Straight Line Numbers in Java

A number n can be said to be a straight-line number if the digits of the number form an arithmetic progression. It is evident that to decide whether the digits are in arithmetic progression or not. There is a requirement of at least three digits. Therefore, straight-line numbers should always contain at least three digits while excluding the leading zeros.

Example 1:

Input: N = 178

Output: No, 178 is not a Straight-Line number.

Explanation: The digits of the number 178 are 1, 7, 8. 7 - 1 = 6, and 8 - 7 = 1. Thus, the common difference is not the same, and hence, the digits are not in the arithmetic progression. Thus, 178 is not a Straight-Line number.

Example 2:

Input: N = 111

Output: Yes, 111 is a Straight-Line number.

Explanation: The digits of the number 111 are 1, 1, and 1. 1 - 1 = 0, and 1 - 1 = 0. Thus, the common difference is the same, and hence, the digits are in the arithmetic progression. Thus, 111 is a Straight-Line number.

Example 3:

Input: N = 25

Output: No, 25 is not a Straight-Line number.

Explanation: The digits of the number 25 are 2 and 5. The two digits are not sufficient to decide whether they are in arithmetic progression or not. Thus, 25 is not a Straight-Line number.

Naïve Approach

The approach is simple. First of all, we have to store all the digits of the number in an array. Then, using a loop, we can find the difference of two consecutive elements while iterating from either left to right or from right to left. If the difference of all of the two consecutive elements is the same, then we can say that the number is a straight-line number; otherwise, it is not.

FileName: StraightLineNumbersNaive.java

// importing ArrayList
import java.util.ArrayList;
public class StraightLineNumbersNaive
{
// The method returns true if the number n is the 
// Straight Line number; otherwise returns false
boolean isStraightLineNumbers(int n)
{
// list for storing the digits of the number n
ArrayList<Integer> al = new ArrayList<Integer>();
while(n > 0)
{
// adding digits to the list al
int dig = n % 10;
al.add(dig);
n = n / 10;
}
int size = al.size();
// if the total number of digits 
// are less than or equal to two, then the number is not 
// a straight line number
if(size <= 2)
{
    return false;
}
// finding the difference of consecutive digits 
// of the number n.
int diff = al.get(1) - al.get(0);
for(int i = 2; i < size; i++)
{
if(diff != (al.get(i) - al.get(i - 1)))
{
    // if the difference is not the same, then it
    // means digits are not in the arithmetic progression
    // Hence, the number n is not a straight-line number. Therefore,
    // false is returned
    return false;
}
}
return true;
}
// main method
public static void main(String argvs[]) 
{
// instantiating the class StraightLineNumbersNaive
StraightLineNumbersNaive obj = new StraightLineNumbersNaive();

int n = 178; // first input

boolean ans = obj.isStraightLineNumbers(n);
if(ans)
{
    System.out.println("Yes, " + n + " is a Straight Line number.");
}
else
{
    System.out.println("No, " + n + " is not a Straight Line number.");
}
n = 111; // second input
ans = obj.isStraightLineNumbers(n);
if(ans)
{
    System.out.println("Yes, " + n + " is a Straight Line number.");
}
else
{
    System.out.println("No, " + n + " is not a Straight Line number.");
}
n = 25; // third input
ans = obj.isStraightLineNumbers(n);
if(ans)
{
    System.out.println("Yes, " + n + " is a Straight Line number.");
}
else
{
    System.out.println("No, " + n + " is not a Straight Line number.");
}
}
}

Output:

No, 178 is not a Straight Line number.
Yes, 111 is a Straight Line number.
No, 25 is not a Straight Line number.

Complexity Analysis: The loops used in the program iterates until all the digits of the number is explored. Thus, making the time complexity of the program O(d). The program is also storing the digits in an array list, which makes the space complexity of the program O(d), where d is the total number of digits present in the input number.

Approach: Using Strings

In this approach, first, we need to convert the number into a string. Then, we can iterate over the characters to find whether they are in arithmetic progression or not, and accordingly, we can decide whether they are straight-line numbers or not. The illustration of it is mentioned in the following program.

FileName: StraightLineNumbersStr.java

public class StraightLineNumbersUsingStr
{
// The method returns true if the number n is the 
// Straight Line number; otherwise returns false
boolean isStraightLineNumbers(int n)
{
String temp = Integer.toString(n);
int size = temp.length();

