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A mission-critical production system has n stages that have to be performed sequentially; stage
i is performed by machine Mi. Each machine Mi has a probability ri of functioning reliably and
a probability 1 − ri of failing (and the failures are independent). Therefore, if we implement
each stage with a single machine, the probability that the whole system works is r1 · r2 · · · rn.
To improve this probability we add redundancy, by having mi copies of the machine Mi that
performs stage i. The probability that all mi copies fail simultaneously is only (1 − ri)mi, so the
probability that stage i is completed correctly is 1 − (1 − ri)mi and the probability that the whole
system works is Qni=1(1 − (1 − ri)mi). Each machine Mi has a cost ci, and there is a total budget
B to buy machines. (Assume that B and ci are positive integers.)
Given the probabilities r1, . . . , rn, the costs c1, . . . , cn, and the budget B, find the redundancies
m1, . . . , mn that are within the available budget and that maximize the probability that the
system works correctly

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Questions to be asked from my profession

I am trying to write a method that will return true if a binary tree is full and complete (each node has 2 children or none and all the leaves of the tree are at the same depth).

My idea is to use recursion. I will check for any node if its left son has number of children that is equal to its right son's number of children. If so, I will return true, otherwise false.

The algorithm will look like this:

public class Utils {


    public boolean isFullCompleteTree(Tree<Integer> t) {
            TreeInfo rootInfo = isFullCompleteTree(t.getRoot());
            return rootInfo.valid;
        }
    public TreeInfo isFullCompleteTree(Node<Integer> node) {
        boolean valid = true;

        if (node == null) {
            return new TreeInfo(true, 0);
        }

        TreeInfo rightInfo = isFullCompleteTree(node.goRight());
        TreeInfo leftInfo = isFullCompleteTree(node.goLeft());

        if ((!rightInfo.valid) || (!leftInfo.valid)) {
            valid = false;
        }
        if (rightInfo.numChildern != leftInfo.numChildern) {
            valid = false;
        }
        return new TreeInfo(valid, rightInfo.numChildern + leftInfo.numChildern
                + 1);
    }
    }

    class TreeInfo {
       public boolean valid;
       public int numChildern;

       public TreeInfo(boolean valid, int numChildern) {
           this.valid = valid;
           this.numChildern = numChildern;
    }

}

I didn't include the tree implementation but it is pretty straightforward.

The idea of the algorithm is to check if in every node the number of right son's children is equal to the left son's children. If a tree is not full and complete, then in some node this rule will not apply.

Do you think that my algorithm is correct or am I missing something?

multiplication of two numbers without actual multiplication ::

Using vedic mathematics

Deck of cards :

1) Put the first card on the table and next at the bottom of the deck
2) Repeat the above until all the cards are on table.
3) Pick up the cards and repeat steps 1 and 2.

Find after how many iterations the original order is restored.

For Ex ::
1 2 3
1st iteration - 2 3 1
2nd iteration - 3 1 2
3rd iteration - 1 2 3

so after 3 iterations. Find for n.

* 54. An array of integers of size n. Generate a random permutation of the array, given a function
rand_n() that returns an integer between 1 and n, both inclusive, with equal probability. What is the
expected time of your algorithm?

Write a program to find out if the binary tree is balance or not. The tree is balance if the difference between the
left node and right node is equal or less than 1. The above considition is applicable for subtree too..
If tree do not have any child, its height will be zero.

What is the order of above program

Write a program to find out the height of the tree. Tree can have two node (one is left and right node).
If tree do not have any child, its height will be zero.

What is the order of above program

1) Write a iterative program to calculate factorial of N.
2) what is the order of above program
3) Write a recursive program to calculate factorial of N.
4) what is the order of above program