How does the `std::next_permutation` algorithm work, and what do the variables `i`, `j`, and `k` represent?

std::next_permutation Implementation Explanation

Question:

How does the std::next_permutation algorithm work? What do the variables i, j, and k represent, and how do their values change during execution?

Understanding the Concept:

To understand std::next_permutation, we can view permutations as numbers with their digits represented by elements. The goal is to generate the next permutation in "ascending" order, minimizing the amount by which the number increases.

The Core Loop:

At the heart of the algorithm lies a while loop:

while (true) {
    It j = i;
    --i;

    if (*i < *j) {
        // ...
    }

    if (i == begin) {
        // ...
    }
}

This loop iterates backwards from the last element to the first. The key insight is that we only need to change the position of a digit when everything to the right is in descending order.

Finding the Leftmost Descending Sequence:

If the elements pointed to by i and j are in ascending order, we have found the leftmost descending sequence.

Swapping and Reordering:

When we find the leftmost descending sequence, we swap the digit pointed to by i with the "next largest" digit to its right. This digit is identified by iterating from the end and stopping when we find a digit greater than i.

After swapping, the remaining digits to the right are already in descending order, so we simply reverse them to obtain the next permutation.

Specific Variables:

• i: Pointer to the leftmost element of the descending sequence.
• j: Pointer to the element to the right of i.
• k: Pointer to the element to the right of i that is immediately greater than i.

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