一个菜鸟的算法导论学习笔记【Chapter 2】

Chapter 2 Getting Started

2.1 Insertion sort

#include<stdio.h>
#include<iostream>
using namespace std;

int a[10]={123,134,3452,234,65,434,234,978,11234,345};
int main()//由小到大排序
{
for(int i=0;i<10;i++)
{
int j=i;
int key=a[i];
for(;j>0&&a[j-1]>=key;j--)
a[j]=a[j-1];
a[j]=key;
}
for(int i=0;i<10;i++)
cout<<a[i]<<"\t";

return 0;
}

2.2 Analyzing algorithms

usually use worst-case analysis

oder of growth :

eg:
n^3/1000 -100n^2-100n, the order of order of growth is theta(n^3)

2.3 Designing algorithms

divide and conquer

Divide>>>Conquer>>>Combine

eg:
Merge sort

int a[100], b[100];
void Merge(int*a,int p,int q,int r)
{
int p1=p,p2=q+1,p3=0;
while(p1<=q&&p2<=r)
b[p3++]=a[p1]<a[p2]?a[p1++]:a[p2++];
while(p1<=q)
b[p3++]=a[p1++];
while(p2<=r)
b[p3++]=a[p2++];
for(int i=p;i<=r;i++)
a[i]=b[i-p];
return;
}
void MergeSort(int *a,int p,int r)//对数组a，从第p位到第r位由小到大排序
{
if(p>=r)
return;
int q=(p+r)/2;
MergeSort(a,p,q);
MergeSort(a,q+1,r);
Merge(a,p,q,r);//Combine
return;
}

theta(nln(n))