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Problem solution · C++

Count Valid Sequences

Count Valid Sequences: 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
61 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 Count Valid Sequences, 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

  • 61 lines of C++ from the credited upstream file count-valid-sequences.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 codeCount Valid Sequences · C++C++
Use this to learn the idea, then write your own version.
// Time:  O(n)// Space: O(n) // stars and bars, combinatoricsstatic const uint32_t MOD = 1e9 + 7; uint32_t addmod(uint32_t a, uint32_t b) {  // avoid overflow    if (MOD - a <= b) {        b -= MOD;  // relied on unsigned integer overflow in order to give the expected results    }    return a + b;} uint32_t submod(uint32_t a, uint32_t b) {    return addmod(a, (MOD - b) % MOD);} // reference: https://stackoverflow.com/questions/12168348/ways-to-do-modulo-multiplication-with-primitive-typesuint32_t mulmod(uint32_t a, uint32_t b)  {  // avoid overflow    uint32_t result = 0;    if (a < b) {        swap(a, b);    }    while (b > 0)  {         if (b & 1) {            result = addmod(result, a);        }        a = addmod(a, a);        b >>= 1;    }     return result; }  vector<int> FACT = {1, 1};vector<int> INV = {1, 1};vector<int> INV_FACT = {1, 1};const int MAX_N = 5e5;const auto& init = [](int n) {    while (size(INV) <= n) {  // lazy initialization        FACT.emplace_back(mulmod(FACT.back(), size(INV)));        INV.emplace_back(mulmod(INV[MOD % size(INV)], MOD - MOD / size(INV)));  // https://cp-algorithms.com/algebra/module-inverse.html        INV_FACT.emplace_back(mulmod(INV_FACT.back(), INV.back()));    }    return 0;}(MAX_N); class Solution {public:    int countValidSequences(int n, int k) {        const auto& nCr = [](int n, int k) {            return mulmod(mulmod(FACT[n], INV_FACT[n - k]), INV_FACT[k]);        };         const auto& nHr = [&](int n, int k) {            return nCr(n + k - 1, k);        };         return submod(nHr(k, n - k), (n - k) % 2 == 0 ? nHr(k, (n - k) / 2) : 0);    }};

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