Just as with functions, we can execute statements in the bodies of loops.
We can use everything we learned in the loop, like conditional constructs. Imagine a function that counts the number of times a letter appears in a sentence. We see an example of how it works here:
Before you look at the contents of a function, think about this:
- Is this an aggregate operation?
- What will be the test condition to determine if we should include the character?
Now, we look at the contents of a function:
It is an aggregation task. It doesn't count all the characters to calculate the amount, but you still should analyze each character. The main difference between this loop and the ones we looked at before is that there's a condition in the body.
We only increment the count variable if the character in question is the same as the expected one. Otherwise, it's a typical aggregate function, returning the number of characters you want.
Edge cases
The my_substr() function you implemented in a previous lesson contains many bugs. It passed the test because it had no edge cases.
The function worked with regular arguments. Now let's imagine that we passed these length options:
- 0
- Negative number
- A number that exceeds the actual size of the string
The creators of Python did not design the my_substr() function for this. The code will run in different situations with different combinations of conditions and data. You can't be sure that the arguments passed to it will always be correct, so you must consider all cases.
Edge cases are a common source of logic errors in programs. There is always something that programmers forget to consider. These errors often don't immediately manifest. They do not cause visible problems for a long time.
The program may continue to work, but eventually, someone will notice an error in the results. It can often be a result of Python's dynamic typing.
As you get more experience, you'll learn how to deal with these errors.
Here is an extended version of the my_substr() function. It takes three arguments: a string, an index, and the length of the substring to extract. The function returns a substring of the specified length starting from the given index.
Let us observe some calling examples:
What edge cases should we consider:
- The extracted substring has a negative length
- The index given is negative
- The index given exceeds the boundary of the entire string
- The length of the substring in the sum with the given index exceeds the boundary of the whole string
When implementing the function, we write each edge case as a separate code piece, most likely with if.
It is worth implementing a separate function that checks the arguments are valid if you want to write my_substr() in a way that protects it against these cases.
Returning from loops
Dealing with loops usually comes down to two cases.
We can:
- Aggregate data during iterations and work with it after the loop (for example, string reversals)
- Execute the loop until we reach the desired result and exit (for example, prime number calculations)
Consider an algorithm that checks whether a number is a prime. We divide the number x by all numbers from two to x - 1 and look at the remainder. We know we have a prime number if we cannot find a divisor in this range that divides x without a remainder.
In this case, we don't need to go to x - 1 - half of x is enough.
For example, 11 isn't divisible by 2, 3, 4, or 5. When we know it, we can be sure that 11 won't be divisible by numbers above its half.
So we can optimize the algorithm and check the divisions only up to x / 2:
Imagine that the algorithm that divides numbers consecutively by numbers up to x / 2 finds one that divides without a remainder.
It means the argument passed is not a prime number, and we don't need further calculations. It is where it returns False.
If you have run the whole loop and have not found a number that divides without a remainder, it means the number is prime.
