Find pairs from the given array

Given an array X, find tuples (xi, xj) such that j>i and xj is the immediate number greater than xi in the given array?

Ex Problem: X: {5, 4, 1, 3, 7}
Solution:
{5, 7}
{4, 7}
{1, 3}
{3, 7}

Random Number Generation - II

Given a function rand5() which generates values between 0-5 with equal probablities, how would you create another function rand7() which generates values between 0-7?

For that matter given a function randM() which generates numbers between 0-M, how would you create another function randN() which generates numbers between 0-N with equal probabilities? Is it possible for every value of M,N?

PS: I'm calling this "Random Number Generation - II" because we already have another version of this problem here.

Think in terms of possible values being generated by the given randX() function and map to all the possible values to be generated by the target randY() function

Find union of two sets in O(1)

Use bit-map

Palindrome in LinkedList

Given a linked list with node as given below:

struct node
{
char info;
struct node *next;
}

Give an O(n) algorithm to find if its a palindrome or not? You can not use more than O(1) space.

Two pointers to explore the list, reach the mid-point reverse the first half and compare the two halves

Maze Searching

Given a 2-d maze of characters, find if there exists a word "Algorithms" in the maze. By exists we mean it exists in a row, a column or like snakes (diagonals prohibited though)?

By snakes, we mean like following

A . . . M S
L G . T H .
. O R I . .
Use DFS and explore the maze as and when letters are found

Generating Graphs

Given n nodes,

1. generate all possible directed subgraphs.
2. generate all possible undirected subgraphs.

Easier version:

Given n nodes,
1. generate all possible directed subgraphs of n nodes,
2. generate all possible undirected subgraphs of n nodes,

PubTrivia - a pub where algos are served alongwith drinks!

You and your friends have gotten together for a Trivia night at a local pub.There are N questions asked during the night.Each question is worth a number of points; the i-th element of the points array corresponds to the score received by you if you correctly answer the i-th question, but you lose that many points if you answer that incorrectly. The questions are given in the order specified and you must answer each question before the next is asked. In addition, after each correct answer you will receive a token. If you then have tokensNeeded tokens, the pub will immediately take all of your tokens and award you additional bonus points. However, if you get the question wrong, the pub will take away all of your tokens without giving you any bonuses. The element i of the bonuses array corresponds to the bonus you receive if you win the bonus on question i.
Note that it is possible to win multiple bonuses during the game.
You know the answer to all the questions and want to maximize the number of points you receive.
Give an algorithm to obtain the maximum points that you can receive if you correctly choose which questions to answer.

Inputs :
N
tokensNeeded
p - array of points
b - array of bonuses