Ashish Patel: Notes

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A problem with complexity O(n) which takes 2^60 times will take 60 times in O(log n) complexity

<-- Fast Slow -->
Name Constant Logarithmic linear Quadratic exponential
Notation O(1) O(logn) O(n) O(n^2) O(k^n)
for(var i...){ // O(n)
	1+1; // O(1)
}
/**
* Complexity = O(n^2) + O(2) 
* We only care about worst case so we consider the worst time complexity only.
* i.e we take the highest order of the polynomial
* So the complexity is O(n^2)
*/
for(var i...){ // O(n)
	for(var j...){ // O(n)
		3+3; // O(1)
		5+6; // O(1)
	}
}

O(log n)

for(let i = 0; i < n; i*2){ //O(log n)
	stmt;
}

$$
\begin{aligned} i >= n \ 2^{k} >= n \ k = \log _{2} n \ \end{aligned} $$

Created 2019-01-23T11:45:03+05:18, updated 2022-02-02T18:00:28+00:00 · History · Edit