Find the dominant term and Time complexity:
Description:
(1) 2n2log4n + 30m2log100m (consider n > m)
Simplifying above expression to find time complexity:
2n2log4n + 30m2log100m
= 2n2(log104 + log10n) + 30m2 (log10100+ log10m)
= 2n2log104 + 2n2log10n +30m2log10100+30m2log10m
Since n>m Dominant term for expression 2n2log4n + 30m2log100m is 2n2log4n
Time complexity: O(n2logn)
(2) 7(n+5)4 + nlogn20
Simplifying above expression to find time complexity:
7(n+5)4 + nlogn20
= 7(n4 +20n3 + 150n2 + 500n +625) + 20nlogn
= (7n4 +140n3 + 1050n2 + 3500n +4375) + 20nlogn
Dominant term for expression 7(n+5)4 + nlogn20 is 7(n+5)4
Time complexity: O(n4)
(3) 30n5logn + 3n log10n
Simplifying above expression to find time complexity:
30n5logn + 3n log10n
= 30n5logn + 3n log10n10
= 30n5logn + 30nlogn
Dominant term for expression 30n5logn + 3n log10n is 30n5logn
Time complexity: O(n5logn)
(4) (2n3(10m3)) + (n/2(n2))2 /100 (consider n > m)
Simplifying above expression to find time complexity:
(2n3(10m3)) + (n/2(n2))2 /100
= (2n3(10m3)) + ( (n/2)2 (n2)2 )/ 100
= 20n3 m3+ ((n2 * n4 ) / 200
= 20n3 m3 + n6 / 200
Since n>m Dominant term for expression (2n3(10m3)) + (n/2(n2))2 /100 is (n/2(n2))2 /100
Time complexity: O(n6)
Question 4: For each of the following, find the dominant term(s) having the sharpest increase in...
The expression is:3nlog8n +30mlog20m I solved it and got 3nlog8n as the dominant term and O term is O(n log n)Is this correct?
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