矩阵连乘 (Multiplying a sequence of matrices)
我们想从两个以上矩阵连乘的式子中得到最佳的次序，使得计算时乘法运算最少。
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| public class DynamicProgramming {
private static final int N = 5;
public static void main(String[] args) {
int[][] C = new int[N][N];
int[][] S = new int[N][N];
int[] r = {4, 5, 3, 6, 4, 5};
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
C[i][j] = 0;
}
}
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
S[i][j] = 0;
}
}
for (int p = 2; p <= N; p++) {
for (int i = 0, j; i < N - p + 1; i++) {
j = i + p - 1;
C[i][j] = C[i][i] + C[i + 1][j] + r[i] * r[i + 1] * r[j + 1];
S[i][j] = i;
for (int k = i; k< j; k++) {
int temp = C[i][k] + C[k + 1][j] + r[i] * r[k + 1] * r[j + 1];
if (temp < C[i][j]) {
C[i][j] = temp;
S[i][j] = k;
}
}
}
}
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
System.out.print(C[i][j] + "\t");
}
System.out.println();
}
System.out.println();
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
if (j > i) System.out.print(S[i][j] + 1 + "\t");
else System.out.print(0 + "\t");
}
System.out.println();
}
}
}
|