Update apply-operations-to-maximize-score.cpp

kamyu104 · web-flow · commit 61aa657706ae · 2023-10-08T19:09:50.000+08:00
diff --git a/C++/apply-operations-to-maximize-score.cpp b/C++/apply-operations-to-maximize-score.cpp
@@ -1,4 +1,4 @@
-// Time:  O(sqrt(r) + nlogr + klogn)
+// Time:  O(sqrt(r) + n * (logr + pi(sqrt(r))) + klogn) = O(sqrt(r) + n * (logr + sqrt(r)/log(sqrt(r))) + klogn), m is max(k for _, k in queries), pi(n) = number of primes in a range [1, n] = O(n/logn) by prime number theorem, see https://en.wikipedia.org/wiki/Prime_number_theorem
 // Space: O(sqrt(r) + n)
 
 // number theory, mono stack, greedy, sort, heap

Original file line number	Diff line number	Diff line change
`@@ -1,4 +1,4 @@`
`1`		`-// Time: O(sqrt(r) + nlogr + klogn)`
	`1`	`+// Time: O(sqrt(r) + n * (logr + pi(sqrt(r))) + klogn) = O(sqrt(r) + n * (logr + sqrt(r)/log(sqrt(r))) + klogn), m is max(k for _, k in queries), pi(n) = number of primes in a range [1, n] = O(n/logn) by prime number theorem, see https://en.wikipedia.org/wiki/Prime_number_theorem`
`2`	`2`	`// Space: O(sqrt(r) + n)`
`3`	`3`
`4`	`4`	`// number theory, mono stack, greedy, sort, heap`