LeetCode 1739: Building Boxes

Explanation:

To solve this problem, we need to find the minimum number of boxes that can touch the floor while following the given placement rules. We can approach this by iteratively placing boxes in layers until we reach the total number of boxes. The key observation is that each layer will have one more box than the previous layer until we have placed all boxes.

1. Initialize variables totalBoxes and currLayerBoxes to 0, and layer to 1.
2. Repeat the following steps while totalBoxes is less than n:
   • Increment currLayerBoxes by layer.
   • Increment totalBoxes by currLayerBoxes.
   • Increment layer by 1.
3. Return the value of layer - 1 as this will be the minimum number of boxes touching the floor.

Time Complexity: O(sqrt(n)) Space Complexity: O(1)

:

class Solution {
    public int minimumBoxes(int n) {
        int totalBoxes = 0;
        int currLayerBoxes = 0;
        int layer = 1;
        
        while (totalBoxes < n) {
            currLayerBoxes += layer;
            totalBoxes += currLayerBoxes;
            layer++;
        }
        
        return layer - 1;
    }
}