2015年英語(yǔ)六級考試流程「匯編」
二筆只有三道題，分值分別為30, 30, 40，題分別如下：
1、實(shí)現strtol函數，其原型如為int strtol(const char *num_str, char **endptr, int base)，num_str存放待轉換的字符串，可以是負數也可以是正數；endptr指向第一個(gè)非法字符的地址，如果endptr為NULL則不指向第一個(gè)非法字符的地址；base用于指示進(jìn)制，若base為0，則根據num_str的指示來(lái)轉換。函數必須檢查溢出，如果正數溢出，返回INT_MAX；若負數溢出，返回INT_MIN。
2、一億個(gè)數找最大的1000個(gè)數，要求效率高占用內存少。函數原型為：find_max_data(int* source_data, int* max_data)，其中source_data是存放一億個(gè)數的數組，max_data用于存放其中最大的1000個(gè)數。
3、將一個(gè)集合拆分成兩個(gè)不相交的子集，兩個(gè)子集元素之和相等，如{1, 2, 3, 4, 5, 6, 7}，拆分成：
{2, 5, 7}, {1, 3, 4, 6}
給出一個(gè)集合，求所有符合上面要求的拆分，效率最高分越高，函數原型為int cal_num(int n);
第三題：
利用回溯剪枝法
空間復雜度：O(n) 棧的最大深度也就是n了
時(shí)間復雜度：接近于O(2^n-1), 因為本質(zhì)上程序時(shí)一個(gè)遍歷樹(shù)的過(guò)程，如果沒(méi)有剪枝，那么樹(shù)是一個(gè)滿(mǎn)二叉樹(shù)，結點(diǎn)共2^n-1個(gè)，也就要遍歷2^n-1次。雖然剪枝，但速度估計仍是 2^n次方級別的。
試了下，調用cal_num(104),好久了結果都沒(méi)有出來(lái)。。。
不知用上DP算法會(huì )不會(huì )好點(diǎn)，不過(guò)聽(tīng)說(shuō)回溯法怎么弄效率都跟不上，最好用遞推？
在哪聽(tīng)說(shuō)的？
/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/
/pic/p>
#ifndef __DIVIDE_SET_H__
#define __DIVIDE_SET_H__
/pic/> /pic/> void divide_set( int set[], int label[], int len, int i_set, int value );
/pic/> void cal_num( int n );
#endif
/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/pic/
/pic/p>
#include "stdafx.h"
#include "divide_set.h"
#include <iostream>
using namespace std;
/pic/>
void divide_set( int set[], int label[], int len, int i_set, int value )
{
/pic/>
if ( value == 0 )
{
cout<<"{ ";
for ( int i=0; i<len; ++i )
{
if ( label[i] )
{
cout<<set[i]<<" ";
}
}
cout<<"} ";
cout<<" , { ";
for ( int i=0; i<len; ++i )
{
if ( 0 == label[i] )
{
cout<<set[i]<<" ";
}
}
cout<<"} ";
cout<<endl;
return;
}
if ( i_set >= len || value <0)
{
return;
}
/pic/>
label[i_set] = 1;
divide_set( set, label, len, i_set+1, value-set[i_set] );
/pic/>
label[i_set] = 0;
divide_set( set, label, len, i_set+1, value );
}
void cal_num( int n )
{
int* set = new int[n];
int* label = new int[n];
/pic/>
int sum_value = 0;
for ( int i=0; i<n; ++i )
{
set[i] = i+1;
sum_value += set[i];
}
memset( label, 0, n*sizeof(int) );
/pic/>
if( sum_value%2 == 0 )
divide_set( set, label, n, 0, sum_value/2 );
delete[] set;
delete[] label;
}
/pic/p>
/pic/> /pic/> /pic/> void divide_set( int set[], int label[], int len, int i_set, int value );
/pic/> int divide_set_v2( int set[], int len, int i_set, int value );
int divide_set_v3( int set[], int len, int** bpHistory, int i_set, int value );
int divide_set_v4( int set[], int len, std::vector< std::vector<int> > &bpHistory, int i_set, int value );
class Bin;
int divide_set_v5( int set[], int len, Bin &bpHistory, int i_set, int value );
/pic/> void cal_num( int n );
