# UVa 264

From Algorithmist

## 264 - Count on Cantor[edit]

## Summary[edit]

No point in brute forcing this thing 10^7 will take a long time :)

## Explanation[edit]

- 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

## Input[edit]

1 3 14 7 10000000

## Output[edit]

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