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josephus.js
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josephus.js
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// A few small JS functions for experimenting with the Josephus problem. Try it in your browser console!
j = function(n, q) {
q = q || 2
var list = range(n)
var p = q < 0 ? 1 : -1
var seq = []
while(list.length > 1) {
p = (p+q) % list.length
if(p<0) p = list.length + p
seq.push(list[p])
list.splice(p, 1) // OPT
if(q >= 0) p--
}
return seq.concat(list[0]||0)
}
range = function(len, off) {
off = off|0
var list = []
for(var i=1; i<=len; i++)
list.push(i+off)
return list
}
last = function(list, k) { return list.slice(-k) }
survive = function(n, q, k) {return last(j(n, q), k||(q-1)||1)}
// r = range(20,20)
// x = r.map(function(n) { return r.map(function(q) { return survive(n, q, 1)[0] }) })
// console.table(x)
// q = [0,1]; for(var i=2; i<1000; i++) { q.push(survive(i,i,1)[0] )}
// q.filter(function(s, i) {return s+1 == i}).map(function(s) {return s+1})
// q.filter(function(s, i) {return s+2 == i}).map(function(s) {return s+2})
// q.filter(function(s, i) {return s*2 == i}).map(function(s) {return s*2})