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Problem solution · C++

Sum of K Digit Numbers in a Range

Sum of K Digit Numbers in a Range: a C++ solution using direct simulation. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Direct simulation
Source
Kamyu LeetCode Solutions
Length
60 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

Direct simulation

For Sum of K Digit Numbers in a Range, the implementation follows the problem’s operations directly while maintaining only the state needed for the next decision.

  1. Translate each rule into one explicit state update.
  2. Maintain the invariant after every processed item.
  3. Return the accumulated state once all relevant input has been handled.

Code notes

  • 60 lines of C++ from the credited upstream file sum-of-k-digit-numbers-in-a-range.cpp.
  • The implementation visibly relies on sequence storage.
  • 2 loop blocks detected.

Complexity

Count the number and nesting of passes over the input, then include the maintained containers in the memory estimate.

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 codeSum of K Digit Numbers in a Range · C++C++
Use this to learn the idea, then write your own version.
// Time:  O(logr), r = MOD// Space: O(1) // mathclass Solution {public:    int sumOfNumbers(int l, int r, int k) {        static const uint32_t MOD = 1e9 + 7;         const auto& addmod = [](uint32_t a, uint32_t b, uint32_t mod) {  // avoid overflow            // a %= mod, b %= mod;  // assumed a, b have been mod            if (mod - a <= b) {                b -= mod;  // relied on unsigned integer overflow in order to give the expected results            }            return a + b;        };         const auto& submod = [&](uint32_t a, uint32_t b, uint32_t mod) {            // a %= mod, b %= mod;  // assumed a, b have been mod            return addmod(a, mod - b, mod);        };         const auto& mulmod = [&](uint32_t a, uint32_t b, uint32_t mod)  {  // avoid overflow            // a %= mod, b %= mod;  // assumed a, b have been mod            uint32_t result = 0;            if (a < b) {                swap(a, b);            }            while (b > 0)  {                 if (b % 2 == 1) {                    result = addmod(result, a, mod);                }                a = addmod(a, a, mod);                b /= 2;             }             return result;         };         const auto& powmod = [&](uint32_t a, uint32_t b, uint32_t mod) {            a %= mod;            uint32_t result = 1;            while (b) {                if (b & 1) {                    result = mulmod(result, a, mod);                }                a = mulmod(a, a, mod);                b >>= 1;            }            return result;        };         const auto& invmod = [&](uint32_t x, uint32_t mod) {            return powmod(x, mod - 2, mod);        };         return mulmod(mulmod((r + l) * (r - l + 1) / 2, powmod(r - l + 1, k - 1, MOD), MOD),                      mulmod(submod(powmod(10, k, MOD), 1, MOD), invmod(10 - 1, MOD), MOD), MOD);    }};

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