Prune and Search Method
The prune and search method refers to optimizing backtracking search algorithms by aggressively pruning branches that cannot lead to solutions.
It involves two phases:
Pruning  Before exploring a branch, prune it if some condition proves it cannot lead to a solution.
Search  If not pruned, explore the branch through standard backtracking search.
This pruning eliminates branches that search would have explored.
Java  N Queens prune and search:


C++  Sudoku solver pruning:


Python  General prune and search:


Prune and search reduces wasteful exploration by pruning provably bad branches before search.
The Prune and Search Method is an algorithmic technique used to efficiently solve problems by iteratively reducing the search space. At each step, the algorithm “prunes” away a portion of the input that is guaranteed not to contain the solution, leaving a smaller set of possibilities to search. The technique is particularly useful in optimization and search problems.
Example Code in Java
Here is an example to find the median in an unsorted array using the Prune and Search Method.


Example Code in C++


Example Code in Python


In each of these examples, the function findMedian
employs Prune and Search to find the median of an array in (O(n)) time, where (n) is the length of the array. It does so by repeatedly partitioning the array around a pivot and discarding the section that doesn’t contain the median.
The prune and search method is a technique for solving optimization problems by iteratively dividing the search space into two parts: the promising one, which contains the optimal value and is recursively searched, and the second part without optimal value, which is pruned (thrown away).
This paradigm is very similar to wellknown divide and conquer algorithms. The main difference is that in prune and search, we are not just dividing the search space in half, but we are also discarding a fraction of the input elements that we know cannot contain the optimal solution. This can lead to a significant speedup in the running time of the algorithm.
One example of a problem that can be solved using the prune and search method is the knapsack problem. In the knapsack problem, we are given a set of items, each with a weight and a value, and a capacity W. We want to find the subset of items that has the maximum total value and that fits within the knapsack.
One way to solve the knapsack problem is to use a bruteforce approach. We can enumerate all possible subsets of items and then check each one to see if it fits within the knapsack. This approach has a time complexity of O(2^n), where n is the number of items.
Another way to solve the knapsack problem is to use the prune and search method. We can start by sorting the items by weight. We then consider the items in decreasing order of weight. For each item, we check to see if it fits within the knapsack. If it does, we add it to the knapsack. If it does not, we prune it (throw it away). We continue this process until we have either found a subset of items that fits within the knapsack or we have pruned all of the items. This approach has a time complexity of O(n*W), where n is the number of items and W is the capacity of the knapsack. This is significantly faster than the bruteforce approach, especially when the number of items is large.