Find the least number for which Proportion of Neutral Numbers is atleast n/m

By | 21.02.2017

Find the least number for which Proportion of Neutral Numbers is at least n/m


Increasing, Decreasing & Neutral Numbers

An increasing number is a number in which values of digits increase when we go from left to right; for example,123455 .

Similarly a decreasing number is a number in which values of digits decrease when we go from left to right; for example,54110 .

We shall call a positive integer that is neither increasing nor decreasing a “neutral” number; for example, 151212 .

The count of Neutral numbers increases and by the time we reach 21780 the proportion of neutral numbers >= 90%.

Find the least number for which the proportion of neutral numbers is at least n/m .


Explanation


Input Format

First line contains an integer denoting the number of test cases.

Each of the following lines contain two integers.

Constraints

1<=T<10^4

1<=n<m<=10^5

Output Format

For each of T test cases print one line containing a single integer – the answer to a problem.

Sample Input

2

1 2

90 100

Sample Output

538

21780

Time Limit:3.0 sec(s) for each input file.

Memory Limit:256 MB

Source Limit:1024 KB


SOURCE CODE : :

import itertools
def compute(a,b):
        count = 0
        for i in itertools.count(1):
                s = str(i)
                t = "".join(sorted(s))
                if s != t and s[::-1] != t:
                        count += 1  # i is neutral
                if count * b == a * i:
                        return str(i)
for i in range(0,input(),1):
        a=map(int,raw_input().strip(' ').split())
        print(compute(a[0],a[1]))

 

OUTPUT : :

2

1 5
175

80 100
4770

 

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About Tunde A

My name is Tunde Ajetomobi, a Tech Enthusiast and Growth Hacker. I enjoy creating helpful content that solves problem across different topics. Codezclub is my way of helping young aspiring programmers and students to hone their skills and find solutions on fundamental programming languages.

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