src/opt/knapsack/mixed_huge/lib.hpp
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|---|---|---|---|
| 1 | #pragma once | ||
| 2 | |||
| 3 | #include "../../../util/alias/others/lib.hpp" | ||
| 4 | #include "../../../util/traits/math/lib.hpp" | ||
| 5 | |||
| 6 | namespace tifa_libs { | ||
| 7 | |||
| 8 | //@param a a[i]={value, weight, count} | ||
| 9 | //@param W max weight | ||
| 10 | //@return max total value while total weight <= W | ||
| 11 | template <int_c T> | ||
| 12 | 60 | CEXP T knapsack_mixed_huge(vec<pt3<T>> a, T W) NE { | |
| 13 | 60 | cu32 n = (u32)a.size(); | |
| 14 |
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60 | assert(n < 500); |
| 15 | 120 | cu32 lim = [k = max(n, 50_u32)] { return k * k * k + 1; }(); | |
| 16 | 60 | vec<T> dp(lim + 1, to_uint_t<T>(-1) / 2 - 1); | |
| 17 | 60 | dp[0] = 0; | |
| 18 |
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1585 | for (auto& [v, w, num] : a) { |
| 19 | 1525 | T have = min(num, (T)n); | |
| 20 | 1525 | num -= have; | |
| 21 |
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9927 | for (T k = 1; k = min(have, k), have; have -= k, k <<= 1) |
| 22 |
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1048756322 | for (u32 j = lim - 1; (T)j >= v * k; --j) dp[j] = min(dp[j], dp[j - v * k] + w * k); |
| 23 | } | ||
| 24 | 60 | vecu id(n); | |
| 25 | 9178 | std::iota(begin(id), end(id), 0), sort(id, [&](auto x, auto y) { return a[x]._0 * a[y]._1 > a[y]._0 * a[x]._1; }); | |
| 26 | 60 | T ans = 0; | |
| 27 |
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7500180 | flt_ (u32, j, 0, lim + 1) { |
| 28 |
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7500120 | if (W < dp[j]) continue; |
| 29 | 33051 | T rest = W - dp[j], now = j; | |
| 30 |
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1265723 | for (auto i : id) { |
| 31 | 1232672 | auto [v, w, num] = a[i]; | |
| 32 | 1232672 | T div = min(num, rest / w); | |
| 33 | 1232672 | rest -= div * w, now += div * v; | |
| 34 | } | ||
| 35 | 33051 | ans = max(ans, now); | |
| 36 | } | ||
| 37 | 120 | return ans; | |
| 38 | 60 | } | |
| 39 | |||
| 40 | } // namespace tifa_libs | ||
| 41 |