Big(o)

The most wanted even after graduation!

Attempt: To understand in most simplest way. "Layman's language."

• What Big(o) means?I want to solve a problem, I want to know how much time is needed to solve it. That's all what Big(o) tells.
• Example:O(1): I have one deck of cards with me. Randomly I have placed 6cards facing its written part towards me. One of the card in it is 7 ofspade.Task1:Pick up 7 of spade. Whats the Time taken?Time: It takes one second to pick up the card. O(1)Task2:Pick up any ONE card from it. Whats the Time taken?Time: It takes one second to pick one card among it. O(1)Task3:All the cards from deck are placed. Pick any ONE card. Whats theTime taken?Time: It takes one second to pick up any one card from deck. O(1)No matter what number of cards is placed (it can be thousand or more ),the amount of time taken to pick any one card will always be 1 secondirrespective of space those cards are covering or quantity of cards.O(n): I have one deck of cards with me. Randomly I have placed 6cards facing its written part downwards. So, now we dont know what arethose 6 cards.Task1: Search for 2 of hearts. Whats the time taken?Time: 2 of hearts may be there or may not be, we dont know. We dontknow what are those 6 cards. So what will we do? Pick up each card oneat a time and look for 2 of hearts. This way we are touching all 6 cardsone time. Time taken is O(6). No matter how many cards are placed we aretouching each cards atleast one time to find 2 of hearts.Task2: 'n' cards are placed, Have to search for Ace of club. What'sthe time taken?Time: O(n), Because to find Ace of club, have to pick up each cardsatleast once.O(n^2): I have randomly placed 8 cards such that some card's writtenpart is facing upwards and some downwards.Task1: Face the cards in the same direction facing upwards. Whats thetime taken?Time: To execute this task we need to visit card 2 times:the card and place facing towards upperside.Two times an individual card is visited. i.e. O(8^2).Same way if 'n' cards are placed and two times we are visiting thecard individually then the time taken would be O(n^2), which meanseach card is visited 2 times.
  1. Pick up a card and check. It is towards which side.
  2. Now flip the card and check If upwards place as it is, if not turn
• O(n^n): Each n element are visited n times. For eample, there are 26cards given, each cards are atleast visited 26 times.
• O(logn): 100 cards are given, check if Joker is present in thedeck. What's the time taken?Task1: To check if Joker is present.Time: Searching 100 cards individually is difficult. To search infaster and efficient way approach will be:and repeat the steps 2 and 3 till card is found.So, Cards will be divided n times untill Joker is found, thus it willbe O(logn).
  1. divide the 100 in two halves.
  2. Search in either one of the halves.
  3. If joker is present, other halv will be discarded.
  4. if joker isn't present, the other half will be divide in two halves