Digit factorials: Find the Sum of All the Curious Numbers
- Time:2020-09-10 12:45:51
- Class:Weblog
- Read:30
145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.
Find the sum of all numbers which are equal to the sum of the factorial of their digits.
Note: as 1! = 1 and 2! = 2 are not sums they are not included.
Pre-computing the Digit factorials
The factorials we all need to know are from 0! to 9!. Therefore, we can pre-compute the digital factorials and store them in a dictionary (or hash map).
1 2 3 4 5 6 7 | let factorials = {}; let s = 1; for (let i = 1; i <= 9; ++ i) { s *= i; factorials[i] = s; } factorials[0] = 1; |
let factorials = {}; let s = 1; for (let i = 1; i <= 9; ++ i) { s *= i; factorials[i] = s; } factorials[0] = 1;
A single loop from 1 to 9 is sufficient as we are iteratively multiple the next number.
Uppper bound of the Curious Numbers
We don’t need to and we can’t search infinite numbers. One upperbound we can use is 9999999 as 7*9! is less than 9999999.
We then bruteforce all the numbers and sum those curious numbers. The curious number can be determined by the following procedure: converted to string, and split into char array, then sum up the digital factorials, finally comparing the sum with the number.
1 2 3 4 5 6 7 8 9 10 | let sum = 0; for (let i = 3; i <= 9999999; ++ i) { let x = String(i).split('').reduce((a, b) => { return a + factorials[b]; }, 0); if (x === i) { sum += i; } } console.log(sum); |
let sum = 0; for (let i = 3; i <= 9999999; ++ i) { let x = String(i).split('').reduce((a, b) => { return a + factorials[b]; }, 0); if (x === i) { sum += i; } } console.log(sum);
The answer is 40730.
–EOF (The Ultimate Computing & Technology Blog) —
Recommend:How To Choose The Best Hosting Service For A WordPress Website
An Idiot’s Guide to Email Automation for Bloggers
Checklist for Choosing a Perfect WordPress Blog Theme
15 Mindset Hacks to Avoid Blogging Failure
Can Retailers Refuse Refunds Using POS Software?
How to Create Sponsorship Proposals For Your Blog
7 Top Investment Blogs For Newbie And Veteran Investors
Algorithm to Find the Winner on a Tic Tac Toe Game
The PUSHD/POPD Implementation in Pure Windows Batch
Three ways to Reverse a List/Array/Tuple in Python
- Comment list
-
- Comment add