Total number of non |  ; dp [ i ] [ j ] contains total count of non decreasing numbers ending with digit i and of length j ; Fill table for non decreasing numbers of length 1 Base cases 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 ; Fill the table in bottom - up manner ; Compute total numbers of non decreasing numbers of length ' len ' ; sum of all numbers of length of len - 1 in which last digit x is <= ' digit ' ; There total nondecreasing numbers of length n wiint be dp [ 0 ] [ n ] + dp [ 1 ] [ n ] . . + dp [ 9 ] [ n ] ; Driver program
class NDN { static int countNonDecreasing ( int n ) { int dp [ ] [ ] = new int [ 10 ] [ n + 1 ] ; for ( int i = 0 ; i < 10 ; i ++ ) dp [ i ] [ 1 ] = 1 ; for ( int digit = 0 ; digit <= 9 ; digit ++ ) { for ( int len = 2 ; len <= n ; len ++ ) { for ( int x = 0 ; x <= digit ; x ++ ) dp [ digit ] [ len ] += dp [ x ] [ len - 1 ] ; } } int count = 0 ; for ( int i = 0 ; i < 10 ; i ++ ) count += dp [ i ] [ n ] ; return count ; } public static void main ( String args [ ] ) { int n = 3 ; System . out . println ( countNonDecreasing ( n ) ) ; } }