Brute Force Method-select sort, bubble sort

Time always makes me feel a sense of frustration after knowing, perhaps because I never want to record the past.

3.1.1 Select sort (n elements, 0~n-1, ascending, unstable)

Make an I scan of array A (0<=i<=n-2), find the smallest element each time from the last N-i element, and then swap it with the AI.

Code implementation

/*** Select sort (Ascending) *@paramarrays sorted by array **/     Public Static voidSelectsort (int[] Array) {         for(inti=0;i<array.length-1;i++){            intmin=i;  for(intj=i+1;j<array.length;j++){                if(array[min]>Array[j]) {min=J; }            }            if(min!=i) {                inttemp=Array[i]; Array[i]=Array[min]; Array[min]=temp; }        }    }

Algorithm analysis

Therefore, for any input, the selection sort is an θ (N2) algorithm.

3.1.1 Bubble sort (n elements, 0~n-1, ascending, stable)

Compare adjacent elements Aj and aj+1, if aj>aj+1, swap their positions, in turn, and finally, the largest element "sinks" to the last position. After repeating the n-1, the order is lined up.

Code implementation

/*** Bubble Sort (Ascending) *@paramarrays sorted by array **/     Public Static voidBubblesort (int[] Array) {         for(inti=0;i<array.length-1;i++){             for(intj=0;j<array.length-1-i;j++){                if(array[j]>array[j+1]){                    inttemp=Array[j]; ARRAY[J]=array[j+1]; Array[j+1]=temp; }            }        }    }

Algorithm analysis

The worst case and average are θ (n2). In fact, it is possible to make some improvements to the above code, and when the array is iterated over again without exchanging elements, then it is already sorted. The code demonstrates the following:

Code implementation

/*** Bubble Sort (Ascending) *@paramarrays sorted by array **/     Public Static voidBubblesort (int[] Array) {         for(inti=0;i<array.length-1;i++){            intCount=0;  for(intj=0;j<array.length-1-i;j++){                if(array[j]>array[j+1]){                    inttemp=Array[j]; ARRAY[J]=array[j+1]; Array[j+1]=temp; Count++; }} System.out.println ("First" + (i+1) + "iterations:"); print (array);//Output Array            if(count==0){                 Break; }        }    }

The result of the original output:

before sorting:11,41,48,3,73,12,40,48,70,37 1th iteration:11,41,3,48,12,40,48,70,37,73 2nd iteration: 11,3,41,12,40,48,48,37,70,73 3rd Iteration:3,11,12,40,41,48,37,48,70,73 4th iteration: 3,11,12,40,41,37,48,48,70,73 5th iteration:3,11,12,40,37,41,48,48,70,73 6th iteration: 3,11,12,37,40,41,48,48,70,73 7th iteration:3,11,12,37,40,41,48,48,70,73 8th iteration: 3,11,12,37,40,41,48,48,70,73 9th iteration:3,11,12,37,40,41,48,48,70,73 after sorting: 3,11,12,37,40,41,48,48,70,73

The result of the improved output:

before sorting:11,41,48,3,73,12,40,48,70,37 1th iteration:11,41,3,48,12,40,48,70,37,73 2nd iteration: 11,3,41,12,40,48,48,37,70,73 3rd Iteration:3,11,12,40,41,48,37,48,70,73 4th iteration: 3,11,12,40,41,37,48,48,70,73 5th iteration:3,11,12,40,37,41,48,48,70,73 6th iteration: 3,11,12,37,40,41,48,48,70,73 7th iteration:3,11,12,37,40,41,48,48,70,73 after sorting: 3,11,12,37,40,41,48,48,70,73

As you can see

, it is true that two iterations are missing when sorting the above array. But in fact, even in the elementary sorting method, bubble sort is not a good choice, and if it is not because it has a good name, we probably won't have any knowledge of it (this is not very cruel, the author of the book said).

Exercise 3.1

4. A. Design a brute force algorithm that calculates the values of the following polynomial for a given x0:

P (x) =anxn+an-1xn-1+...+a1x+a0

and determine the worst efficiency type of the algorithm.

B. If the algorithm you are designing belongs to Θ (N2), design a linear algorithm for the problem.

C. Can you design an algorithm that is better than linear efficiency for this problem?

Solution:

A. Code implementation:

/*** Exercise 4.a Computational polynomial P (x) *@paramconstant entry for array polynomial *@paramx Variable *@returnreturns the result of the calculation **/     Public Static intPolynomialevaluation (int[] Array,intx) {        intResult=0;  for(inti=0;i<array.length;i++){            inttemp=Array[i];  for(intj=0;j<i;j++) {Temp*=x; } result+=temp; }        returnresult; }

Efficiency analysis:

So the algorithm belongs to Θ (N2).

B. Code implementation:

/*** Exercise 4.b Computational polynomial P (x) *@paramconstant entry for array polynomial *@paramx Variable *@returnreturns the result of the calculation **/     Public Static intPolynomialevaluation (int[] Array,intx) {        intResult=0; intTemp=1;  for(inti=0;i<array.length;i++) {result+=array[i]*temp; Temp*=x; }        returnresult; }

C. Because the problem must solve the n+1 of the addend, so we can not design a better than linear efficiency algorithm.

Brute Force Method-select sort, bubble sort