An Articulation of the O(KN) Solution to 'Leetcode 887: Super Egg Drop'

Fri, 01 Jan 2021 20:00:00 +0000

‘Super Egg Drop’ is a very classic DP problem. Good articles explaining the O(KN*N) and the O(KN*logN) solutions can be easily found from the internet. Better than that, there is a solution of O(KN). However, there isn’t much about the O(KN) solution and the rare posts about it aren’t very clear. The article you are reading now is an endeavor to fill this gap.

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You are given K eggs, and you have access to a building with N floors from 1 to N

[LeetCode 233, AC] Number of Digit One Done With DP

Mon, 25 May 2020 19:39:16 +0000

Given an integer n, count the total number of digit 1 appearing in all non-negative integers less than or equal to n.

Example:

Input: 13
Output: 6 
Explanation: Digit 1 occurred in the following numbers: 1, 10, 11, 12, 13.

Let’s try to solve this problem by dividing it into smaller quizzes:

For example, to caculate the result for 2954:

count(2954)=count(2000)+count(954)
count(954)=count(900)+count(54)
count(54)=count(50)+count(4)

Now we got the conclusion that count(2954)=count(2000)+count(900)+count(50)+count(4), which is leading us to the question of how to get count(i*10^j)

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An Articulation of the O(KN) Solution to 'Leetcode 887: Super Egg Drop'

Check Out The Problem

[LeetCode 233, AC] Number of Digit One Done With DP