/*

* @fileMemoMatrixchain.cpp

* @briefa solution of martrix chain with memorized way.

* @author/Univ.taoxiaoxiao/XMU

* @versionv1.0

* @date11-3-2013

*/

//實例 A1-A6：30X35 35X15 15X5 5X10 10X20 20X25

#include

#include

using namespace std;

#define N 6

#define INF 0x3f3f3f3f

int m[N + 1][N + 1];

int LookupChain(vectorp, int i, int j)

{

if (m[i][j] < INF)

return m[i][j];

if (i == j)

m[i][j] = 0;

else

{

for (int k = i; k <= j - 1; ++k)

{

int q = LookupChain(p, i, k) + LookupChain(p, k + 1, j)

+ p[i - 1] * p[k] * p[j];

if (q < m[i][j])

m[i][j] = q;

}

}

return m[i][j];

}

void MemorizedMatrixChain(vectorp)

{

int n = p.size() - 1;

for (int i = 1; i <= n; ++i)

{

for (int j = i; j <= n; ++j)

m[i][j] = INF;

}

LookupChain(p, 1, n);

}

int main()

{

vector p{ 30, 35, 15, 5, 10, 20, 25 };

cout << "矩陣維度為: ";

for (auto i = p.begin(); i < p.end(); ++i)

cout << *i << " ";

cout << endl;

MemorizedMatrixChain(p);

cout << "最小乘法次數: " << m[1][6] << endl;

return 0;

}

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