A common way to solve a problem is to use loops to build a solution step-by-step. There are several variations of this approach:
Input-centric strategy: In this approach, we process one input at a time and build a partial solution in each iteration of the loop.
Output-centric strategy: With this approach, we add one output at a time to the solution and iteratively build parts of the solution.
Iterative improvement strategy: This involves starting with a few easily accessible approximate solutions and then continuously improving them until you reach the final solution.
There are also several loop-based approaches: using single loops and variables, using nested loops and variables, increasing loops by one constant (greater than 1), using loops twice (double traversal), using single loops and prefix arrays (or extra memory), etc.
Roman numerals to whole numbers.
Leader in the array.
Effective mountain formations. Fitzbaz problem.
Insert, bubble, and select sorting.
Find the maximum and minimum values in the array.
Sorts arrays in the waveform.
Balanced indexes of arrays.
Find products other than yourself.
Rotate the matrix 90 degrees.
Spiral traversal of the matrix.
Find the row with the maximum number of rows.
The decreasing strategy involves solving a problem by finding a solution to a sub-problem. This often leads to a recursive algorithm that breaks down the problem into smaller input sizes and continues to do so until the basic case is reached.
Euclidean algorithm for GCD.
Binary search algorithm.
Josephus Question.
Search in the binary search tree.
Insert in the binary search tree.
Deletion in the binary search tree.
The fast selection algorithm finds the k-th smallest.
When an array has some sort of sequential property, such as sorted, the idea of a dichotomous search can be used to effectively solve the search problem. With this approach, we can find a solution within the o(logn) time complexity.
To use binary search, we need to modify the standard binary search algorithm according to the specifics of the problem. The core idea is to compute the middle index and iterate over the left or right half of the array.
Find the square root of an integer.
Search in the rotation-sort array.
Fixed points in an array.
Search for sorted 2D matrices.
The median of the sorted array.
Sort the first and last positions of elements in the array.
Find the maximum value in the increment or subtraction array.
The divide-and-conquer strategy involves breaking down a problem into multiple sub-problems, solving each sub-problem, and then combining their solutions to get a solution to the original problem. This approach can be an effective way to solve many of the fundamental problems in DSA.
By dividing the problem into smaller parts, it is easier to solve each part individually and then combine the solutions to get the final solution to the entire problem.
Merge sort algorithm.
Quick sort algorithm.
The divide-and-conquer solution for the sum of the largest subarrays.
Find the divide-and-conquer solution for the largest difference in the array.
Find the divide and conquer of the maximum and minimum values in an array.
Divide and conquer to find solutions for most of the elements in the array.
The idea of dividing and conquering to construct a segment tree.
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