/**
  * @file	Opt.java
  * @synopsis 	A simple program to compute the optimal Binary Search tree
  *		in which you are given an input vector p of frequencies. 
  *		CONVENTION:
  *		the first index (i=0) of vectors and arrays are not used.
  *
  * @author	Chee Yap
  * @date	Apr 23, 2001 (for Basic Algorithms class)
  */

public class Opt {

  // Members:
	int n;		// number of keys
	int[]   p;	// this is the probabality or frequency vector
			//  NOTE: indexing is from 1 (not 0) to n 
	int[][] cost;	// This is A(i,j) in lectures and text
	int[][] prob; 	// This is P(i,j) in lectures

  // Constructors:

	Opt(int[] q) {
	  n = q.length - 1;
	  p = q;
	  cost = new int[n+1][n+1];
	  prob = new int[n+1][n+1];

	  best();  // calls the main subroutine
	} //Opt(q, k)

  // Methods:

	/******************************************************
	 THIS IS THE MAIN ROUTINE
	 ******************************************************/
	void best() {
	  // init:
		for (int i = 1; i <= n; i++) {
		  cost[i][i] = p[i];
		  prob[i][i] = p[i];
		  cost[i][i-1] = 0;
		}
	  // loop:
		for (int k = 2; k <= n; k++) {
		  for (int i = 1; i <= n-k+1; i++) {
		    // initial guess at optimal root is rr = i+k-1:
		    prob[i][i+k-1] = p[i+k-1] + prob[i][i+k-2];
		    int val = cost[i][i+k-2];
		    
		    for (int r = i; r < i+k-1; r++) 
			if (val > cost[i][r-1] + cost[r+1][i+k-1]) {
			  val = cost[i][r-1] + cost[r+1][i+k-1];
			}
		    cost[i][i+k-1] = prob[i][i+k-1] + val;
		  } // for i
		} // for k
	} // best()

	/******************************************************
	 prints all subproblems
		EXERCISE: modify this to print the optimal tree
	 ******************************************************/
	void output() {
	  for (int k = 1; k <= n; k++) {
	    System.out.println("Size k = " + k); 
	    for (int i = 1; i <= n-k+1; i++) {
	    	int j = i+k-1; 
		System.out.println("Subproblem (i,j) = (" + i 
			+ ", " +  j
			+ "): cost = " + cost[i][j]);
	    }
	  }
	} // output()


	/******************************************************
	 Main method
	 ******************************************************/
	public static void main( String[] args) {

	  // sample input with 6 keys
	  //	(the first is a dummy key)
	  // String[] keys = { "dummy", "a", "and", "he", "of", "the", "to"};
	  int[]  p    =   { 0,       13,  16,    12,   11,   40,    12};

	  // construct the opitmal tree:
	  Opt S = new Opt(p);

	  // print the optimal tree;
	  System.out.println(
	    "**************************************************\n"
	    + "    ALL SUBPROBLEMS\n"
	  + "**************************************************");
	  S.output();
  	} // main

}//class Opt