// any number that is containing less than or equal to two digits
// can't be considered as the straight line number
if(size <= 2)
{
    return false;
}
// computing the common difference
int cd = (int)temp.charAt(1) - (int)temp.charAt(0);
for(int i = 2; i < size; i++)
{
    int diff = (int)temp.charAt(i) - (int)temp.charAt(i - 1);
    if(cd != diff)
    {
        return false;
    }
}

return true;
}

// main method
public static void main(String argvs[]) 
{
// instantiating the class StraightLineNumbersUsingStr
StraightLineNumbersUsingStr obj = new StraightLineNumbersUsingStr();

int n = 178; // first input

boolean ans = obj.isStraightLineNumbers(n);
if(ans)
{
    System.out.println("Yes, " + n + " is a Straight Line number.");
}
else
{
    System.out.println("No, " + n + " is not a Straight Line number.");
}
n = 111; // second input
ans = obj.isStraightLineNumbers(n);
if(ans)
{
    System.out.println("Yes, " + n + " is a Straight Line number.");
}
else
{
    System.out.println("No, " + n + " is not a Straight Line number.");
}
n = 25; // third input
ans = obj.isStraightLineNumbers(n);
if(ans)
{
    System.out.println("Yes, " + n + " is a Straight Line number.");
}
else
{
    System.out.println("No, " + n + " is not a Straight Line number.");
}
}
}

Output:

No, 178 is not a Straight Line number.
Yes, 111 is a Straight Line number.
No, 25 is not a Straight Line number.

Complexity Analysis: The time, as well as the space complexity of the program, is the same as the previous program.

We can avoid using strings and array list to reduce the space complexity. The illustration of it is mentioned below.

FileName: StraightLineNumbersOptimized.java

public class StraightLineNumbersOptimized
{
// the method returns true, if the number n is the 
// Straight Line number; otherwise returns false
boolean isStraightLineNumbers(int n)
{
// taking the last two digits of the number
int dig1 = n % 10;
n = n / 10;
int dig2 = n % 10;
n = n / 10;

// any number that is containing less than or equal to two digits
// can't be considered as the straight line number
if(n == 0)
{
    return false;
}

int cd = dig2 -  dig1;

while(n > 0)
{
dig1 = dig2;
dig2 = n % 10;
n = n / 10;

if(cd != (dig2 - dig1))
{
    return false;
}
}
return true;
}
// main method
public static void main(String argvs[]) 
{
// instantiating the class StraightLineNumbersOptimized
StraightLineNumbersOptimized obj = new StraightLineNumbersOptimized();

int n = 178; // first input

boolean ans = obj.isStraightLineNumbers(n);
if(ans)
{
    System.out.println("Yes, " + n + " is a Straight Line number.");
}
else
{
    System.out.println("No, " + n + " is not a Straight Line number.");
}
n = 111; // second input
ans = obj.isStraightLineNumbers(n);
if(ans)
{
    System.out.println("Yes, " + n + " is a Straight Line number.");
}
else
{
    System.out.println("No, " + n + " is not a Straight Line number.");
}
n = 25; // third input
ans = obj.isStraightLineNumbers(n);
if(ans)
{
    System.out.println("Yes, " + n + " is a Straight Line number.");
}
else
{
    System.out.println("No, " + n + " is not a Straight Line number.");
}
}
}

Output:

No, 178 is not a Straight Line number.
Yes, 111 is a Straight Line number.
No, 25 is not a Straight Line number.

Complexity Analysis: The time, as well as the space complexity of the program, is the same as the previous program.

Output:

No, 178 is not a Straight Line number.
Yes, 111 is a Straight Line number.
No, 25 is not a Straight Line number.

Complexity Analysis: The time complexity of the program is O(d), where d is the total number of digits present in the number. The space complexity of the program is O(1).

Finding Straight Line Numbers Within a Range

In this section, we will see how to filter the straight-line numbers within a range.

FileName: StraightLineNumbersRange.java

public class StraightLineNumbersRange
{
// The method returns true if the number n is the 
// Straight Line number; otherwise returns false
boolean isStraightLineNumbers(int n)
{
// taking last two digits of the number
int dig1 = n % 10;
n = n / 10;
int dig2 = n % 10;
n = n / 10;

// any number that is containing less than or equal to two digits
// can't be considered as the straight line number
if(n == 0)
{
    return false;
}

int cd = dig2 -  dig1;

while(n > 0)
{
dig1 = dig2;
dig2 = n % 10;
n = n / 10;

if(cd != (dig2 - dig1))
{
    return false;
}
}
return true;
}

// main method
public static void main(String argvs[]) 
{
// instantiating the class StraightLineNumbersRange
StraightLineNumbersRange obj = new StraightLineNumbersRange();

// finding the range
int n1 = 100;
int n2 = 1000;

System.out.println("Straight Line Numbers from range " + n1 + " and " + n2 + " are:");

for(int i = n1; i <= n2; i++)
{
if(obj.isStraightLineNumbers(i))
{
    System.out.print(i + " ");
}    
}

}
}

Output:

Straight Line Numbers from range 100 and 1000 are:
111 123 135 147 159 210 222 234 246 258 321 333 345 357 369 420 432 444 456 468 531 543 555 567 579 630 642 654 666 678 741 753 765 777 789 840 852 864 876 888 951 963 975 987 999

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