Inductive method of algorithm series

Select Sort:

#include <iostream>using namespace std; #define LENGTH 10int data[length];void selectsort (int i,int num) {    if (i < num)    {        int k = i;        for (int j = i+1;j <= num; j + +)            if (Data[j]<data[k])                k = j;        if (k!=i)        {            int temp = data[i];            Data[i] = data[k];            DATA[K] = temp;        }        Selectsort (I+1,num);    }} int main () {    int num;    cin>>num;    for (int i = 1;i <= num; i++)        cin>>data[i];    Selectsort (1,num);    for (int i = 1;i <= num; i++)        cout<<data[i]<< "";    cout<<endl;    return 0;}

Insert Sort:

#include <iostream>using namespace std; #define LENGTH 10int data[length];void insertsort (int i) {    if (i > 1) c1/>{        int x = data[i];        Insertsort (i-1);        int j = i-1;        while (j>0&&data[j]>x)        {            data[j+1] = data[j];            j = j-1;        }        DATA[J+1] = x;    }} int main () {    int num;    cin>>num;    for (int i = 1;i <= num; i++)        cin>>data[i];    Insertsort (num);    for (int i = 1;i <= num; i++)        cout<<data[i]<< "";    cout<<endl;    return 0;}

Integer power

Usually for the n power of X, a straightforward method is to squared n times for X in an iterative way, which is very inefficient. An efficient method can be introduced in the following way, so that M = [N/2], assuming already know how to calculate the M power of X. Then there are two kinds of situations: if n is an even number, then the n power of x equals the square of the M power of X, otherwise the n power of x is equal to the square of x multiplied by the M power of X. This idea can produce a recursive algorithm as shown in Exprec.

#include <iostream>using namespace Std;int power (int x,int m) {    int y;    if (m==0)    y = 1;    else    {        y = power (X,M/2);        y = y*y;        if (m%2==1)        y = x*y;    }    return y;} int main () {    int num1,num2;    cin>>num1>>num2;    Cout<<power (num1,num2) <<endl;    return 0;}

　　

Inductive method of algorithm series