矩阵连乘动态规划代码
时间: 2024-01-01 20:23:42 浏览: 22
以下是矩阵连乘动态规划的代码示例:
```cpp
#include <iostream>
using namespace std;
const int N = 100; // 矩阵链的最大长度
void MatrixChainOrder(int p[], int n, int m[][N], int s[][N]) {
for (int i = 1; i <= n; i++) {
m[i][i] = 0; // 当i=j时,A[i][j]表示一个矩阵,不需要进行乘法运算,因此m[i][i]=0
}
for (int l = 2; l <= n; l++) {
for (int i = 1; i <= n - l + 1; i++) {
int j = i + l - 1;
m[i][j] = INT_MAX;
for (int k = i; k <= j - 1; k++) {
int q = m[i][k] + m[k + 1][j] + p[i - 1] * p[k] * p[j];
if (q < m[i][j]) {
m[i][j] = q;
s[i][j] = k; // 记录断链点
}
}
}
}
}
void Traceback(int i, int j, int s[][N]) {
if (i == j) {
cout << "A" << i; } else {
cout << "(";
Traceback(i, s[i][j], s);
Traceback(s[i][j] + 1, j, s);
cout << ")";
}
}
int main() {
int p[] = {30, 35, 15, 5, 10, 20, 25}; // 矩阵链的维度
int n = sizeof(p) / sizeof(p[0]) - 1; // 矩阵链的长度
int m[N][N]; // 存储最小乘法次数
int s[N][N]; // 存储断链点
MatrixChainOrder(p, n, m, s);
cout << "Optimal Parenthesization: ";
Traceback(1, n, s);
cout << endl;
return 0;
}
```