/pic/> int cal_num_v2( int n );
/pic/> int cal_num_v3( int n );
/pic/> int cal_num_v4( int n );
/pic/> int cal_num_v5( int n );
/pic/> long getSetsNum1(int n);
void test_cal_num();
/pic/p>
int divide_set_v2( int set[], int len, int i_set, int value )
{
if ( 0 == value )
return 1;
if ( i_set >= len || value <0)
return 0;
int rst = divide_set_v2(set, len, i_set+1, value-set[i_set]) + divide_set_v2(set, len, i_set+1, value);
/pic/>
return rst;
}
int divide_set_v3( int set[], int len, int** bpHistory, int i_set, int value )
{
if ( 0 == value )
return 1;
if ( i_set >= len || value <0)
return 0;
int left = 0;
int right = 0;
if ( (value-set[i_set]) >=0 )
{
/pic/>
if ( bpHistory[i_set+1][value-set[i_set]] == -1 )
{
bpHistory[i_set+1][value-set[i_set]] = divide_set_v3(set, len, bpHistory, i_set+1, value-set[i_set]);
}
left = bpHistory[i_set+1][value-set[i_set]];
}
if ( value >=0 )
{
/pic/>
if ( bpHistory[i_set+1][value] == -1 )
{
bpHistory[i_set+1][value] = divide_set_v3(set, len, bpHistory, i_set+1, value);
}
right = bpHistory[i_set+1][value];
}
return left + right;
}
int divide_set_v4( int set[], int len, std::vector< std::vector<int> > &bpHistory, int i_set, int value )
{
if ( 0 == value )
return 1;
if ( i_set >= len || value <0)
return 0;
int left = 0;
int right = 0;
if ( (value-set[i_set]) >=0 )
{
/pic/>
if ( bpHistory[i_set+1][value-set[i_set]] == -1 )
{
bpHistory[i_set+1][value-set[i_set]] = divide_set_v4(set, len, bpHistory, i_set+1, value-set[i_set]);
}
left = bpHistory[i_set+1][value-set[i_set]];
}
if ( value >=0 )
{
/pic/>
if ( bpHistory[i_set+1][value] == -1 )
{
bpHistory[i_set+1][value] = divide_set_v4(set, len, bpHistory, i_set+1, value);
}
right = bpHistory[i_set+1][value];
}
return left + right;
}
int divide_set_v5( int set[], int len, Bin &bpHistory, int i_set, int value )
{
if ( 0 == value )
return 1;
if ( i_set >= len || value <0)
return 0;
int left = 0;
int right = 0;
if ( (value-set[i_set]) >=0 )
{
/pic/>
/pic/>
int tmp;
if ( !bpHistory.Find( i_set+1, value-set[i_set], tmp ) )
{
tmp = divide_set_v5(set, len, bpHistory, i_set+1, value-set[i_set]);
bpHistory.Insert( i_set+1, value-set[i_set], tmp );
}
left = tmp;
}
if ( value >=0 )
{
/pic/>
/pic/>
int tmp;
if ( !bpHistory.Find( i_set+1, value, tmp ) )
{
tmp = divide_set_v5(set, len, bpHistory, i_set+1, value);
bpHistory.Insert( i_set+1, value, tmp );
}
right = tmp;
}
return left + right;
}
void cal_num( int n )
{
int* set = new int[n];
int* label = new int[n];
/pic/>
int sum_value = 0;
for ( int i=0; i<n; ++i )
{
set[i] = i+1;
sum_value += set[i];
}
memset( label, 0, n*sizeof(int) );
/pic/>
if( sum_value%2 == 0 )
