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Problem solution · C++

Maximum Subarray Sum After Multiplier

Maximum Subarray Sum After Multiplier: a C++ solution using dynamic programming. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Dynamic programming
Source
Kamyu LeetCode Solutions
Length
25 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

Dynamic programming

For Maximum Subarray Sum After Multiplier, the implementation records answers for smaller states and reuses them to build the requested result without repeating work.

  1. Define precisely what one DP state represents.
  2. Establish the base cases before transitions are evaluated.
  3. Process states in dependency order and combine only already-known values.

Code notes

  • 25 lines of C++ from the credited upstream file maximum-subarray-sum-after-multiplier.cpp.
  • The implementation visibly relies on sequence storage, cached states.
  • 1 loop block detected.

Complexity

Multiply the number of reachable states by the work performed for each transition, then include the stored state table in memory usage.

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 codeMaximum Subarray Sum After Multiplier · C++C++
Use this to learn the idea, then write your own version.
// Time:  O(n)// Space: O(1) // dp, kadane's algorithmclass Solution {public:    long long maxSubarraySum(vector<int>& nums, int k) {        static const auto& NEG_INF = numeric_limits<int64_t>::min();        enum {INIT, MULT, DIV, DONE};         int64_t result = NEG_INF;        vector<int64_t> dp(4, NEG_INF);        for (const int64_t x : nums) {            dp = {                max(dp[INIT], static_cast<int64_t>(0)) + x,                max({dp[MULT], dp[INIT], static_cast<int64_t>(0)}) + x * k,                max({dp[DIV], dp[INIT], static_cast<int64_t>(0)}) + x / k,                max({dp[DONE], dp[MULT], dp[DIV], static_cast<int64_t>(0)}) + x,            };            result = max(result, ranges::max(dp));        }        return result;    }};

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