【编程练习】3*3 的矩阵，值限定为1-9不重复，已知横竖的和，和一个斜着的值，求这个矩阵


x x x 11

x x x 15

x x x 19

16 14 15 15

讨论贴：

http://bbs.csdn.net/topics/391816265

先求横竖斜三行的精确匹配方法：

// puzzl.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"

// puzzle.cpp : Defines the entry point for the console application.
//

#include "stdafx.h"
#include <vector>
#include <set>
#include <iostream>

using namespace std;

int result[3][3] = {0};

bool check(int a, int b, int c, int sum)
{
if((a + b  + c )== sum)
return true;
else
return false;
}

int lastValue(int a, int b,int sum)
{
return (sum - a - b);
}

//min max
vector<vector<int> > zuhe(int min,int max,int sum)
{

vector<vector<int> > quanji;
for(int i = min;i < max; ++i)
{
for(int j = 1;j < max; ++j)
{
if(i + j > sum)
continue;
else
{
for(int k = 1; k <max ;++k)
{
if(check(i,j,k,sum))
{
vector<int> ziji;
ziji.push_back(i);
ziji.push_back(j);
ziji.push_back(k);
if (i!=j&&j!=k&&i!=k)
{
quanji.push_back(ziji);
}

}
else
{
continue;
}
}
}
}

}

return quanji;
}

vector<vector<int> > filter_zuhe(int key,vector<vector<int> > temp)
{
vector<vector<int> >::iterator iter ;
for(iter = temp.begin(); iter!=temp.end(); )
{
if( (*iter)[0] != key)
iter = temp.erase(iter);
else
iter ++ ;
}

return temp;
}

bool isOk()
{
set<int> mySet;

for(int i = 0;i <3; ++i)
{
for(int j = 0;j<3;++j)
{
if(result[i][j]>0&&result[i][j]<10)
{
mySet.insert(result[i][j]);
}
}
}

if(mySet.size()!=9)
{return false;}
else
{
if(mySet.size()==9)
{
for(int i = 0;i <3; ++i)
{
cout <<endl;
for(int j = 0;j<3;++j)
{
cout<<result[i][j]<<" ";
}
}

return true;
}
}
}

void dayin()
{
for(int i = 0;i <3; ++i)
{
cout <<endl;
for(int j = 0;j<3;++j)
{
cout<<result[i][j]<<" ";
}
}

cout<<endl;
}

void qingling()
{
for(int i = 0;i <3; ++i)
{
for(int j = 0;j<3;++j)
{
(result[i][j]=0);
}
}
}

int _tmain(int argc, _TCHAR* argv[])
{
vector<vector<int> > quanjiheng = zuhe(1,9,11);
vector<vector<int> > quanjishu = zuhe(1,9,16);
vector<vector<int> > quanjixie = zuhe(1,9,15);

int sizeheng = quanjiheng.size();
int sizeshu = quanjishu.size();
int sizexie = quanjixie.size();

int key = 0,last_key = 0;

vector<vector<int> > quanjishufilter;
vector<vector<int> > quanjixiefilter;

for(int i = 0;i < sizeheng ; ++i)
{
key = quanjiheng[i][0];
if (key!=last_key)
{
quanjishufilter = filter_zuhe(key,quanjishu);
quanjixiefilter = filter_zuhe(key,quanjixie);
}
last_key = key;
//给横行赋值
for (int j = 0;j< 3;++j)
{
result[0][j] = quanjiheng[i][j];

}

int sizeshu = quanjishufilter.size();
for (int k = 0; k< sizeshu;++k)
{
//给竖行赋值
for(int j = 0;j<3;++j)
{
result[j][0] = quanjishufilter[k][j];
}

int sizexie = quanjixiefilter.size();
for(int x = 0; x < sizexie; ++x)
{
for(int j = 0; j < 3 ;++j)
{
result[j][j] = quanjixiefilter[x][j];
}
result[2][1] = 14 - result[0][1]-result[1][1];
result[1][2] = 15-  result[1][0]-result[1][1];
if(isOk())
{
//dayin();
getchar();
//return 0;
}
else
{

}
}

}

qingling();

}

getchar();
system("pause");
return 0;
}

排列组合的方法：

template <typename T>
void swap(T* array, unsigned int i, unsigned int j)
{
T t = array[i];
array[i] = array[j];
array[j] = t;
}

void FullArray(int* array, size_t array_size, unsigned int index)
{
if (index >= array_size)
{
if ((array[0] + array[1] + array[2] == 11) &&
(array[3] + array[4] + array[5] == 15) &&
(array[6] + array[7] + array[8] == 19) &&
(array[0] + array[3] + array[6] == 16) &&
(array[1] + array[4] + array[7] == 14) &&
(array[2] + array[5] + array[8] == 15) &&
(array[0] + array[4] + array[8] == 15))
{
printf("%d,%d,%d\n", array[0], array[1], array[2]);
printf("%d,%d,%d\n", array[3], array[4], array[5]);
printf("%d,%d,%d\n\n", array[6], array[7], array[8]);
}

return;
}

for (unsigned int i = index; i < array_size; ++i)
{
swap(array, i, index);

FullArray(array, array_size, index + 1);

swap(array, i, index);
}
}

int main(int argc, char* argv[])
{
int value[9] = { 1, 2, 3, 4, 5, 6, 7, 8, 9 };

FullArray(value, 9, 0);
}

模仿人做的方法，任意填写3个空位，保证不同行不同列，或者不在一个斜线。就可以算出来剩下的。