divide_set( set, label, n, 0, sum_value/2 );
delete[] set;
delete[] label;
}
int cal_num_v2( int n )
{
int rst = 0;
int* set = new int[n];
/pic/>
int sum_value = 0;
for ( int i=0; i<n; ++i )
{
set[i] = i+1;
sum_value += set[i];
}
/pic/>
if( sum_value%2 == 0 )
rst = divide_set_v2( set, n, 0, sum_value/2 );
delete[] set;
return rst;
}
int cal_num_v3( int n )
{
int rst = 0;
int* set = new int[n];
/pic/>
int sum_value = 0;
for ( int i=0; i<n; ++i )
{
set[i] = i+1;
sum_value += set[i];
}
/pic/>
if( sum_value%2 == 0 )
{
int half_value = sum_value>>1;
/pic/>
int rows = n+1;
int cols = half_value+1;
int** bpHistory = malloc2d<int>(rows, cols, -1);
bpHistory[0][half_value] = rst = divide_set_v3( set, n, bpHistory, 0, half_value );
/pic/> /pic/> /pic/> /pic/> /pic/> /pic/> /pic/> /pic/> /pic/> /pic/(float)(rows*cols)<<endl;
free2d( bpHistory, rows, cols );
}
delete[] set;
return rst;
}
int cal_num_v4( int n )
{
int rst = 0;
int* set = new int[n];
/pic/>
int sum_value = 0;
for ( int i=0; i<n; ++i )
{
set[i] = i+1;
sum_value += set[i];
}
/pic/p>
if( sum_value%2 == 0 )
{
int half_value = sum_value>>1;
vector<vector<int>> bpHistory( n+1, vector<int>(half_value+1, -1) );
bpHistory[0][half_value] = rst = divide_set_v4( set, n, bpHistory, 0, half_value );
}
delete[] set;
return rst;
}
int cal_num_v5( int n )
{
int rst = 0;
int* set = new int[n];
/pic/>
int sum_value = 0;
for ( int i=0; i<n; ++i )
{
set[i] = i+1;
sum_value += set[i];
}
/pic/p>
if( sum_value%2 == 0 )
{
int half_value = sum_value>>1;
int rows = n+1;
int cols = half_value + 1;
Bin bin(rows, cols);
rst = divide_set_v5( set, n, bin, 0, half_value );
}
delete[] set;
return rst;
}
long getSetsNum1(int n)
{
/pic/>
long sum = 0;
for (int i = 1; i <= n; ++i) sum += i;
if ((sum & 1) == 1) return 0;
sum >>= 1;
/pic/>
long N = ((n * (n + 1)) >> 1) + 2;
long* dp = new long[N];
for (long i = 1; i < N; ++i) dp[i] = 0;
/pic/>
dp[0] = 1;
long max = 0;
for (long i = 1; i <= n; ++i)
{
for (long j = max < sum ? max : sum; j >= 0; --j)
dp[j + i] += dp[j];
max += i;
}
/pic/>
/pic/>
/pic/>
return dp[sum] >> 1;
}
void test_cal_num()
{
FPSController fps;
int n=104;/pic/pic/pic/pic/pic/pic/pic/p>
/pic/> /pic/> /pic/> /pic/p>
/pic/> /pic/> /pic/> /pic/p>
cout<<endl;
fps.BeginFrame();
cout<<cal_num_v3(n)<<endl;
cout<<"elapse time : "<<fps.GetElapseTime()<<"秒"<<endl;
cout<<endl;
fps.BeginFrame();
cout<<cal_num_v4(n)<<endl;
cout<<"elapse time : "<<fps.GetElapseTime()<<"秒"<<endl;
/pic/> /pic/> /pic/> /pic/p>
cout<<endl;
fps.BeginFrame();
cout<<getSetsNum1(n)<<endl;
cout<<"elapse time : "<<fps.GetElapseTime()<<"秒"<<endl;
}
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