From 96254947699986c59f0dc63d69fd4b76bd3ed43e Mon Sep 17 00:00:00 2001 From: Sebastiano Tronto Date: Mon, 6 Jul 2026 19:08:08 +0200 Subject: Initial commit --- 03_dynamic_programming/a.out | Bin 0 -> 13520 bytes .../coin_combinations_i_1635.cpp | 25 ++++++++++++ .../coin_combinations_ii_1636.cpp | 28 +++++++++++++ 03_dynamic_programming/counting_towers_2413.cpp | 38 ++++++++++++++++++ 03_dynamic_programming/dice_combinations_1633.cpp | 19 +++++++++ 03_dynamic_programming/edit_distance_1639.cpp | 22 +++++++++++ .../longest_common_subsequence_3403.cpp | 44 +++++++++++++++++++++ 03_dynamic_programming/minimizing_coins_1634.cpp | 33 ++++++++++++++++ 03_dynamic_programming/removing_digits_1637.cpp | 28 +++++++++++++ 9 files changed, 237 insertions(+) create mode 100755 03_dynamic_programming/a.out create mode 100644 03_dynamic_programming/coin_combinations_i_1635.cpp create mode 100644 03_dynamic_programming/coin_combinations_ii_1636.cpp create mode 100644 03_dynamic_programming/counting_towers_2413.cpp create mode 100644 03_dynamic_programming/dice_combinations_1633.cpp create mode 100644 03_dynamic_programming/edit_distance_1639.cpp create mode 100644 03_dynamic_programming/longest_common_subsequence_3403.cpp create mode 100644 03_dynamic_programming/minimizing_coins_1634.cpp create mode 100644 03_dynamic_programming/removing_digits_1637.cpp (limited to '03_dynamic_programming') diff --git a/03_dynamic_programming/a.out b/03_dynamic_programming/a.out new file mode 100755 index 0000000..f4fc9b1 Binary files /dev/null and b/03_dynamic_programming/a.out differ diff --git a/03_dynamic_programming/coin_combinations_i_1635.cpp b/03_dynamic_programming/coin_combinations_i_1635.cpp new file mode 100644 index 0000000..696c1f6 --- /dev/null +++ b/03_dynamic_programming/coin_combinations_i_1635.cpp @@ -0,0 +1,25 @@ +#include +#include + +static constexpr int mod = 1000000007; +static constexpr int X = 1000001; + +int f(const std::vector& c, std::vector& a, int x) { + if (x < 0) return 0; + if (a[x] != -1) return a[x]; + if (x == 0) return a[x] = 1; + + a[x] = 0; + for (auto m : c) + a[x] = (a[x] + f(c, a, x-m)) % mod; + return a[x]; +} + +int main() { + int n, x; + std::cin >> n >> x; + std::vector c(n), a(X, -1); + for (int i = 0; i < n; i++) + std::cin >> c[i]; + std::cout << f(c, a, x) << "\n"; +} diff --git a/03_dynamic_programming/coin_combinations_ii_1636.cpp b/03_dynamic_programming/coin_combinations_ii_1636.cpp new file mode 100644 index 0000000..75642da --- /dev/null +++ b/03_dynamic_programming/coin_combinations_ii_1636.cpp @@ -0,0 +1,28 @@ +#include +#include +#include + +static constexpr int mod = 1000000007; +static constexpr int X = 1000001; + +int main() { + int n, x; + std::cin >> n >> x; + std::vector c(n); + for (int i = 0; i < n; i++) + std::cin >> c[i]; + + std::vector> a(n, std::vector(X, 0)); + for (int i = 0; i < (int)c.size(); i++) a[i][0] = 1; + for (int j = c.back(); j <= x; j += c.back()) a[c.size()-1][j] = 1; + for (int i = c.size()-2; i >= 0; i--) { + for (int j = 1; j <= x; j++) { + a[i][j] = a[i+1][j]; + if (j >= c[i]) { + a[i][j] += a[i][j-c[i]]; + a[i][j] %= mod; + } + } + } + std::cout << a[0][x] << "\n"; +} diff --git a/03_dynamic_programming/counting_towers_2413.cpp b/03_dynamic_programming/counting_towers_2413.cpp new file mode 100644 index 0000000..902956b --- /dev/null +++ b/03_dynamic_programming/counting_towers_2413.cpp @@ -0,0 +1,38 @@ +#include +#include + +// Recurrence relation: +// f(n) = sum over i from 0 to n-1 of f(i) * p(n-i) +// where p(n) is the number of indivisible towers of height n, +// which is easily seen to be 3^(n-1)+1. +// Then we can expand: +// f(n) = sum_{i=0}^{n-1} f(i)(3^{n-i-1}+1) = g(n) + h(n) +// where we define g(n) = sum f(i)3^{n-i-1} and h(n) = sum f(i). +// Then it's easy to see that: +// g(n+1) = f(n) + 3g(n) +// h(n+1) = f(n) + h(n) +// Initial values are h(1) = 1 and g(1) = 1. + +constexpr size_t mod{1000000007}; +constexpr size_t maxn{1000001}; +std::vector f(maxn); +std::vector g(maxn); +std::vector h(maxn); + +int main() { + g[1] = h[1] = 1; + f[1] = 2; + for (size_t i = 2; i < maxn; i++) { + g[i] = (f[i-1] + 3*g[i-1]) % mod; + h[i] = (f[i-1] + h[i-1]) % mod; + f[i] = (g[i] + h[i]) % mod; + } + + size_t t; + std::cin >> t; + for (size_t