## Answer in 60

### Input

### Exact result

### Alternate form assuming n>0

### Root

### Series expansion at n=0

### Series expansion at n=∞

### Derivative

### Indefinite integral

### Alternative representation

**Key moments in video**

From 00:30 — Imagine an Array of 3 Items

From 00:58 — Example of a pair comparison

From 06:27 — Maximum number of potential leaves

From 07:02 — Minimum Leaf Count

From 09:12 — Minimum number of leaves in a tree

From 11:03 — Applying logarithm to both sides

**Key moments in video**

From 00:26 — Visual Input Pipeline

From 01:05 — Primary Visual Cortex

## Related querie

### Which is better O n or O log n?

O(n) means that the algorithm's maximum running time is proportional to the input size. basically, O(something) is an upper bound on the algorithm's number of instructions (atomic ones). therefore, **O(logn) is tighter than O(n)** and is also better in terms of algorithms analysis.

### What is LGN in math?

Usage notes. This symbol, lg, is defined as the **base 10 logarithm in the ISO 80000-2:2019 standard**, which instead prescribes the symbol lb for the binary logarithm.

### Which is asymptotically larger lg lg * n or lg * lg n?

Then, as you see, **lg ∗ ( lg n ) \lg^{*} \left( \lg n \right) lg∗(lgn)** is asymptotically bigger \textbf{asymptotically bigger} asymptotically bigger than lg lg ∗ n \lg \lg^{*} n lglg∗n.

### What is on * log n?

O(log N) basically means **time goes up linearly while the n goes up exponentially**. So if it takes 1 second to compute 10 elements, it will take 2 seconds to compute 100 elements, 3 seconds to compute 1000 elements, and so on. It is O(log n) when we do divide and conquer type of algorithms e.g binary search.

### What is log * n function?

Logarithmic time complexity log(n): Represented in Big O notation as O(log n), when an algorithm has O(log n) running time, it means that **as the input size grows, the number of operations grows very slowly**. Example: binary search.

### What is log n equal to?

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, **x is the logarithm of n to the base b if b ^{x} = n**, in which case one writes x = log

_{b}n. For example, 2

^{3}= 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log

_{2}8.

### Which of the following is asymptotically smaller lg lg * n lg *( LGN lg n !) lg *( n !)?

lg(lg*n) < lg*(lgn) < lg(n!) < lg*(n!). So, **option (A)** is correct.

### What is lg lg * n?

lg* n (read "log star") is the **iterated logarithm**. It is defined as recursively as 0 if n <= 1 lg* n = 1 + lg*(lg n) if n > 1. Another way to think of it is the number of times that you have to iterate logarithm before the result is less than or equal to 1.

### Is O n log n faster than O n?

Yes for Binary search the time complexity in Log(n) not nlog(n). So it will be less than O(n). But **N*Log(N) is greater than O(N)**.

### Is O log n better than O 1?

**Sometimes, O(log n) will outperform O(1)** but as the input size 'n' increases, O(log n) will take more time than the execution of O(1).