Editorial for Mock CCC '19 Contest 1 J2 - Froggo's Numbers - Thornhill Secondary School Online Judge

Editorial for Mock CCC '19 Contest 1 J2 - Froggo's Numbers

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Authors: jsumabat

If we want to determine the how many integers are divisible by $x$ ~x~ in the range of $l$ ~l~ to $r$ ~r~, then lets represent this as a function, such that $f(n)$ ~f(n)~ is equal to the number of integers that are divisible by $x$ ~x~ greater than or equal to $0$ ~0~, and less than or equal to $n$ ~n~.

If we represent $f(n)$ ~f(n)~ using the above definition, then realistically, $f(r) - f(l-1)$ ~f(r) - f(l-1)~ (like a prefix sum array, or inclusion-exclusion principle) is the solution. However, if $l = 0$ ~l = 0~, then we end up having $f(-1)$ ~f(-1)~, which is invalid.

We can rewrite $f(n)$ ~f(n)~ like so, where in division, decimals are truncated:

$\displaystyle f(n) = \begin{cases}n/x+1 & (n \ge 0)\\0 & (n = -1)\end{cases}$

Comments

0

Jonathan_Hong commented on Dec. 12, 2019, 1:25 p.m.

I can't read I need help : ^)