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Big O Notations Exercise Solutions #29

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Big O Notations Exercise Solutions #29

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35 changes: 25 additions & 10 deletions big_o_exercise/readme.md
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Original file line number Diff line number Diff line change
Expand Up @@ -4,16 +4,16 @@

Simplify the following big O expressions as much as possible:

1. `O(n + 10)`
2. `O(100 * n)`
3. `O(25)`
4. `O(n^2 + n^3)`
5. `O(n + n + n + n)`
6. `O(1000 * log(n) + n)`
7. `O(1000 * n * log(n) + n)`
8. `O(2^n + n^2)`
9. `O(5 + 3 + 1)`
10. `O(n + n^(1/2) + n^2 + n * log(n)^10)`
1. `O(n + 10)` --> `O(n)`
2. `O(100 * n)` --> `O(n)`
3. `O(25)` --> `O(1)`
4. `O(n^2 + n^3)` --> `O(n^3)`
5. `O(n + n + n + n)` --> `O(n)`
6. `O(1000 * log(n) + n)` --> `O(n)`
7. `O(1000 * n * log(n) + n)` --> `O(n * log(n))`
8. `O(2^n + n^2)` --> `O(2^n)`
9. `O(5 + 3 + 1)` --> `O(1)`
10. `O(n + n^(1/2) + n^2 + n * log(n)^10)` --> `O(n^2)`

### Part 2

Expand All @@ -29,6 +29,9 @@ function logUpTo(n) {
}
}

Time Complexity: O(n)
Space Complexity: O(1)

// 2.

function logAtMost10(n) {
Expand All @@ -37,6 +40,9 @@ function logAtMost10(n) {
}
}

Time Complexity: O(1)
Space Complexity: O(1)

// 3.

function logAtLeast10(n) {
Expand All @@ -45,6 +51,9 @@ function logAtLeast10(n) {
}
}

Time Complexity: O(n)
Space Complexity: O(1)

// 4.

function onlyElementsAtEvenIndex(array) {
Expand All @@ -57,6 +66,9 @@ function onlyElementsAtEvenIndex(array) {
return newArray;
}

Time Complexity: O(n)
Space Complexity: O(n)

// 5.

function subtotals(array) {
Expand All @@ -70,4 +82,7 @@ function subtotals(array) {
}
return subtotalArray;
}

Time Complexity: O(n^2)
Space Complexity: O(n)
```