Reducibility
Reducibility refers to transforming one problem into an instance of another problem. If problem A can be reduced to problem B, then solving B allows solving A. Reducibility enables proving relationships between problems.
Some examples:
 Sorting reduces to minimum finding
 Shortest path reduces to minimum edge
 3SAT reduces to vertex cover
Java  Sorting to minimum finding:


C++  Shortest path to minimum edge:


Python  3SAT to vertex cover:


Reducibility enables transferring of solutions and complexity results between problems. Useful technique for proofs.
Reducibility is a concept in computational theory that provides a formal way to show that one problem is “at least as hard as” another. In essence, if you can solve problem B quickly, then you can also solve problem A quickly. The most common form of reduction is polynomialtime reduction, often denoted as ( A \leq_p B ).
In simple terms, if you can reduce problem A to problem B, then any solution to B can be used to solve A.
Example Code in Java
Here’s an example to show how you could reduce the problem of calculating the square of a number to the problem of multiplication.


Example Code in C++


Example Code in Python


These examples trivially reduce the problem of squaring a number to multiplication, showing that if you have a fast method for multiplication, you can also square a number quickly.