Problem Link

Practice

Contest

Author:Adlet Zeineken

Tester:Misha Chorniy

Editorialist:Bhuvnesh Jain

Difficulty

CAKEWALK

Prerequisites

Probability, Looping

Problem

You are given an N sided dice. You roll it twice and need to find the probability of getting A on the first throw and B on the second throw.

Explanation

The probability of obtaining a number on the consecutive throw of a dice is independent of each other. For more details, you may refer here. The probability of getting a number $X$ on throwing a $N$ sided dice is given by:

$$\text{Probability} = \frac{\text{Number of times X appears on the dice}}{N}$$

Thus, the overall probability of obtaining A on the first throw and B on the second throws is given by:

$$\text{Required Probability} = \frac{\text{Number of times A appears on the dice}}{N} * \frac{\text{Number of times B appears on the dice}}{N}$$

Thus, the problem reduces to finding the frequency of a number in an array. This can be easily done in $O(1)$ space complexity and $O(n)$ time complexity using a simple for loop as below

    def count_frequency(array a, integer x):
        count = 0
        for number in a:
            if number == x:
                count += 1
        return count

The constraints of the problem were such that all the operations can be done in integers only without any overflow issues.

Time Complexity

$O(n)$ per test case.

Space Complexity

$O(1)$

AUTHOR'S AND TESTER'S SOLUTIONS:

Tester's solution can be found here.

Editorialist's solution can be found here.