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Calculating the Number of Calculations in a Loopeach Comparison

Is there some formula that allows us to calculate the number of calculations in a loopcomparasion?

Suppose you have 5 numbers and want to calculate the number of comparisons :

  • Comparison 1: (1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3, 5), (4,5) : 10 Calculations

  • Comparison 2: (1,1), (1,2), (1,3), (1,4), (1,5), (2,2), (2,3), (2,4), (2,5), (3,3), (3,4), (3, 5), (4,4), (4,5), (5,5) : 15 Calculations

  • Comparison 3: (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3, 5), (4,1), (4,2), (4,3), (4,4), (4,5), (5,1), (5,2), (5,3), (5,4), (5,5) : 25 Calculations

My Question: Are there some general formulas that can be used to "predict" in advance how many calculations will be required in each one of these comparisons? Could some formulas be used to extend this for "n" number of numbers? E.g. (1,1,1) ... (5,5,5)?

Thanks!

Calculating the Number of Calculations in a Loop

Is there some formula that allows us to calculate the number of calculations in a loop?

Suppose you have 5 numbers and want to calculate the number of comparisons :

  • Comparison 1: (1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3, 5), (4,5) : 10 Calculations

  • Comparison 2: (1,1), (1,2), (1,3), (1,4), (1,5), (2,2), (2,3), (2,4), (2,5), (3,3), (3,4), (3, 5), (4,4), (4,5), (5,5) : 15 Calculations

  • Comparison 3: (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3, 5), (4,1), (4,2), (4,3), (4,4), (4,5), (5,1), (5,2), (5,3), (5,4), (5,5) : 25 Calculations

My Question: Are there some general formulas that can be used to "predict" in advance how many calculations will be required in each one of these comparisons? Could some formulas be used to extend this for "n" number of numbers? E.g. (1,1,1) ... (5,5,5)?

Thanks!

Calculating the Number of Calculations in each Comparison

Is there some formula that allows us to calculate the number of calculations in a comparasion?

Suppose you have 5 numbers and want to calculate the number of comparisons :

  • Comparison 1: (1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3, 5), (4,5) : 10 Calculations

  • Comparison 2: (1,1), (1,2), (1,3), (1,4), (1,5), (2,2), (2,3), (2,4), (2,5), (3,3), (3,4), (3, 5), (4,4), (4,5), (5,5) : 15 Calculations

  • Comparison 3: (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3, 5), (4,1), (4,2), (4,3), (4,4), (4,5), (5,1), (5,2), (5,3), (5,4), (5,5) : 25 Calculations

My Question: Are there some general formulas that can be used to "predict" in advance how many calculations will be required in each one of these comparisons? Could some formulas be used to extend this for "n" number of numbers? E.g. (1,1,1) ... (5,5,5)?

Thanks!

Source Link
stats_noob
stats_noob
  • 4.2k
  • 6
  • 20
  • 71

Calculating the Number of Calculations in a Loop

Is there some formula that allows us to calculate the number of calculations in a loop?

Suppose you have 5 numbers and want to calculate the number of comparisons :

  • Comparison 1: (1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3, 5), (4,5) : 10 Calculations

  • Comparison 2: (1,1), (1,2), (1,3), (1,4), (1,5), (2,2), (2,3), (2,4), (2,5), (3,3), (3,4), (3, 5), (4,4), (4,5), (5,5) : 15 Calculations

  • Comparison 3: (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3, 5), (4,1), (4,2), (4,3), (4,4), (4,5), (5,1), (5,2), (5,3), (5,4), (5,5) : 25 Calculations

My Question: Are there some general formulas that can be used to "predict" in advance how many calculations will be required in each one of these comparisons? Could some formulas be used to extend this for "n" number of numbers? E.g. (1,1,1) ... (5,5,5)?

Thanks!