CF221 - Editorial

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PROBLEM LINK:

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Author: Ishpreet
Tester: Karan

DIFFICULTY:

SIMPLE

PROBLEM:

There are total N stairs. A person climbs A stairs upwards in day and comes downstairs in night by B stairs. Find number of days person will take to reach the top of staircase.

EXPLANATION:

Let us start by solving the problem day wise.
Day1: A               Night1: A-B
Day2: (A-B)+A      Night2: 2*(A-B)
Day3: 2*(A-B)+A    Night3: 3(A-B)

DayX: (A - B) * (X - 1) + A,

Let us assume, on day X, he crossed N stairs.

So,
(A - B) * (X - 1) + A >= N
AX - BX + B >= N
X (A - B) >= N - B
X >= (N - B) / (A - B)

All we need is the integer value of X which is >= (N - B) / (A - B).

TESTER’S SOLUTION:

Ideone