dp on digits

finding interesting numbers

abridged, find # of numbers between $0$ and $Y$ that fulfill cond that at least half of the number contains the same digit

build numbers starting with the prefix
with $p os$ : position to add digit, $k$ : balance of $t a r g e t$ present (at end, non-negative achieves half cond), $u n d er$ : cond if under $Y$ , $s t a r t e d$ : if non-zero digit has been placed
for each digit 0-9, pick as a $t a r g e t$ for the entire dp run for solving $d p (p os : 0, k : 0, u n d er : f a l se, s t a r t e d : f a l se)$ , for the entire algorithm on a given $Y$
for a given $d p$ , try adding a digit 0-9 $i$ at $p os$ . update $p os$ (inc), $u n d er$ (if confirmed to be under $Y$ ), $s t a r t e d$ (if $i$ is non-zero). for $k$ , if $i = t a r g e t$ , then inc, else decr. then calc $d p (p os, k, u n d er, s t a r t e d)$ as sum of those
duplicate handling omitted, basically checking for exactly half $i$ and half $j$ (counted as one by problem statement, counted as two by program)