Bzoj 4145: [amppz2014]the prices (pressure DP + 01 backpack)

I can only think of O (n*3^m) approach .... Will definitely t

O (nm*2^m) Practice:

DP (x, s) indicates that the first X stores are considered, and the set of items bought is S.

Consider transfer: First suppose we go to the X store, so initial DP (x, s) = DP (x-1, s) + d[x]

We can then make 01 backpacks for the X shop, DP (x, S + {h}) = Min (DP (x, S + {h}), DP (x, s) + c[x][h])) (h∉s).

Then we'll compare it to the first X shop. No cost: DP (x, s) = Min (DP (x-1, s), DP (x, s))

Answer = DP (M, {1, 2, ... n})

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#include <cstdio>#include <cstring>#include <algorithm>#include <iostream>#define REP (i, n) for (int i = 0; i < n; i++)#define CLR (x, C) memset (x, C, sizeof (x))#define B (i) (1 << (i))using namespace std;const int MAXN = MAXM = +, oo = int (1e9); int D, C[MAXM], dp[2][b (MAXM)], A = 0, b = 1;inline int Read () {char C = getchar ();For (;!isdigit (c); c = GetChar ());int ans = 0;For (; IsDigit (c); c = GetChar ())ans = ans * + C-' 0 ';return ans;}int main () {freopen ("test.in", "R", stdin);int n = read (), M = Read (), all = B (m);Rep (s, all) dp[a][s] = oo;dp[a][0] = 0;Rep (i, N) {swap (A, B);d = Read ();Rep (J, m) c[j] = read ();Rep (s, all) dp[a][s] = Dp[b][s] + D;Rep (J, M)Rep (s, all) if (! ( S & B (j)))Dp[a][s | b (j)] = min (Dp[a][s | b (j)], Dp[a][s] + c[j]);Rep (s, all) dp[a][s] = min (Dp[a][s], dp[b][s]);}printf ("%d\n", Dp[a][all-1]);return 0;}

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4145: [Amppz2014]the Prices Time Limit:Sec Memory Limit:+ MB
Submit:156 Solved:99
[Submit] [Status] [Discuss] Description you want to buy one of the M-type items, there are n shops, you go to the first store of D[i], at the first store to buy J items of the cost of c[i][j], to find the minimum total cost.

The first line of input contains two positive integer n,m (1<=n<=100,1<=m<=16), which indicates the number of stores and items. Next n rows, the first positive integer per line d[i] (1<=d[i]<=1000000) represents the fare to the shop I store, followed by M positive integers, which in turn represent C[i][j] (1<=c[i][j]<=1000000).

Output a positive integer, which is the minimum total cost.

Sample Input 3 4
5 7 3) 7 9
2 1 20) 3 2
8 1 1 1Sample Output -HINT

Buy Item 2nd at the first store and buy the rest in the second store.

Source

Acknowledgement Claris Upload

Bzoj 4145: [amppz2014]the prices (pressure DP + 01 backpack)