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It should check if a given string contains a specified letter (regardless of case). The function takes two parameters:\n\n* The string\n* The letter to search for\n\nAnd returns the result of the check as a boolean value.\n\n```python\nprint(has_char('Hexlet', 'H')) # => True\nprint(has_char('Hexlet', 'h')) # => True\nprint(has_char('Awesomeness', 'd')) # => False\n```\n","prepared_readme":"## src/solution.py\n\nImplement the function `has_char()`. It should check if a given string contains a specified letter (regardless of case). The function takes two parameters:\n\n* The string\n* The letter to search for\n\nAnd returns the result of the check as a boolean value.\n\n```python\nprint(has_char('Hexlet', 'H')) # => True\nprint(has_char('Hexlet', 'h')) # => True\nprint(has_char('Awesomeness', 'd')) # => False\n```\n","has_solution":true,"entity_name":"Conditions in the loop body"},"units":[{"id":8986,"name":"theory","url":"/courses/python-basics/lessons/conditions-inside-loops/theory_unit"},{"id":9391,"name":"quiz","url":"/courses/python-basics/lessons/conditions-inside-loops/quiz_unit"},{"id":9809,"name":"exercise","url":"/courses/python-basics/lessons/conditions-inside-loops/exercise_unit"}],"links":[],"ordered_units":[{"id":8986,"name":"theory","url":"/courses/python-basics/lessons/conditions-inside-loops/theory_unit"},{"id":9391,"name":"quiz","url":"/courses/python-basics/lessons/conditions-inside-loops/quiz_unit"},{"id":9809,"name":"exercise","url":"/courses/python-basics/lessons/conditions-inside-loops/exercise_unit"}],"id":3968,"slug":"conditions-inside-loops","state":"approved","name":"Conditions in the loop body","course_order":350,"goal":"Learning to control the behavior of programs in loops","self_study":null,"theory_video_provider":null,"theory_video_uid":null,"theory":"\n\nJust as with functions, we can execute statements in the bodies of loops.\n\nWe can use everything we learned in the loop, like conditional constructs. Imagine a function that counts the number of times a letter appears in a sentence. We see an example of how it works here:\n\n```python\ncount_chars('Fear cuts deeper than swords.', 'e') # 4\n# If nothing is found, the result is 0 matches\ncount_chars('Sansa', 'y') # 0\n```\n\nBefore you look at the contents of a function, think about this:\n\n* Is this an aggregate operation?\n* What will be the test condition to determine if we should include the character?\n\nNow, we look at the contents of a function:\n\n```python\ndef count_chars(string, char):\n index = 0\n count = 0\n while index < len(string):\n if string[index] == char:\n # We only count the matching characters\n count = count + 1\n # The counter is incremented anyway\n index = index + 1\n return count\n```\n\nIt is an **aggregation task**. It doesn't count all the characters to calculate the amount, but you still should analyze each character. The main difference between this loop and the ones we looked at before is that there's a condition in the body.\n\nWe only increment the `count` variable if the character in question is the same as the expected one. Otherwise, it's a typical aggregate function, returning the number of characters you want.\n\n## Edge cases\n\nThe `my_substr()` function you implemented in a previous lesson contains many bugs. It passed the test because it had no **edge cases**.\n\nThe function worked with regular arguments. Now let's imagine that we passed these length options:\n\n* `0`\n* Negative number\n* A number that exceeds the actual size of the string\n\nThe creators of Python did not design the `my_substr()` function for this. The code will run in different situations with different combinations of conditions and data. You can't be sure that the arguments passed to it will always be correct, so you must consider all cases.\n\nEdge cases are a common source of logic errors in programs. There is always something that programmers forget to consider. These errors often don't immediately manifest. They do not cause visible problems for a long time.\n\nThe program may continue to work, but eventually, someone will notice an error in the results. It can often be a result of Python's dynamic typing.\n\nAs you get more experience, you'll learn how to deal with these errors.\n\nHere is an extended version of the `my_substr()` function. It takes three arguments: a string, an index, and the length of the substring to extract. The function returns a substring of the specified length starting from the given index.\n\nLet us observe some calling examples:\n\n```python\nstring = 'If I look back I am lost'\nprint(my_substr(string, 0, 1)) # => 'I'\nprint(my_substr(string, 3, 6)) # => 'I look'\n```\n\nWhat edge cases should we consider:\n\n* The extracted substring has a negative length\n* The index given is negative\n* The index given exceeds the boundary of the entire string\n* The length of the substring in the sum with the given index exceeds the boundary of the whole string\n\nWhen implementing the function, we write each edge case as a separate code piece, most likely with `if`.