Direct Insert Sort comparison, number of moves and number of assignments min/MAX/avg

Direct Insert Sort comparison, number of moves and number of assignments min /MAX /avg

Based on the program:

Number of comparisons: refers to the number of times a while loop moves

Number of moves: refers to the number of times the data is moved in a vector (one-dimensional array ), including R[0]<-r[i],r[j+1]<-r[0], and r[j+1]<-r[j in the while Loop ]

Number of assignments: include all assignment statements

About the relationship between the number of comparisons and the number of assignments:

For a while loop, the program compares T-times to exit the loop, moves t-1 times, assigns a value 2t-2 times, because the front t-1 a while loop executes, and the first t while Loop does not execute.

For A For loop, the program moves 2 extra times each time, assigning 3 times.

So each for loop compares t times, moves t+1[(t-1) +2] times, assigns a value 2t+1 times [(2t-2) +3].

I. Average number of comparisons and number of assignments

For placing the number of I (i=2,3,..., n) in the corresponding position,

The program exits the while loop at the J position ,A[i] into the a[j+1] place,

the probability of J equals i-1 ~ 0 is the same (the probability of all probabilities is equal for the position of a number in a sequence )

So

Ii. minimum number of comparisons and number of assignments

The minimum value is the First Direct exit of the while loop, with a comparison of 1 occurrences.

Iii. maximum number of comparisons and assignments

The maximum value is the case when j=0 exits while loop, and the number of comparisons is i times.

Summarize:

Number of comparisons:

Number of moves:

Number of assignments:

Then I do not know my understanding of the concept and calculation of understanding is right ...

Anyway, I think some of the ppt is not right, I can be rude to say, this is a little pit dad ah ...

Direct Insert Sort comparison, number of moves and number of assignments min/MAX/avg