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Mastering Algorithms for Problem Solving in C++

Solution: Backtracking

Explore how to use recursive backtracking to determine the minimum length addition chain for an integer. This lesson guides you through the algorithm’s logic and teaches how to implement it in C++. By the end, you will understand how to apply backtracking to solve this classic problem and enhance your algorithm design skills.

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Let's practice what we've learned so far.

Task

An addition chain for an integer nn is an increasing sequence of integers that starts with 11 and ends with nn, such that each entry after the first is the sum of two earlier entries. More formally, the integer sequence x0<x1<x2<⋅⋅⋅<xlx_0 < x_1 < x_2 < ··· < x_l is an addition chain for nn if, and only if,

  • x0=1x_0 = 1,
...