\n\nIt is worth implementing a separate function that checks the arguments are valid if you want to write `my_substr()` in a way that protects it against these cases.\n\n## Returning from loops\n\nDealing with loops usually comes down to two cases.\n\nWe can:\n\n* Aggregate data during iterations and work with it after the loop (for example, string reversals)\n* Execute the loop until we reach the desired result and exit (for example, prime number calculations)\n\nConsider an algorithm that checks whether a number is a prime. We divide the number `x` by all numbers from two to `x - 1` and look at the remainder. We know we have a prime number if we cannot find a divisor in this range that divides `x` without a remainder.\n\nIn this case, we don't need to go to `x - 1` - half of `x` is enough.\n\nFor example, `11` isn't divisible by `2`, `3`, `4`, or `5`. When we know it, we can be sure that `11` won't be divisible by numbers above its half.\n\nSo we can optimize the algorithm and check the divisions only up to `x / 2`:\n\n```python\ndef is_prime(number):\n if number < 2:\n return False\n\n divider = 2\n\n while divider <= number / 2:\n if number % divider == 0:\n return False\n\n divider += 1\n\n return True\n\nprint(is_prime(1)) # => False\nprint(is_prime(2)) # => True\nprint(is_prime(3)) # => True\nprint(is_prime(4)) # => False\n```\n\nImagine that the algorithm that divides numbers consecutively by numbers up to `x / 2` finds one that divides without a remainder.\n\nIt means the argument passed is not a prime number, and we don't need further calculations. It is where it returns `False`.\n\nIf you have run the whole loop and have not found a number that divides without a remainder, it means the number is prime.\n"},"lessonMember":null,"courseMember":null,"course":{"start_lesson":{"exercise":null,"units":[{"id":8918,"name":"theory","url":"/courses/python-basics/lessons/intro/theory_unit"}],"links":[{"id":424684,"name":"The Python Developer Profession","url":"https://en.hexlet.io/programs/python"}],"ordered_units":[{"id":8918,"name":"theory","url":"/courses/python-basics/lessons/intro/theory_unit"}],"id":3932,"slug":"intro","state":"approved","name":"Introduction","course_order":100,"goal":"Learning about Python Basics course","self_study":null,"theory_video_provider":null,"theory_video_uid":null,"theory":"Python is one of the most popular programming languages in science and application development. The Python programmer profession in Hexlet gives you all the information you need to find work. 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<p>Just as with functions, we can execute statements in the bodies of loops.</p>
<p>We can use everything we learned in the loop, like conditional constructs. Imagine a function that counts the number of times a letter appears in a sentence. We see an example of how it works here:</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">count_chars('Fear cuts deeper than swords.', 'e') # 4
# If nothing is found, the result is 0 matches
count_chars('Sansa', 'y') # 0</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>Before you look at the contents of a function, think about this:</p>
<ul>
<li>Is this an aggregate operation?</li>
<li>What will be the test condition to determine if we should include the character?</li>
</ul>
<p>Now, we look at the contents of a function:</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">def count_chars(string, char):
index = 0
count = 0
while index < len(string):
if string[index] == char:
# We only count the matching characters
count = count + 1
# The counter is incremented anyway
index = index + 1
return count</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>It is an <strong>aggregation task</strong>. It doesn't count all the characters to calculate the amount, but you still should analyze each character. The main difference between this loop and the ones we looked at before is that there's a condition in the body.</p>
<p>We only increment the <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">count</code> variable if the character in question is the same as the expected one. Otherwise, it's a typical aggregate function, returning the number of characters you want.</p>
<h2 id="heading-2-1">Edge cases</h2>
<p>The <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">my_substr()</code> function you implemented in a previous lesson contains many bugs. It passed the test because it had no <strong>edge cases</strong>.</p>
<p>The function worked with regular arguments. Now let's imagine that we passed these length options:</p>
<ul>
<li><code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">0</code></li>
<li>Negative number</li>
<li>A number that exceeds the actual size of the string</li>
</ul>
<p>The creators of Python did not design the <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">my_substr()</code> function for this. The code will run in different situations with different combinations of conditions and data. You can't be sure that the arguments passed to it will always be correct, so you must consider all cases.</p>
