49 lines
1.1 KiB
C++
49 lines
1.1 KiB
C++
/*
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* 背包 DP：考虑前 i 个物品的最大价值，在仅有 t 容量的情况下。
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* 建议两个维度调换一下，方便乒乓/滚动。
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*/
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#include <iostream>
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using namespace std;
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struct Item {
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int weight, value;
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};
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constexpr int MAX_N = 105, MAX_CAPACITY = 1005;
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int capacity, n;
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Item items[MAX_N];
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int dp[MAX_CAPACITY][MAX_N];
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void solve_dp() {
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for (int i = 0; i <= capacity; i++) { dp[i][0] = 0; }
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for (int i = 0; i <= n; i++) { dp[0][i] = 0; }
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for (int stop_item = 1; stop_item <= n; stop_item++) {
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for (int w = 1; w <= capacity; w++) {
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dp[w][stop_item] = dp[w][stop_item - 1];
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if (w >= items[stop_item - 1].weight) { // 负数
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dp[w][stop_item] =
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max(dp[w][stop_item],
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dp[w - items[stop_item - 1].weight][stop_item - 1] + items[stop_item - 1].value);
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}
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}
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}
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}
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int main() {
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ios::sync_with_stdio(false);
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cin.tie(nullptr);
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cin >> capacity >> n;
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for (int i = 0; i < n; i++) {
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cin >> items[i].weight >> items[i].value;
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}
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solve_dp();
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cout << dp[capacity][n] << endl;
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return 0;
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}
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