算法导论 练习题 2.3-7

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>

void merge(int a[],int p,int q,int r)
{
int n1=q-p+1;
int n2=r-q;
int i,j,k;

int *t1=(int*)malloc(sizeof(int)*(n1+1));
int *t2=(int*)malloc(sizeof(int)*(n2+1));

for(i=0;i<n1;i++)
{
t1[i]=a[p+i];
}
t1[n1]=INT_MAX;

for(i=0;i<n2;i++)
{
t2[i]=a[q+1+i];
}
t2[n2]=INT_MAX;

i=j=0;
for(k=p;k<=r;k++)
{
if(t1[i]<=t2[j])
{
a[k]=t1[i];
i++;
}
else
{
a[k]=t2[j];
j++;
}
}
}

//归并排序
void mergeSort(int a[],int p,int r)
{
if(p<r)
{
int q=(p+r)/2;
mergeSort(a,p,q);
mergeSort(a,q+1,r);
merge(a,p,q,r);
}
}

//二分查找有序数组，返回目标值的下标或小于目标值的最大下标
int halfSearch(int a[],int low,int high,int key)
{
int mid=(low+high)/2;
while(a[mid]!=key && a[low]<key && a[high]>key)
{
mid=(low+high)/2;
if(a[mid]>key)
{
high=mid-1;
}
else
{
low=mid+1;
}
}
if(a[mid]==key)
{
return mid;
}
if(a[low]>key)
{
return low-1;
}
if(a[high]<key)
{
return high;
}
}

bool check(int a[],int len,int x)
{
//merge排序耗时nlgn
//for循环耗时上界n，内层halfSearch耗时上界lgn
//总耗时上界nlgn
mergeSort(a,0,len-1);
int mid=halfSearch(a,0,len-1,x/2);
int iSmall,iBig;
for(iSmall=0;iSmall<=mid;iSmall++)
{
iBig=halfSearch(a,iSmall+1,len-1,x-a[iSmall]);
if(a[iSmall]+a[iBig]==x)
return true;
}
return false;
}

int main()
{
int a[8]={99,4,123,6764,26,324,6,88};
int x=6764+26;
if(check(a,8,x))
{
printf("Found!");
}
else
{
printf("Not Found!");
}
getchar();
}