Question

A human pyramid is a way of stacking people vertically in a triangle. With the exception of the people in the bottom row, each person splits their weight evenly on the two people below them in the pyramid. For example, in the pyramid to the right, person A splits her weight across people B and C, and person H splits his weight – plus the accumulated weight of the people he’s supporting – onto people L and M.

write a recursive function

double weightOnBackOf(int row, int col);

that takes as input the row and column number of a person in a human pyramid, then returns the total weight on that person's back. The row and column are each zero-indexed, so the person at row 0, column 0 is on top of the pyramid, and person M in the above picture is at row 4, column 2. So if we look at the above example, weightOnBackOf(1, 1) would return 100 pounds (since person C is shouldering 100 pounds on her back), and weightOnBackOf(4, 2) should return 625 (since person M is shouldering a whopping 625 pounds on her back).

Your implementation of weightOnBackOf must be implemented recursively and must not use any loops (for, while, or do ... while).

          Your program will ask for a weight for the humans in your human pyramid . You can assume that all humans in the pyramid (like in the example above everyone weighs 200lbs) will be that weight . You should test for up to 5 rows. If it works for five it will work for an infinite number of rows and columns. This assignment MUST use RECURSION in Java.

Answer 1

SOLUTION

//Assuming that everyones' weight is 200lbs

import java.util.Scanner;

public class backweight {
   static double every_ones_weight;
  
   public static void main(String[] args) {
       Scanner sc= new Scanner(System.in);
       System.out.println("Enter everyones' weight:");
       every_ones_weight=sc.nextDouble();
       System.out.println("Whose weight on the back you want to know. Please enter row and column value:");
       System.out.print(weightOnBackOf(sc.nextInt(),sc.nextInt()));
   }

   static double weightOnBackOf(int row, int col) {
       if (row == 0 && col == 0){
                return 0;
            }
            if (row >= 1 && col == 0){
                return (every_ones_weight)/2 + 0.5*weightOnBackOf(row-1,col);
            }
            if (row >= 1 && col == row){
                return (every_ones_weight)/2 + 0.5*weightOnBackOf(row-1,col-1);
            }
            if (row >= 1 && (col > 0 && col < row)){
                return every_ones_weight + 0.5*(weightOnBackOf(row-1,col-1) + weightOnBackOf(row-1,col));
            }
            // returns 0.0 if the row and col are out of bounds.
       return 0.0;
   }
      
}

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