Substring Minimum Function

` It's your birthday today! So, you ask your dad to buy a brand new bicycle. But your dad knows you are weak in math. Hence he gives you the following task. If you solve it, he will purchase the bicycle you want! The task is:` You are given a binary string. $N$ denotes the length of a binary string and $M$ denotes the number of occurrences of the character $1$ in the string $S$. Let $F(S)$ be a