Q2)Following are the various algorithms time complexities expressions. Find the dominant terms and specify the Big-Oh complexity of each algorithm

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Q1In manual car gear system, pressing down the clutch pedal allows the driver to change the car’s gears to drive the vehicle on the road with different speed. Following are the dummy details about gear number and their relevant speed limit.

 

  • 1st Gear 0 – 10 mile per hour (mph)
  • 2nd Gear 10 – 20 mile per hour (mph)
  • 3rd Gear 20 – 60 mile per hour (mph)
  • 4th Gear 60 – 100 mile per hour (mph)

 

Suppose an expert driver is going from Haji Camp Peshawar to Sarhad University Peshawar using the following route drawn as Yellow line with three roundabouts (Red Circles).

  1. In manual car gear system, pressing down the clutch pedal allows the driver to change the car’s gears to drive the vehicle on the road with different speed. Following are the dummy details about gear number and their relevant speed limit.

 

  • 1st Gear 0 – 10 mile per hour (mph)
  • 2nd Gear 10 – 20 mile per hour (mph)
  • 3rd Gear 20 – 60 mile per hour (mph)
  • 4th Gear 60 – 100 mile per hour (mph)

 

Suppose an expert driver is going from Haji Camp Peshawar to Sarhad University Peshawar using the following route drawn as Yellow line with three roundabouts (Red Circles).

  1. In manual car gear system, pressing down the clutch pedal allows the driver to change the car’s gears to drive the vehicle on the road with different speed. Following are the dummy details about gear number and their relevant speed limit.

 

  • 1st Gear 0 – 10 mile per hour (mph)
  • 2nd Gear 10 – 20 mile per hour (mph)
  • 3rd Gear 20 – 60 mile per hour (mph)
  • 4th Gear 60 – 100 mile per hour (mph)

 

Suppose an expert driver is going from Haji Camp Peshawar to Sarhad University Peshawar using the following route drawn as Yellow line with three roundabouts (Red Circles).

Design an algorithm for the above driving task to reach the university safe and sound keeping in view all the Traffic rules and regulations and the speed limit mentioned above.

Q2)Following are the various algorithms time complexities expressions. Find the dominant terms and specify the Big-Oh complexity of each algorithm

Peshawar Cny
Haji Camp
Adda Peshawar
Chughal Pura
war
Fort Ad
Peshawar Railway
Peshawar Citye
Pes
G
Din
Bahadur Kalay
Sanmad University of
Science & Information
Transcribed Image Text:Peshawar Cny Haji Camp Adda Peshawar Chughal Pura war Fort Ad Peshawar Railway Peshawar Citye Pes G Din Bahadur Kalay Sanmad University of Science & Information
S. No.
Dominant term(s)
О (...)
Expression
75 + 0.001n1.3 + 0.025n + (1000)4
500n + 100n + 50n log10 n
(10n!.5)4 + 0.3n + 5nº.5 + 2.5 · n2.75
150n³ + n² log2 n+ n(log2 n)ª
3 log10 n+ log2 log2 n
100n4 + 0.01n² + 200(log2 n)4
1.
2.
3.
4.
5.
6.
7.
n3 + 0.01n + 100n2 + 5n³
8.
2n0.5 + n0.35 + 0.5n0.25
0.01n2 log2 n+ n(log2 n)
50n3 log; n+ n log; n+ 100nt
9.
10.
Transcribed Image Text:S. No. Dominant term(s) О (...) Expression 75 + 0.001n1.3 + 0.025n + (1000)4 500n + 100n + 50n log10 n (10n!.5)4 + 0.3n + 5nº.5 + 2.5 · n2.75 150n³ + n² log2 n+ n(log2 n)ª 3 log10 n+ log2 log2 n 100n4 + 0.01n² + 200(log2 n)4 1. 2. 3. 4. 5. 6. 7. n3 + 0.01n + 100n2 + 5n³ 8. 2n0.5 + n0.35 + 0.5n0.25 0.01n2 log2 n+ n(log2 n) 50n3 log; n+ n log; n+ 100nt 9. 10.
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