Sorry, but no matter how many times I read this question I still don't have an idea what it is you want to achieve in this puzzle. Please elaborate a bit on how you came to 1000 in your sample output or maybe reword your question so that it makes more sense.

After reading this question several times, I still do not understand what I am supposed to do.

The question NEEDS rewording as it seems out I am not the only one with problems.

I love solving challenges, but I HATE trying to decipher questions poorly asked.

My interpretation, using the sample input for explanation:

From the sample input, n=6 and m=7.

I'm using array convention, where a[0] is left most value and a[5] is right most value.

a[0] can be any digit from 0 to 9. Same for indices 1 through 5.

Therefore, you can think of the possible values of a as: [0,0,0,0,0,0] all the way to [9,9,9,9,9,9].

Another way to think about this is, we are considering the range of numbers from 0 to (10**n)-1

The number 654321 is in this range. Does 654321 fit all m requirements? m={(1 3),(0 1),(2 4),(0 4),(2 5),(3 4),(0 2)}

m[1] = (0 1) => requirement that value@index0 <= value@index1

For 654321, value@index0 is 6 and value@index1 is 5.

Therefore, requirement m[1] is not met, so 654321 is not a valid assignment.

For all but 3 of the test cases, it is possible (in C) to pass essentially by counting one-by-one the valuations that satisfy the requirements without timing out; you just have to do a tiny amount of work to minimize the amount of time spent on failed valuations.

I've got a recursive solution with worst case (i.e. requirements = [[0,1]]) O(10**(m-1)) that passes all but 4 of the test cases (1, 3, 6 & 7).

1. Can anyone point me to an algorithm with better time complexity than this?
2. Has anyone figured out a strategy to memoize tail digit runs? This has proven remarkably difficult in the cases where the loop min iterator value depends on a digit much farther back in the digits (i.e. [0,m-1] is a requirement)