How To Approach The Binary Search Problems

How can we know, that a problem can be solve using Binary Search? ☹️

If a problem satisfies points which are mentioned below, then a problem can be solved using Binary Search.

So the points are :

1.  The answer of a problem is Integer ( because decimal numbers are very weird numbers 🤪 until there is no termination after some decimal place).
2. The answer lies between any range of Integers.
3. And there are many numbers between our range which are satisfying the conditions of our answer ( means that they also can be our answer ) but we want a particular one from these numbers. 
4. Most important Point: These numbers ( which I mentioned in point number 3rd ) must be continuous.
5. Why continuous?
6. Suppose our range of answer is [L, R], Mid = (L + R) / 2, and if we somehow check that Mid cannot be our answer then we will sure that our answer is either lies between [L, Mid-1] or [Mid+1, R] ( because the numbers which are satisfying the conditions of the answer are continuous, So these numbers lies in any one interval, not both ).
7. Suppose if they are not continuous then how we can decide in which interval our answer lies🤔 ( Means we cannot choose one interval between any of ( [L, Mid-1], [Mid+1, R] ) these two because maybe there are several numbers which are satisfying the conditions of our answer and some of these numbers are lies in [L, Mid-1] and some in [Mid+1, R]. That's why we want continuous numbers🤓 ).

So let's solve a Problem👨🏻‍💻

Read Problem By Hitting Me

John has n stalls that have fixed positions and c cows.

And he wants that the minimum distance between any two cows is as large as possible And he has to find the largest minimum distance.

Example: 

number of stalls = 6 , cows = 3

and positions of stalls are 1, 2, 4, 5, 8, 9.

The possible ways to place 3 cows are 

       Positions                         The minimum distance between any two cows

• 1, 2, 4                                                       1
• 1, 2, 5                                                       1
• 1, 2, 8                                                       1
• 1, 2, 9                                                       1
• 1, 4, 5                                                       1
• 1, 4, 8                                                       3
• 1, 4, 9                                                       3
• 1, 5, 8                                                       3
• 1, 5, 9                                                       4
• 2, 4, 5                                                       2
• 2, 4, 8                                                       2
• 2, 4, 9                                                       2
• 4, 5, 8                                                       1
• 4, 5, 9                                                       1
• 5, 8, 9                                                       1

So the answer is 4 for ( 1, 5, 9 ).

So let's see how we can come up with the thinking that this problem can be solved using Binary Search.  

1. Yes, our answer is Integer.
2. Yes, our answer lies between the range [ 0 (i.e maybe all cow have the same position),  N( maximum distance between any two stalls i.e 9 - 1 = 8) ].
3. Yes, the numbers which are satisfying the conditions of our answer are continuous ( because if 3 is the number which satisfies the conditions and it may not be the largest then we will sure that now our answer is lies between [4, R] not in [L, 2] ).

So we can solve this problem by using a binary search.

Code of this Problem 👨🏻‍💻.