# Every genuine coin weighs 10 grams every fake weighs

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Every genuine coin weighs 10 grams; every fake weighs 11 grams. You have an analytical scale that can determine the exact weight of any number of coins.
Fake Coins Devise a brute force algorithm to identify the stack with the fake coins and determine its worst- case efficiency class. Devise a clever algorithm with the minimum number of weighings needed to identify the stack with the fake coins? Magic with numbers ……
Fake Coins A = 10n(n+1)/2 = 5n(n+1) B = Weight of all the coins from 1 to n stack, taking 1 coin from stack 1 and 2 coins from stack 2 and so on, taking n coins from stack n B – A will yield the number of stack with fake coins
Design Problem Suppose you have an array of n distinct elements. Write an algorithm that picks ith array element and place it at the position such that all array elements present at left are less than it and all array elements present at right are greater than it. Also gives the time complexity of your algorithm in notation.
Design Problem A man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits will be there in a year if the initial pair of rabbits (male and female) are newborn and all rabbit pairs are not fertile during their first month of life but thereafter give birth to one new male/female pair at the end of every month? 30
Computing the nth Fibonacci Number F(n) = F(n − 1) + F(n − 2) for n > 1 F(0) = 0, F(1) = 1. Exponentiation problem: compute a n for nonzero number a and nonnegative integer n . By the definition of exponentiation 31
Not a source of clever and efficient algorithm But….. the brute-force approach should not be overlooked as an important algorithm design strategy applicable to a very wide variety of problems 32

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