i = 0; i < t; i++) { + size_t n; + std::cin >> n; + std::cout << f[n] << "\n"; + } +} diff --git a/03_dynamic_programming/dice_combinations_1633.cpp b/03_dynamic_programming/dice_combinations_1633.cpp new file mode 100644 index 0000000..4e76d1d --- /dev/null +++ b/03_dynamic_programming/dice_combinations_1633.cpp @@ -0,0 +1,19 @@ +#include +#include +#include + +// We use a funny memory optimization: we only store the last 7 values. + +int main() { + constexpr unsigned mod = 1e9+7; + int n; + std::cin >> n; + std::array v{0}; + v[0] = 1; + for (int i = 1; i <= n; i++) { + v[i%7] = 0; + for (int j = std::max(0, i-6); j < i; j++) + v[i%7] = (v[i%7]+v[j%7]) % mod; + } + std::cout << v[n%7] << "\n"; +} diff --git a/03_dynamic_programming/edit_distance_1639.cpp b/03_dynamic_programming/edit_distance_1639.cpp new file mode 100644 index 0000000..0d8c6ef --- /dev/null +++ b/03_dynamic_programming/edit_distance_1639.cpp @@ -0,0 +1,22 @@ +#include +#include +#include +#include + +int d(const std::string& a, const std::string& b, size_t i, size_t j, + std::vector>& t) { + if (t[i][j] != -1) return t[i][j]; + if (i == a.size()) return t[i][j] = b.size()-j; + if (j == b.size()) return t[i][j] = a.size()-i; + if (a[i] == b[j]) return t[i][j] = d(a, b, i+1, j+1, t); + return t[i][j] = 1+std::min(d(a, b, i+1, j+1, t), + std::min(d(a, b, i+1, j, t), d(a, b, i, j+1, t))); +} + +int main() { + std::string a, b; + std::cin >> a >> b; + std::vector> + t(a.size()+1, std::vector(b.size()+1, -1)); + std::cout << d(a, b, 0, 0, t) << "\n"; +} diff --git a/03_dynamic_programming/longest_common_subsequence_3403.cpp b/03_dynamic_programming/longest_common_subsequence_3403.cpp new file mode 100644 index 0000000..ca94722 --- /dev/null +++ b/03_dynamic_programming/longest_common_subsequence_3403.cpp @@ -0,0 +1,44 @@ +#include +#include +#include + +int f(const std::vector& a, const std::vector& b, size_t i, size_t j, + std::vector>& t) { + if (i == a.size() || j == b.size()) return t[i][j] = 0; + if (t[i][j] != -1) return t[i][j]; + if (a[i] == b[j]) return t[i][j] = 1+f(a, b, i+1, j+1, t); + return t[i][j] = std::max(f(a, b, i+1, j, t), f(a, b, i, j+1, t)); +} + +std::vector read(size_t n) { + std::vector a(n); + for (size_t i = 0; i < n; i++) + std::cin >> a[i]; + return a; +} + +int main() { + std::size_t n, m; + std::cin >> n >> m; + std::vector a = read(n); + std::vector b = read(m); + std::vector> t(n+1, std::vector(m+1, -1)); + int x = f(a, b, 0, 0, t); + std::cout << x << "\n"; + + std::vector s; + size_t i{0}, j{0}; + while (x > 0) { + if (a[i] == b[j]) { + s.push_back(a[i]); + i++; j++; x--; + } else { + if (t[i+1][j] == x) i++; + else j++; + } + } + + for (auto x : s) + std::cout << x << " "; + std::cout << "\n"; +} diff --git a/03_dynamic_programming/minimizing_coins_1634.cpp b/03_dynamic_programming/minimizing_coins_1634.cpp new file mode 100644 index 0000000..f6189da --- /dev/null +++ b/03_dynamic_programming/minimizing_coins_1634.cpp @@ -0,0 +1,33 @@ +#include +#include +#include +#include + +int f(const std::vector& c, int x) { + static constexpr int max = 999999999; + std::vector a(x+1, max); + std::queue q; + a[0] = 0; + q.push(0); + while (!q.empty()) { + auto i = q.front(); + q.pop(); + for (auto k : c) { + if (i + k > x || a[i+k] <= a[i]+1) continue; + if (i + k == x) return a[i] + 1; + a[i+k] = a[i] + 1; + q.push(i + k); + } + } + return -1; +} + +int main() { + int n, x; + std::cin >> n >> x; + std::vector c(n); + for (int i = 0; i < n; i++) + std::cin >> c[i]; + + std::cout << f(c, x) << "\n"; +} diff --git a/03_dynamic_programming/removing_digits_1637.cpp b/03_dynamic_programming/removing_digits_1637.cpp new file mode 100644 index 0000000..8b5b334 --- /dev/null +++ b/03_dynamic_programming/removing_digits_1637.cpp @@ -0,0 +1,28 @@ +#include +#include +#include + +static constexpr int inf = 1999999999; + +std::vector digits(int n) { + std::vector d; + for (int i = n; i != 0; i /= 10) + d.push_back(i % 10); + return d; +} + +int f(std::vector& a, int n) { + if (a[n] != inf) return a[n]; + for (auto d : digits(n)) + if (d != 0) + a[n] = std::min(a[n], 1+f(a, n-d)); + return a[n]; +} + +int main() { + int n; + std::cin >> n; + std::vector a(n+1, inf); + a[0] = 0; + std::cout << f(a, n) << "\n"; +} -- cgit v1.3