NY10E - Non-Decreasing Digits

A number is said to be made up of non-decreasing digits if all the digits to the left of any digit is less than or equal to that digit.For example, the four-digit number 1234 is composed of digits that are non-decreasing.  Some other four-digit numbers that are composed of non-decreasing digits are 0011, 1111, 1112, 1122, 2223.  As it turns out, there are exactly 715 four-digit numbers composed of non-decreasing digits.
Notice that leading zeroes are required: 0000, 0001, 0002 are all valid four-digit numbers with non-decreasing digits.
For this problem, you will write a program that determines how many such numbers there are with a specified number of digits.


The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow.  Each data set is a single line that contains the data set number, followed by a space, followed by a decimal integer giving the number of digits N, (1 ≤ N ≤ 64).


For each data set there is one line of output.  It contains the data set number followed by a single space, followed by the number of N digit values that are composed entirely of non-decreasing digits.


1 2
2 3
3 4

1 55
2 220
3 715

hide comments
lnxdx: 2019-10-04 15:25:20

AC in three goes :\

sanket17: 2019-08-06 09:51:53

two things to take care
1. dont forget the case of 1
2. Use long long int

dkkv0000: 2019-05-11 11:31:31

excellent problem must do for beginners like me took 3hrs but worth it

ayushgupta1997: 2019-02-11 18:28:41

start from the left most digit, and try and build the possible recursion tree of possibilities, you will find a pattern then, turn the pattern into a 2D dp, precomputation matrix.

Last edit: 2019-02-11 18:29:10
sauravraj62: 2018-11-10 06:03:31

why so weird output format... it costs 2 WA!!!

jmr99: 2018-10-30 08:43:20

1.'spoiler' will do the job
2. formula will also do the job

ankit1cool: 2018-06-14 14:39:54

Remember to use long long costed me 1wa

spojabhi: 2017-12-17 17:18:10

"OEIS" best site for getting sequences.

vishesh197: 2017-09-26 15:04:03

simple problem.... just use dp and long long and state of dp as dp(last digit chosen,number of digits).AC in 1st go...

code_aim: 2017-09-04 15:52:59


Added by:John Mario
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
Resource:ACM Greater New York Regionals 2010