matrix_chain_order

to calculate the min step of multiplicate some matixs

 package dynamic_programming;

 public class matrix_chain_order { //input is a sequence p = p0,p1..pn,where p.length = n+1  (matrix n is pn-1pn)
     int[] p;
     int[][] cost;
      public matrix_chain_order(int[] a){
          p = a;
      }
      public int order(){
         int q = 0;
         int n = p.length -1;
         cost = new int[n][n];
         for(int i = 0;i<= n-1;i++){
             cost[i][i] = 0;
         }
         for(int l = 2;l<n;l++){  //the chain length,like merge sort
             for(int i=0;i<n-l;i++){
                 int j = i+l -1;
                 cost[i][j] =Integer.MAX_VALUE;
                 for(int k = i;k <=j -1;k++){
                     q = cost[i][k] + cost[k+1][j] + p[i-1]*p[k]*p[j];
                     if(q < cost[i][j]){
                         cost[i][j] = q; //remeber the best step of i to j
                     }
                 }
             }
         }
         return cost[n-1][n-1];
      }

 }