<p>Edge cases are a common source of logic errors in programs. There is always something that programmers forget to consider. These errors often don't immediately manifest. They do not cause visible problems for a long time.</p>
<p>The program may continue to work, but eventually, someone will notice an error in the results. It can often be a result of Python's dynamic typing.</p>
<p>As you get more experience, you'll learn how to deal with these errors.</p>
<p>Here is an extended version of the <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">my_substr()</code> function. It takes three arguments: a string, an index, and the length of the substring to extract. The function returns a substring of the specified length starting from the given index.</p>
<p>Let us observe some calling examples:</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">string = 'If I look back I am lost'
print(my_substr(string, 0, 1)) # => 'I'
print(my_substr(string, 3, 6)) # => 'I look'</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>What edge cases should we consider:</p>
<ul>
<li>The extracted substring has a negative length</li>
<li>The index given is negative</li>
<li>The index given exceeds the boundary of the entire string</li>
<li>The length of the substring in the sum with the given index exceeds the boundary of the whole string</li>
</ul>
<p>When implementing the function, we write each edge case as a separate code piece, most likely with <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">if</code>.</p>
<p>It is worth implementing a separate function that checks the arguments are valid if you want to write <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">my_substr()</code> in a way that protects it against these cases.</p>
<h2 id="heading-2-2">Returning from loops</h2>
<p>Dealing with loops usually comes down to two cases.</p>
<p>We can:</p>
<ul>
<li>Aggregate data during iterations and work with it after the loop (for example, string reversals)</li>
<li>Execute the loop until we reach the desired result and exit (for example, prime number calculations)</li>
</ul>
<p>Consider an algorithm that checks whether a number is a prime. We divide the number <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">x</code> by all numbers from two to <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">x - 1</code> and look at the remainder. We know we have a prime number if we cannot find a divisor in this range that divides <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">x</code> without a remainder.</p>
<p>In this case, we don't need to go to <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">x - 1</code> - half of <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">x</code> is enough.</p>
<p>For example, <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">11</code> isn't divisible by <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">2</code>, <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">3</code>, <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">4</code>, or <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">5</code>. When we know it, we can be sure that <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">11</code> won't be divisible by numbers above its half.</p>
<p>So we can optimize the algorithm and check the divisions only up to <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">x / 2</code>:</p>
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if number < 2:
return False
divider = 2
while divider <= number / 2:
if number % divider == 0:
return False
divider += 1
return True
print(is_prime(1)) # => False
print(is_prime(2)) # => True
print(is_prime(3)) # => True
print(is_prime(4)) # => False</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>Imagine that the algorithm that divides numbers consecutively by numbers up to <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">x / 2</code> finds one that divides without a remainder.</p>
<p>It means the argument passed is not a prime number, and we don't need further calculations. It is where it returns <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">False</code>.</p>
<p>If you have run the whole loop and have not found a number that divides without a remainder, it means the number is prime.</p></div></div></div></div><style data-mantine-styles="inline">.__m__-_R_1bdub_{--col-flex-grow:auto;--col-flex-basis:8.333333333333334%;--col-max-width:8.333333333333334%;}@media(min-width: 48em){.__m__-_R_1bdub_{--col-flex-grow:auto;--col-flex-basis:16.666666666666668%;--col-max-width:16.666666666666668%;}}</style><div style="min-width:0rem;height:100%;min-height:0rem" class="m_96bdd299 mantine-Grid-col __m__-_R_1bdub_"><div style="margin-inline:var(--mantine-spacing-xs)" class="mantine-visible-from-sm"><button style="--button-color:var(--mantine-color-white);margin-bottom:var(--mantine-spacing-lg);text-decoration:none" class="mantine-focus-auto m_849cf0da mantine-focus-auto m_77c9d27d mantine-Button-root m_87cf2631 mantine-UnstyledButton-root m_b6d8b162 mantine-Text-root mantine-Anchor-root" data-underline="hover" data-disabled="true" data-block="true" 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