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small typo fix in algorithm-performance (#36294)

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* Update index.md

* fixed typo mistakes
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Rajiv Ranjan Singh
2019-06-15 02:10:56 +05:30
committed by Randell Dawson
parent 2366cf2e6b
commit 678fda34bf
1 changed files with 6 additions and 6 deletions
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guide/english/algorithms/algorithm-performance/index.md
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@ -3,20 +3,20 @@ title: Algorithm Performance
--- ---
## Algorithm Performance ## Algorithm Performance
To understand the performance of algorithms, first we need to know the big-O notation. To understand the performance of algorithms, you first need to know the big-O notation.
### The Big-O Notation ### The Big-O Notation
In mathematics, big-O notation is a symbolism used to describe and compare the _limiting behavior_ of a function. In mathematics, the big-O notation is a symbolism used to describe and compare the _limiting behavior_ of a function.
A function's limiting behavior is how the function acts as it approaches a specific value (usually trends towards infinity). A function's limiting behavior is how the function acts as it approaches a specific value (usually trends towards infinity).
In short, big-O notation is used to describe the growth or decline of a function, usually with respect to another function. In short, the big-O notation is used to describe the growth or decline of a function, usually with respect to another function.
In algorithm design, we usually use big-O notation because we can see how good or bad an algorithm's performance will be. From a denotative perspective, big-O denotes the runtime in the worst possible case scenario. However, in many instances, people use it as a synonym for average expected runtime. In algorithm design, we usually use big-O notation because we can see how good or bad an algorithm's performance will be. From a denotative perspective, big-O denotes the runtime in the worst possible case scenario. However, in many instances, people use it as a synonym for average expected runtime.
In mathematics, the big-O notation is a symbolism used to describe and compare the _limiting behavior_ of a function. In mathematics, the big-O notation is a symbolism used to describe and compare the _limiting behavior_ of a function.
In short, big-O notation is used to describe the growth or decline of a function, usually with respect to another function. In programming, big-O notation compares the growth/decline of the runtime in respects to the size of the input. In short, the big-O notation is used to describe the growth or decline of a function, usually with respect to another function. In programming, big-O notation compares the growth/decline of the runtime in respects to the size of the input.
NOTE: x^2 is equivalent to x * x or 'x-squared' NOTE: x^2 is equivalent to x * x or 'x-squared'
@ -25,7 +25,7 @@ The symbol of a claim like x = O(x^2) for all x > _n_ can be substituted with x
Effectively, we say that a function f(x) that is O(g(x)) grows slower than g(x) does. Effectively, we say that a function f(x) that is O(g(x)) grows slower than g(x) does.
Comparatively, in computer science and software development we can use big-O notation in order to describe the efficiency of algorithms via its time and space complexity. Comparatively, in computer science and software development, we can use big-O notation in order to describe the efficiency of algorithms via its time and space complexity.
**Space Complexity** of an algorithm refers to its memory footprint with respect to the input size. **Space Complexity** of an algorithm refers to its memory footprint with respect to the input size.
@ -52,7 +52,7 @@ The following 3 notations are mostly used to represent the time complexity of al
<img src = "https://cdncontribute.geeksforgeeks.org/wp-content/uploads/AlgoAnalysis-2.png"/> <img src = "https://cdncontribute.geeksforgeeks.org/wp-content/uploads/AlgoAnalysis-2.png"/>
3. **Ω Notation**: Ω notation provides a lower bound to algorithm. it shows fastest possible answer for that algorithm. 3. **Ω Notation**: Ω notation provides a lower bound to algorithm. it shows the fastest possible answer for that algorithm.
>Ω (g(n)) = {f(n): there exist positive constants c and n0 such that 0 <= cg(n) <= f(n) for all n >= n0}. >Ω (g(n)) = {f(n): there exist positive constants c and n0 such that 0 <= cg(n) <= f(n) for all n >= n0}.
<img src = "https://cdncontribute.geeksforgeeks.org/wp-content/uploads/AlgoAnalysis-3.png"/> <img src = "https://cdncontribute.geeksforgeeks.org/wp-content/uploads/AlgoAnalysis-3.png"/>