Aug 6th, 2022

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hello friends my name is - char and today Im going to talk about fan victory or binary Index free before going into the details of what when victory is lets look at the use case which finding trade is trying to solve so finding tree is used to get profits sum of an array for example if Im given an array of 7 elements from 0 to 6 so family tree will help people answer queries like what is the sum from 0 to 4 so the sum from 0 to 4 is 3 + 2 5 5 + 6 11 11 + 5 16 what is the sum from 0 to 6 so the sum from 0 to 6 is 60 minus 1 15 + 2 17 so queries like this is why I use one directory what are the other alternate solutions that we did not use friend victory one solution is to keep a prefix some base array so for 0 its the sum to 0 is 3 for 1 the sum till 1 is 3 + 2 5 4 to the sampler till 2 is 5 + 0 5 some till 3 is 5 plus 6 11 some till 4 is 11 plus 5 60 16 minus 1 15 + 15 + 2 17 and this would also help me answer the same query what is a sum from 0 to 4 and you directly over here and

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To insert 1 element you need log n time. So to insert k elements it would be O(k log n).

Binary search works this way because each search attempt cuts the number of records to search in half. That said, databases typically use some other binary tree-like data structure such as b-trees or red-black trees to perform the indexing.

For example, if we have 5 elements in the array and need to insert an element in arr[0], we need to shift all those 5 elements one position to the right. In general, if we have n elements we need to shift all n elements. So, worst case time complexity will be O(n). where n = number of elements in the array.

Binary search is used to find the index of an element in a sorted array, and if the element doesnt exist, that can be determined efficiently as well.

To insert 1 element you need log n time.

Binary Insertion Sort Algorithm Step 1: Iterate the array from the second element to the last element. Step 2: Store the current element A[i] in a variable key. Step 3: Find the position of the element just greater than A[i] in the subarray from A[0] to A[i-1] using binary search.

The worst-case (and average-case) complexity of the insertion sort algorithm is O(n). Meaning that, in the worst case, the time taken to sort a list is proportional to the square of the number of elements in the list. The best-case time complexity of insertion sort algorithm is O(n) time complexity.

The computational complexity of inserting an element in the middle of an array is O(N), where N is the number of elements in the array. The elements in the array must all be shifted up one index after the insertion, or all the elements must be copied to a new array big enough to hold the inserted element.

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