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week 1, day 1 hw - big O exercises #28

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week 1, day 1 hw - big O exercises #28

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completed big O exercises
bigrobsf Aug 1, 2017
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remove console.log
bigrobsf Aug 1, 2017
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38 changes: 25 additions & 13 deletions big_o_exercise/readme.md
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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)
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careful with this one - which grows faster, n or nlog(n)?

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ah, right. I overlooked the '*' between n and log(n)

8. `O(2^n + n^2)` -> O(n^2)
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2^n grows more quickly than n^2, but we didn't talk about exponential growth in class so i wouldn't sweat this one too much.

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... oh wow! I totally missed that.

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 @@ -28,22 +28,28 @@ function logUpTo(n) {
console.log(i);
}
}
// TIME: O(n)
// SPACE: O(1)

// 2.
// 2.

function logAtMost10(n) {
for (var i = 1; i <= Math.min(n, 10); i++) {
console.log(i);
}
}
// TIME: O(1)
// SPACE: O(1)

// 3.
// 3.

function logAtLeast10(n) {
for (var i = 1; i <= Math.max(n, 10); i++) {
console.log(i);
}
}
// TIME: O(n)
// SPACE: O(1)

// 4.

Expand All @@ -56,8 +62,10 @@ function onlyElementsAtEvenIndex(array) {
}
return newArray;
}
// TIME: O(n)
// SPACE: O(n)

// 5.
// 5.

function subtotals(array) {
var subtotalArray = Array(array.length);
Expand All @@ -70,4 +78,8 @@ function subtotals(array) {
}
return subtotalArray;
}

subtotals([0,1,2,3,4,5])
// TIME: O(n^2)
// SPACE: O(n)
```