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Problem solution · C++

Largest Prime from Consecutive Prime Sum

Largest Prime from Consecutive Prime Sum: a C++ solution using binary search. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Binary search
Source
Kamyu LeetCode Solutions
Length
64 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Binary search

For Largest Prime from Consecutive Prime Sum, the implementation exploits a monotonic condition to discard half of the remaining search space after every check.

  1. Identify the ordered answer range or sorted search domain.
  2. Write a predicate whose truth changes only once.
  3. Move the appropriate boundary after each midpoint check and return the final feasible position.

Code notes

  • 64 lines of C++ from the credited upstream file largest-prime-from-consecutive-prime-sum.cpp.
  • The implementation visibly relies on sequence storage.
  • 4 loop blocks detected.

Complexity

Multiply the logarithmic number of midpoint checks by the cost of one predicate evaluation.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeLargest Prime from Consecutive Prime Sum · C++C++
Use this to learn the idea, then write your own version.
// Time:  precompute: O(sqrt(r) * sqrt(r)) = O(r)//        runtime:    O(logp), p = len(PRIMES)// Space: O(sqrt(r)) // precompute, number theory, binary searchconst auto& is_prime = [](int n) {    if (n <= 1 || (n != 2 && n % 2 == 0)) {        return false;    }    for (int i = 3; i <= n; i += 2) {        if (i * i > n) {            break;        }        if (n % i == 0) {            return false;        }    }    return true;}; const auto& linear_sieve_of_eratosthenes = [](int n) {  // Time: O(n), Space: O(n)    vector<int> spf(n + 1, -1);    vector<int> primes;    for (int i = 2; i <= n; ++i) {        if (spf[i] == -1) {            spf[i] = i;            primes.emplace_back(i);        }        for (const auto& p : primes) {            if (i * p > n || p > spf[i]) {                break;            }            spf[i * p] = p;        }    }    return pair(primes, spf);}; const auto& precompute = [](int n, int sqrt_n) {    const auto& [primes, spf] = linear_sieve_of_eratosthenes(sqrt_n);    vector<int> result = {0};    int total = 0;    for (const auto& p : primes) {        total += p;        if (total > n) {            break;        }        if ((total < size(spf) && spf[total] == total) || is_prime(total)) {            result.emplace_back(total);        }    }    return result;}; const int MAX_NUM = 5e5;const int SQRT_MAX_NUM = 2729;  // by precomputationconst auto& PRIMES = precompute(MAX_NUM, SQRT_MAX_NUM);class Solution {public:    int largestPrime(int n) {        return *prev(upper_bound(cbegin(PRIMES), cend(PRIMES), n));    }};

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