# Omprakash Sridharan

Problem URL: Hit the lottery

Allen has a LOT of money. He has n dollars in the bank. For security reasons, he wants to withdraw it in cash (we will not disclose the reasons here). The denominations for dollar bills are 1, 5, 10, 20, 100. What is the minimum number of bills Allen could receive after withdrawing his entire balance?

Input The first and only line of input contains a single integer n (1≤n≤109).

Output Output the minimum number of bills that Allen could receive.

This problem uses a greedy approach.

``````use std::io;

fn get_single_number_from_stdin() -> u64 {
let mut buffer = String::new();
buffer.trim().parse::<u64>().expect("Not an integer")
}

fn main(){
let mut dollars = get_single_number_from_stdin();
let denominations = vec![100,20,10,5,1];
let mut total_bills = 0;
for denomination in denominations {
if dollars == 0 {
break;
}
if dollars >= denomination {
let q = (dollars/denomination) as u64;
dollars -= denomination * q;
total_bills += q;
}else{
continue;
}
}
print!("{}",total_bills);
}
``````

Although for denominations that are not regular, the above algorithm will not give the least number of bills possible. We can use Dynamic Programming approach where we memorise the solution for the overlapping subproblems which drastically reduces the number of computations if the input is huge. Here is a version of the problem solved using dynamic programming.

``````use std::io;
use std::collections::HashMap;

fn get_single_number_from_stdin() -> usize {
let mut buffer = String::new();
buffer.trim().parse::<usize>().expect("Not an integer")
}

fn main(){
let dollars = get_single_number_from_stdin();
let denominations = vec![100,20,10,5,1];
let mut result = HashMap::new();
result.insert(0, 0);
for i in 1..=dollars {
for d in &denominations {
if *d <= i {
let sub_result = result.get(&(i - *d)).unwrap();
if result.contains_key(sub_result) && sub_result + 1 < *result.get(&i).unwrap_or(&(std::i64::MAX as usize)) {
result.insert(i, sub_result + 1);
}
}
}
println!("amount {}",i);
}
println!("{}",result.get(&dollars).unwrap());
}
``````