Given:
$m$ chocolates and $n$ students with jealousy value $\{j_1, j_2,...j_n\}$ where $0<j_i<100$.
To Do:
- Distribute these chocolates among students $\{c_1, c_2,...c_n\}$ such that $\sum_{i=1}^{n}c_i=m$ and,
- Minimise total jealousy $J(c_1,c_2,..c_n)= \sum_{i=1}^n j_i*x_{c_i}$
Note:- $x_{c_i}$ is the number of students who received $>c_i$ chocolates.
- $j_i*x_{c_i}$ represents jealousy of $i^{th}$ student.
- $c_i \ge0$. It can be $0$ too.
Example:
There are $9$ chocolates and $3$ students with jealousy values $\{10, 20, 30\}.$
$\therefore$ minimum value of total jealousy will be $0$ as we can distribute $3$ chocolates to each student $\implies x_1=x_2=x_3=0$.
If we distributed chocolates as $\{1,4,4\}$
$\implies J = 10*2+20*0+30*0=20$.