最優矩陣鏈乘

public class MatrixChain {
	public static final int N = 6; 
	public static void main(String[] args) {
		int[] p = new int[]{30,35,15,5,10,20,25};
		int[][] m = new int[N+1][N+1];
		int[][] s = new int[N+1][N+1];
		MatrixChain mc = new MatrixChain();
		mc.matrix_chain_order(p, m, s);
		mc.print(s, 1, N);
		System.out.println();
	}
	
	private void matrix_chain_order(int[] p, int[][]m, int[][]s) {
		int i,j;
		int n = p.length - 1;//矩陣鏈長度
		for(i=1; i<=n; i++) m[i][i] = 0;// 初始化長度爲1的鏈代價
		for(int l=2; l<=n; l++) {// 矩陣鏈長度依次增加
			for(i=1; i<=n-l+1; i++) {//i，j的位置在變化  保證長度是l
				j = i+l-1;
				m[i][j] = Integer.MAX_VALUE;//初始化m[i][j]
				for(int k=i; k<=j-1; k++) {//k的位置可以從i變化到j-1
					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;//記錄最優k值
					}
				}
			}
		}
	}
	
	private void print(int[][] s, int i, int j) {
		if(i == j) System.out.print("A" + i);//長度爲1
		else {
			System.out.print("(");//左括號
			print(s,i,s[i][j]);//遞歸以k爲分割的左半邊
			System.out.print(" x ");//乘號
			print(s,s[i][j]+1,j);//遞歸以k爲分割的右半邊
			System.out.print(")");//右括號
		}
	}
}