《算法導論》2.3-7很值得一練。其中用到了歸并排序、二分查找等等：

Give a Q(n lg n) time algorithm for determining if there exist two elements in an set S whose sum is exactly some value x.

以下是答案，其實想想很簡單的。

代碼如下，以備日后查找:)

代碼 #include?<stdio.h>
#include?<math.h>
#define?N?100

void?quicksort(float?*data,?int?start,?int?end);
void?merge(float?*data1,?int?length1,?float?*data2,?int?length2,
??float?*newlist);
int?binary_search(float*?a,?int?start,?int?end,?double?val);

/**************************************************************************/
/*?Purpose:?This?program?reads?a?list?of?numbers,?divides?the?list?into???*/
/*??two?sublists,?performs?a?quicksort?on?each?sublist,?then?merges?the???*/
/*??two?sorted?lists?of?numbers?to?form?a?single?sorted?list.?????????????*/
/**************************************************************************/

FILE?*datafile;?/*?pointer?to?data?file?*/

void?main(int?argc,?char?*argv[])
{
??char?temp[60];
??int?i,?midpoint,?X,?idx;
??float?data1[N/2+1],?data2[N/2+1],?newlist[N];

??strcpy(temp,?argv[1]);

??/*?open?data?file?*/
??datafile?=?fopen(temp,"r");
??if?(!datafile)
??{
????printf("***?Error?opening?%s?***\n",temp);
????return;
??}

??midpoint?=?N/2;

??/*?read?entries?from?data?file,?storing?first?half?in?data1?
?????and?second?half?in?data2?*/
??for?(i=0;?i<midpoint;?i++)
????fscanf(datafile,?"%f\n",&data1[i]);
??for?(i=midpoint;?i<N;?i++)
????fscanf(datafile,?"%f\n",&data2[i-midpoint]);

??/*?perform?quicksort?on?each?list?*/
??quicksort(data1,0,midpoint-1);
??quicksort(data2,0,N-1-midpoint);

??/*?merge?the?two?sublists?*/
??merge(data1,midpoint,data2,N-midpoint,newlist);

??/*?print?the?sorted?list?*/
//???for?(i=0;i<N;++i)
//?????printf("newlist[%d]?=?%f\n",?i,?newlist[i]);
??X?=?15;
??for?(i?=?0;?i?<?N;?i++)
??{

??????idx?=?binary_search(?newlist,?0,?N?-?1,?X?-?newlist[i]);

????if?(?idx?>=?0)
????{
????????//printf("%f\n",?newlist[idx]);
????????printf("Yes:\tA[%d]?=?%f,?A[%d]?=?%f\n",?i,?newlist[i],?idx,?newlist[idx]);
????}
??}

??fclose(datafile);
??return;
}

void?quicksort(float?*data,?int?begin,?int?end)
{
??/***********************************************************************/
??/*?Purpose:?sorts?a?list?of?numbers?in?increasing?order????????????????*/
??/*?Input:??????????????????????????????????????????????????????????????*/
??/*???data:?an?unsorted?array?of?numbers????????????????????????????????*/
??/*???begin:?the?beginning?index?of?"data"??????????????????????????????*/
??/*???end:?the?final?index?of?"data"????????????????????????????????????*/
??/*?Output:?????????????????????????????????????????????????????????????*/
??/*???upon?termination?of?the?subroutine,?"data"?contains?the?sorted????*/
??/*?????list?of?numbers?????????????????????????????????????????????????*/
??/***********************************************************************/

??int?leftarrow,?rightarrow;
??float?temp,?pivot;

??leftarrow?=?begin;
??rightarrow?=?end;
??pivot?=?data[(begin+end)/2];
??while?(1)
??{
????while?(data[rightarrow]?>?pivot)
??????rightarrow?=?rightarrow?-?1;

????while?(data[leftarrow]?<?pivot)
??????leftarrow?=?leftarrow?+?1;

????if?(leftarrow?<=?rightarrow)
????{
??????temp?=?data[leftarrow];
??????data[leftarrow]?=?data[rightarrow];
??????data[rightarrow]?=?temp;
??????leftarrow?=?leftarrow?+?1;
??????rightarrow?=?rightarrow?-?1;
????}

????if?(rightarrow?<?leftarrow)
??????break;
??}?

??if?(begin?<?rightarrow)
????quicksort(data,begin,rightarrow);
??if?(leftarrow?<?end)
????quicksort(data,leftarrow,end);

??return;
}

void?merge(float?*data1,?int?length1,?float?*data2,?int?length2,
??float?*newlist)
{
??/***********************************************************************/
??/*?Purpose:?merges?two?sorted?sublists?(in?increasing?order)?to?form???*/
??/*???a?single?sorted?list??????????????????????????????????????????????*/
??/*?Input:??????????????????????????????????????????????????????????????*/
??/*???data1:?a?sorted?array?of?numbers??????????????????????????????????*/
??/*???length1:?the?length?of?array?data1????????????????????????????????*/
??/*???data2:?a?second?sorted?array?of?numbers???????????????????????????*/
??/*???length2:?the?length?of?array?data2????????????????????????????????*/
??/*?Output:?????????????????????????????????????????????????????????????*/
??/*???upon?termination?of?the?subroutine,?"newlist"?contains?the????????*/
??/*?????merged?list?of?numbers,?sorted?in?increasing?order??????????????*/
??/***********************************************************************/

??int?leftarrow1,?rightarrow1,?leftarrow2,?rightarrow2,?i;

??/*?initialize?variables?*/
??leftarrow1?=?0;
??rightarrow1?=?length1-1;
??leftarrow2?=?0;
??rightarrow2?=?length2-1;
??i=0;
??
??/*?while?both?arrays?are?nonempty,?copy?the?smallest?element?
?????appearing?in?either?array,?into?newlist?*/
??while?((leftarrow1?<=?rightarrow1)?&&?(leftarrow2?<=?rightarrow2))
??{
????if?(data1[leftarrow1]?<?data2[leftarrow2])
????{
??????newlist[i]?=?data1[leftarrow1];
??????leftarrow1++;
????}
????else
????{
??????newlist[i]?=?data2[leftarrow2];
??????leftarrow2++;
????}
????i++;
??}
?
??/*?finish?nonempty?array?data1,?if?necessary?*/
??while?(leftarrow1?<=?rightarrow1)
??{
????newlist[i]?=?data1[leftarrow1];
????leftarrow1++;
????i++;
??}

??/*?finish?nonempty?array?data2,?if?necessary?*/
??while?(leftarrow2?<=?rightarrow2)
??{
????newlist[i]?=?data2[leftarrow2];
????leftarrow2++;
????i++;
??}

??return;
}


int?binary_search(float*?a,?int?start,?int?end,?double?val)
{
????int?ii?=?(int)((end?+?start)?/?2);
????double?mid?=?(double)(a[ii]);
????int?res;
????if(mid?==?val)
????{
????????res?=?ii;
????????return?res;
????}
????else?if?(val?<?mid)
????{
????????if?(?ii?==?start)
????????{
????????????return?-1;
????????}
????????res?=?binary_search(a,?start,?ii?-?1,?val);
????}
????else?if?(val?>?mid)
????{
????????if?(?ii?==?end)
????????{
????????????return?-1;
????????}
????????res?=?binary_search(a,?ii?+?1,?end,?val);
????}
????return?res;
????
}

?

?

轉載于:https://www.cnblogs.com/luweiseu/archive/2010/01/04/1638728.html

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