矩阵连乘动态规划算法

来源：互联网发布：淘宝十大创意网店编辑：程序博客网时间：2024/05/17 22:33
矩阵连乘动态规划算法

题目描述：
这里写图片描述
Java实现：
import java.util.Scanner;public class MatrixChain {    public static void main(String[] args) {        // TODO 自动生成的方法存根        Scanner scan = new Scanner(System.in);        int n = scan.nextInt();        int p[] = new int[n+1];        for(int i=0; i<=n; i++)            p[i] = scan.nextInt();//      int n = 6;//      int p[] = {30, 35, 15, 5, 10, 20, 25};        //非递归        int m[][] = new int[n+1][n+1];        int s[][] = new int[n+1][n+1];        MatrixChain1(p, n, m, s);        t(1, n, s);        System.out.println();        String sss = traceBack(1, n, s);        System.out.println(sss);        //自底向上 递归 动态规划        int s1[][] = new int[n+1][n+1];        RecurMatrixChain(1, n, p, s1);        t(1, n, s1);        System.out.println();        //自顶向下 递归 动态规划        int m2[][] = new int[n+1][n+1];        int s2[][] = new int[n+1][n+1];        MemoizedMatrixChain(n, m2, s2, p);        t(1, n, s2);    }    //输出计算最优计算次序,括号分离    public static void t(int i, int j, int s[][]) {        if (i == j)            System.out.print("A" + i);        else {              System.out.print("(");            t(i, s[i][j], s);            t(s[i][j]+1, j, s);            System.out.print(")");        }    }    public static String traceBack(int i,int j,int s[][]){        if(i==j){              return "A"+i;        }        else{               return"("+traceBack(i,s[i][j],s)+traceBack(s[i][j]+1,j,s)+")";        }    }    //非递归方法    //一维数组P存储n个矩阵的行列值, 二维数组m存储最优值, 二维数组s记录最优断开位置    public static void MatrixChain1(int p[], int n, int m[][], int s[][]){        for(int i=1; i<=n; i++)//单个矩阵            m[i][i] = 0;        for(int r=2; r<=n; r++){//多个矩阵            for(int len=1; len<=n-r+1; len++){                int j = len + r -1;                m[len][j] = m[len+1][j] +p[len-1]*p[len]*p[j];                s[len][j] = len;                for(int k=len+1; k<j; k++){                    int t = m[len][k] + m[k+1][j] + p[len-1]*p[k]*p[j];                    if(t < m[len][j]){                        m[len][j] = t;                        s[len][j] = k;                    }                }            }        }    }       //一维数组P存储n个矩阵的维数值, 二维数组s记录最优断开位置    //自底向上 递归 动态规划    public static int RecurMatrixChain(int i, int j, int p[], int s[][]) {        if(i==j) return 0;        int u = RecurMatrixChain(i, i, p, s) + RecurMatrixChain(i+1, j, p, s) + p[i-1]*p[i]*p[j];        s[i][j] = i;        for(int k=i+1; k<j; k++){            int t = RecurMatrixChain(i, k, p, s) + RecurMatrixChain(k+1, j, p, s) + p[i-1]*p[k]*p[j];            if(t < u){                u = t;                s[i][j] = k;            }        }        return u;    }    //一维数组P存储n个矩阵的维数值, 二维数组m存储最优值, 二维数组s记录最优断开位置    //自顶向下 递归 动态规划(备忘录方法)    public static int MemoizedMatrixChain(int n, int m[][], int s[][], int p[]) {        for(int i=1; i<=n; i++)            for(int j=i; j<=n; j++)                m[i][j] = 0;        return LookupChain(1, n, m, s, p);    }    public static int LookupChain(int i, int j, int m[][], int s[][], int p[]){        if(m[i][j] > 0) return m[i][j];        if(i==j) return 0;        int u = LookupChain(i, i, m, s, p) + LookupChain(i+1, j, m, s, p) + p[i-1]*p[i]*p[j];        s[i][j] = i;        for(int k=i+1; k<j; k++){            int t = LookupChain(i, k, m, s, p) + LookupChain(k+1, j, m, s, p) + p[i-1]*p[k]*p[j];            if(t < u){                u = t;                s[i][j] = k;            }        }        m[i][j] =u;        return u;    }}
阅读全文
0 0