Computer Engineering and Applications ›› 2018, Vol. 54 ›› Issue (16): 266-270.

### Calculation of minimum count of money and determination of money denomination

XIAO Hongde

1. School of Mathematics and Statistics, Henan University, Kaifeng, Henan 475004, China
• Online:2018-08-15 Published:2018-08-09

### 最少钱币数量的计算与钱币面额的确定

1. 河南大学 数学与统计学院，河南 开封 475004

Abstract: The issuance and determination of coins will remain stable for a relatively long time. The total amount and denomination of coins is determined by planning and budgeting in a medium and long time. How to determine the denomination of coins so that they can bring convenience to people as much as possible when they are in use? They are not only convenient for calculation, but also can reduce the use frequency as much as possible. This is a practical and useful problem. For a given range and a given coin denomination, with the help of sieve of Eratosthenes method, Dijkstra method, breadth first traversal of graph algorithm, this paper designs a fast calculation of the minimum number of coins for each numerical method which is the least number of coins sieve method to calculate the average amount of coins. For a given range of coins and number of types, for the problem how to determine the optimal combination of coins, this paper presents the process of optimal combination for 3 kinds of coins, and finds out their regularities through the numerical analysis of characteristics of each coin in optimal combination, then fits the curve of optimal combination of each coin denomination by the principle of least squares method. By the fitting curve of limit, this paper greatly reduces the number of traversal to find out the optimal combination of coins.