Digit Counting

Digit Counting
A Programming Pattern

Prof. David Bernstein
James Madison University

Computer Science Department

bernstdh@jmu.edu

Motivation

The Context:
- There are many situations in which a program needs to know the number of digits in an integer.
The Complication:
- Numbers don’t "know anything" about themselves (i.e., don't have any attributes other than their value)

Review

Positional Representation:
- The digit in position $n$ (counting from the right, starting with 0) corresponds to the $10^n$s place
Reversing the Process:
- To find the position of a particular place you need use a logarithm (recall that the $\log_{10}(x)$ is the value of $n$ that satisfies $x = 10^n$)

Thinking About the Problem

Some Observations:
- Evaluating the $\log_{10}(x)$ can be difficult
- Approximating it is easy
The Process:
- Since $log_{10}(100)$ is 2, $log_{10}(1000)$ is 3, and logarithms are monotonic, it follows that $log_{10}(x)$ is in the interval $[2,3)$ for any $x \in [100, 1000)$

Thinking About the Problem (cont.)

The Number 7198:
- Math.log10(7198) is approximately 3.8572118423168926 which is in the interval $[3,4)$
The Number 462:
- Math.log10(462) is approximately 2.6646419755561257 which is in the interval $[2,3)$

The Pattern

The Idea:
- $log_{10}()$ of any $n$-digit number will be in the interval $[n-1, n)$

The Pattern:

javaexamples/programmingpatterns/DigitCounting.java

(Fragment: pattern)

            /**
     * Determine the number of digits in an integer.
     *
     * @param x  The integer of interest
     * @return   The number of digits
     */
    public static int digits(int x) {
        return (int) Math.log10(x) + 1;
    }

An Example

The Problem:
- We need to convert a dollar amount (e.g., an income or a house price) into a phrase like "6 figures" or "7 figures"
A Specific Example:
- A person who earns $156,720 per year has a (int)Math.log10(156720) + 1 (i.e., 6) figure salary