Step by Step solution about How to resolve the algorithm Negative base numbers step by step in the C++ programming language

The provided C++ code defines two functions, encodeNegativeBase and decodeNegativeBase, for converting integers to and from a negative base representation. Negative bases are used in certain mathematical applications, such as computer arithmetic and cryptography.

1. encodeNegativeBase Function:

   • This function takes two arguments:
     • n: The integer to be encoded.
     • b: The negative base to use for encoding. Valid values for b are between -62 and -1.
   • It encodes n in the specified negative base b and returns the encoded string.
   • The encoding process involves repeated division of n by b, taking the remainder after each division, and then reversing the sequence of remainders.
   • If b or n are out of range, it throws a runtime error.

2. decodeNegativeBase Function:

   • This function takes two arguments:
     • ns: The encoded string to be decoded.
     • b: The negative base in which the string was encoded. Valid values for b are between -62 and -1.
   • It decodes the given string ns from the specified negative base b and returns the decoded integer.
   • The decoding process involves multiplying each digit in ns by the corresponding power of b and summing the results.
   • If b or ns are invalid, it throws a runtime error.

3. main Function:

   • The main function demonstrates the usage of the encodeNegativeBase and decodeNegativeBase functions.
   • It defines a vector of pairs where each pair contains an integer and its corresponding negative base.
   • For each pair in the vector, it encodes the integer in the given negative base, prints the encoded string, and then decodes the encoded string back to the original integer.

In summary, this code provides functions for encoding and decoding integers using negative bases, which are useful in certain mathematical and computational scenarios.

#include <iomanip>
#include <iostream>
#include <tuple>
#include <vector>

const std::string DIGITS = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";

std::string encodeNegativeBase(int64_t n, int b) {
    if (b < -62 || b > -1) {
        throw std::runtime_error("Argument out of range: b");
    }
    if (n == 0) {
        return "0";
    }

    std::string output;
    int64_t nn = n;
    while (nn != 0) {
        int rem = nn % b;
        nn /= b;
        if (rem < 0) {
            nn++;
            rem -= b;
        }
        output += DIGITS[rem];
    }

    std::reverse(output.begin(), output.end());
    return output;
}

int64_t decodeNegativeBase(const std::string& ns, int b) {
    if (b < -62 || b > -1) {
        throw std::runtime_error("Argument out of range: b");
    }
    if (ns == "0") {
        return 0;
    }

    int64_t total = 0;
    int64_t bb = 1;

    for (auto it = ns.crbegin(); it != ns.crend(); it = std::next(it)) {
        auto ptr = std::find(DIGITS.cbegin(), DIGITS.cend(), *it);
        if (ptr != DIGITS.cend()) {
            auto idx = ptr - DIGITS.cbegin();
            total += idx * bb;
        }
        bb *= b;
    }
    return total;
}

int main() {
    using namespace std;

    vector<pair<int64_t, int>> nbl({
        make_pair(10, -2),
        make_pair(146, -3),
        make_pair(15, -10),
        make_pair(142961, -62)
        });

    for (auto& p : nbl) {
        string ns = encodeNegativeBase(p.first, p.second);
        cout << setw(12) << p.first << " encoded in base " << setw(3) << p.second << " = " << ns.c_str() << endl;

        int64_t n = decodeNegativeBase(ns, p.second);
        cout << setw(12) << ns.c_str() << " decoded in base " << setw(3) << p.second << " = " << n << endl;

        cout << endl;
    }

    return 0;
}