS of that length ending at $i$ When extending from $j$ to $i$ (where $arr[j] < arr[i]$):

$1.$ If $length[j] + 1 > length[i]$: found a longer path. Set $length[i] = length[j] + 1$ and $count[i] = count[j]$.

$2.$ If $length[j] + 1 = length[i]$: found another path of same length. Add $count[j]$ to $count[i]$. Base case: $length[i] = 1$, $count[i] = 1$ for all $i$.