264 - Count on Cantor
No point in brute forcing this thing 10^7 will take a long time :)
- We can generalize this pattern in order to figure out the fraction.
- Try to sum up all the numbers sequentially until you have figured out the range in which your number will belong.
- Once we establish the range, you can simply figure out the distance from the current position and finish off the problem.
- Follow this general algorithm. Pre-compute an array of summations 4500 in length. Binary search to find exactly what diagonal in the matrix would be referenced. Next, note the when to add/subtract from the numerator and denominators. Easy solution from there.
fzort: This problem also has a O(1) solution. It's easy to compute the index d of the diagonal a given number n is in. The number of elements before diagonal d is
, so the number n is in diagonal
1 3 14 7 10000000
TERM 1 IS 1/1 TERM 3 IS 2/1 TERM 14 IS 2/4 TERM 7 IS 1/4 TERM 10000000 IS 2844/1629