The floor division is the arithmetic operation that is used to divide two numbers and return the quotient rounded down to the nearest integer. It is denoted by the double forward slash"//" in Python. When both operands of floor division are positive, the result is the same as regular integer division. However, when one or both of the operands are negative.
When performing floor division with negative numbers, the result is rounded toward negative infinity. In other words, the quotient is rounded to the nearest integer if it is less than or equal to the precise result. Let's take an example to understand this better:
>>> -7 // 3
-3{codeBox}
In the above example, the expression -7 // 3 returns -3. The exact result of -7/3 is -2.333..., but the result of floor division is rounded towards negative infinity to the nearest integer that is less than or equal to the exact result, which is -3.
Similarly, if we perform floor division with a positive number and a negative number, the result is rounded toward negative infinity:
>>> 7 // -3-3{codeBox}
In the above example, the expression 7 // -3 returns -3. The exact result of 7/-3 is -2.333..., but the result of floor division is rounded towards negative infinity to the nearest integer that is less than or equal to the exact result, which is -3.
When both operands of floor division are negative, the result is rounded toward positive infinity. This indicates that the quotient is rounded up to the next larger or equal to the exact result integer. Let's take an example to understand this better:
>>> -7 // -32{codeBox}
In the above example, the expression -7 // -3 returns 2. The exact result of -7/-3 is 2.333..., but the result of floor division is rounded towards positive infinity to the nearest integer that is greater than or equal to the exact result, which is 2.
It is important to keep in mind that the behavior of floor division with negative numbers can be different in other programming languages or even different versions of Python. As a result, it is always a good idea to test your code using various inputs to make sure that the outcomes match your expectations.
If you still do not understand the concept let's take one more example
For example, 7 // 2 would result in 3 because 2 goes into 7 three times with a remainder of 1. However, when negative numbers are involved in floor division, it can lead to unexpected results.
When a negative number is divided using floor division, the result is rounded toward negative infinity. This means that the quotient is shifted towards negative infinity, which results in a smaller absolute value. For example, -7 // 2 would result in -4 instead of -3, because -3 is closer to zero than -4.
Consider the number line to help you understand this.
Starting at -7 and moving 2 units to the right, we arrive at -5. However, since we are using floor division, we round down to the nearest integer, which is -4.
Now let us take a big expression to understand
what is the output?
1+(2-3)*4**5//6
When evaluating the expression 1+(2-3)*4**5//6, Python follows the order of operations:
- First, it evaluates the exponentiation operator **. In this case, 4 raised to the power of 5 is 1024.
- Next, it evaluates the multiplication operator *. Since there are no parentheses indicating a different order of operations, it multiplies 1024 by the result of (2-3), which is -1.
- Then, it evaluates the floor division operator //, which divides the product of -1024 by 6 and rounds down to the nearest integer. This results in -171.
- Finally, it evaluates the addition operator +, which adds 1 to -171, resulting in a final answer of -170.
Therefore, the final result of the expression 1+(2-3)*4**5//6 is -170.
