Split a problem, solve parts, and combine; merge sort is a classic.
Divide and conquer splits a problem into smaller independent subproblems, solves them recursively and combines results: merge sort, quicksort, binary search, FFT, Karatsuba, Strassen. Complexity via recurrences T(n)=aT(n/b)+f(n) and the master theorem.
Merge sort halves the list, sorts each half and merges in linear time.
Divide and conquer breaks a problem into independent parts and combines the answers, which yields efficient algorithms like merge sort.
Split a problem, solve parts, and combine; merge sort is a classic.
Divide and conquer breaks a problem into independent parts and combines the answers, which yields efficient algorithms like merge sort.
Work of the form T(n) equals two T(n over 2) plus linear work gives n log n time, as in merge sort.
Divide and conquer subproblems are independent, while dynamic programming subproblems overlap and their results are reused.
Typical applications include sorting a very large array by splitting it into halves, finding the closest pair of points in a plane and multiplying large integers with a faster method than the schoolbook approach.
Study "Greedy algorithms" first (topic 30 of 104 in Software & Computing). It covers the groundwork this topic builds on.
Recurrence relations. Parallelisable. Base case thresholds.
Merge sort halves the list, sorts each half and merges in linear time.
The next topic is "Backtracking", which builds directly on this one.
It is classed as Beginner in Software & Computing (topic 31 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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