You are given a binary string floor representing the colors of tiles along a floor, where floor[i] = $'1'$ indicates that the tile at index i is white, and floor[i] = $'0'$ indicates that the tile at index i is black.

You are also given two integers numCarpets and carpetLen. You have numCarpets black carpets, each of length carpetLen tiles. Each carpet can cover carpetLen consecutive tiles on the floor.

Return the minimum number of white tiles that remain visible after optimally placing the carpets.

Note: Carpets are permitted to overlap with each other.

Constraints:

• $1 \leq$ carpetLen $\leq$ floor.length $\leq 1000$

• floor[i] is either $'0'$ or $'1'$.

• $1 \leq$ numCarpets $\leq 1000$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.