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.
Input
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).
Output
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.
Example
Input:
3
1 2
2 3
3 4
Output:
1 55
2 220
3 715
hide comments
it_nyx:
2021-06-05 12:55:14
Easy, but a very nice exercise for beginners in DP that I can recommend to my students. Thx! |
|
yash5507:
2020-12-31 15:39:37
AC in one GO! ( Simplest Digit Dp) |
|
singhgur_123:
2020-08-11 18:39:28
Mayb for i digit no place j=0 to 9 at last place and count no i-1 no satisfying the condition
|
|
berserkk:
2020-08-02 07:00:50
AC in one go |
|
robosapien:
2020-07-13 00:05:24
Observing sample cases, you can notice a formula.
|
|
ujjwal_jain10:
2020-06-25 09:37:35
AC in 69th go
|
|
manish_thakur:
2020-05-20 09:05:55
who puts input format like this? :( |
|
abhishek_2002:
2020-05-15 12:44:19
AC aaya hi ni....
|
|
amansahu112:
2020-04-30 12:57:38
solve some maths . there is a formula hidden |
|
saketvajp_123:
2020-04-18 06:46:50
AC in two go !!
|
Added by: | John Mario |
Date: | 2011-03-22 |
Time limit: | 1s |
Source limit: | 50000B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All except: ASM64 |
Resource: | ACM Greater New York Regionals 2010 |