背包九讲
背包九讲链接：https://www.cnblogs.com/jbelial/articles/2116074.html
01背包：
题目链接：https://www.acwing.com/problem/content/2/
二维数组优化前：
1 #include <iostream> 2 3 4 5 using namespace std; 6 7 const int N = 1e3 + 10; 8 int v[N], w[N]; 9 int f[N][N]; 10 11 int main() { 12 int N, V; 13 cin >> N >> V; 14 for (int i = 1; i <= N; i++) cin >> v[i] >> w[i]; 15 for (int i = 1; i <= N; i++) { 16 for (int j = 1; j <= V; j++) { 17 f[i][j] = f[i - 1][j]; 18 if (j >= v[i]) f[i][j] = max(f[i - 1][j], f[i - 1][j - v[i]] + w[i]); 19 } 20 } 21 cout << f[N][V] << endl; 22 return 0; 23 } 优化后：
#include <iostream> #include <algorithm> using namespace std; const int N = 1e3 + 10; int v[N], w[N]; int f[N]; int main() { int N, V; cin >> N >> V; for (int i = 1; i <= N; i++) cin >> v[i] >> w[i]; for (int i = 1; i <= N; i++) for (int j = V; j >= v[i]; j--) f[j] = max(f[j], f[j - v[i]] + w[i]); cout << f[V] << endl; return 0; } 完全背包：
题目链接：https://www.acwing.com/problem/content/3/
优化前：
#include <iostream> using namespace std; const int maxn = 1e3 + 10; int v[maxn], w[maxn]; int f[maxn][maxn]; int main() { int N, V; cin >> N >> V; for (int i = 1; i <= N; i++) cin >> v[i] >> w[i]; for (int i = 1; i <= N; i++) for (int j = 1; j <= V; j++) { f[i][j] = f[i - 1][j]; if (j >= v[i]) f[i][j] = max(f[i][j], f[i][j - v[i]] + w[i]); } cout << f[N][V] << endl; return 0; } 优化后：
#include <iostream> using namespace std; const int N = 1e3 + 10; int v[N], w[N]; int f[N]; int main() { int n, V; cin >> n >> V; for (int i = 1; i <= n; i++) cin >> v[i] >> w[i]; for (int i = 1; i <= n; i++) for (int j = 1; j <= V; j++) if (j >= v[i]) f[j] = max(f[j], f[j - v[i]] + w[i]); cout << f[V] << endl; return 0; } 多重背包：
题目链接：https://www.acwing.com/problem/content/4/
数据范围小，不用优化：
来源：博客园
作者：DreamInPal
链接：https://www.cnblogs.com/DreamInPal/p/11560782.html