# Problem 199: Iterative Circle Packing

## Problem Explanation

• Placing three circles that are the same size and as big as they can be without overlapping inside a bigger circle leaves four gaps
• The first iteration of adding more circles, puts another maximum sized circle in each gap
• Each iteration after that fills the gaps left over with another maximum sized circle
• In this challenge you need to find the area not filled after `n` iterations

## Solutions

Solution 1 (Click to Show/Hide)
``````function iterativeCirclePacking(n) {
let k1 = 1;
let k0 = k1 * (3 - 2 * Math.sqrt(3));
let a0 = 1 / (k0 * k0);
let a1 = 3 / (k1 * k1);
a1 += 3 * getArea(k0, k1, k1, n);
a1 += getArea(k1, k1, k1, n);
let final = ((a0 - a1) / a0).toFixed(8);

return parseFloat(final);
function getArea(k1, k2, k3, depth) {
if (depth == 0) return 0.0;
let k4 = k1 + k2 + k3 + 2 * Math.sqrt(k1 * k2 + k2 * k3 + k3 * k1);
let a = 1 / (k4 * k4);
a += getArea(k1, k2, k4, depth - 1);
a += getArea(k2, k3, k4, depth - 1);
a += getArea(k3, k1, k4, depth - 1);
return a;
}
}
``````