How to resolve the algorithm Mian-Chowla sequence step by step in the Wren programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Mian-Chowla sequence step by step in the Wren programming language
Table of Contents
Problem Statement
The Mian–Chowla sequence is an integer sequence defined recursively.
Mian–Chowla is an infinite instance of a Sidon sequence, and belongs to the class known as B₂ sequences.
The sequence starts with: then for n > 1, an is the smallest positive integer such that every pairwise sum is distinct, for all i and j less than or equal to n.
Demonstrating working through the first few terms longhand: Speculatively try a2 = 2 There are no repeated sums so 2 is the next number in the sequence. Speculatively try a3 = 3 Sum of 4 is repeated so 3 is rejected. Speculatively try a3 = 4 There are no repeated sums so 4 is the next number in the sequence. And so on...
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Mian-Chowla sequence step by step in the Wren programming language
Source code in the wren programming language
var mianChowla = Fn.new { |n|
var mc = List.filled(n, 0)
var sums = {}
var ts = {}
mc[0] = 1
sums[2] = true
for (i in 1...n) {
var j = mc[i-1] + 1
while (true) {
mc[i] = j
for (k in 0..i) {
var sum = mc[k] + j
if (sums[sum]) {
ts.clear()
break
}
ts[sum] = true
}
if (ts.count > 0) {
for (key in ts.keys) sums[key] = true
break
}
j = j + 1
}
}
return mc
}
var start = System.clock
var mc = mianChowla.call(100)
System.print("The first 30 terms of the Mian-Chowla sequence are:\n%(mc[0..29].join(" "))")
System.print("\nTerms 91 to 100 of the Mian-Chowla sequence are:\n%(mc[90..99].join(" "))")
System.print("\nTook %(((System.clock - start)*1000).round) milliseconds")
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