Complete Backpack Variant (hdu5410)

This is the 2015 last multi-school DP problem, at that time only blame their foundation is too poor, think for 1 hours to think out, hey, September to consolidate the foundation for regional races to prepare. Topic Portal

The title means give you n yuan, M candy, each kind of candy have p, a, B, p for unit price, assuming pay w*p yuan, then he can get A*w + b candy. Find the maximum number of candies.

At that time saw this question, think is a complete backpack, set DP[I][J] said to buy the first item I have spent J Yuan, get the most candy number.

It is easy to think of the transfer equation as:

DP[I][J] = max (Dp[i-1][j], dp[i-1][j-k * p] + A * k + b);(k > 0 && k * P <= J)

When the confidence is ready to knock suddenly found that the time complexity of O (n^3), and N maximum of 1000, no doubt will time out. What to do?

Then we think we use the 01 knapsack thinking to think about this problem, we can optimize it to O (n^2), and then suddenly found a problem, because more than a B, found to consider whether the first time to buy, then we open a vis array to indicate that there is no buy, 1 said to buy, 0 said no.

Enclose the total code:

1#include <cstdio>2#include <cstring>3#include <algorithm>4 using namespacestd;5 6 Const intN = -+5;7 8 intT, N, M;9 Ten intP[n], a[n], b[n]; One  A intVis[n][n], dp[n][n]; -  - voidWork () { theMemset (DP,0,sizeof(DP)); -memset (Vis,0,sizeof(Vis)); -      for(inti =1; I <= N; i + +){ -          for(intj =0; J <= M; J + +){ +DP[I][J] = dp[i-1][j]; -             if(J >=P[i]) { +                 intt = Dp[i][j-p[i]] +A[i]; A                 if(!vis[i][j-p[i]) T + =B[i]; at                 intT1 = dp[i-1][j-p[i]] + a[i] +B[i]; -                 if(T1 > t) t =T1; -                 if(T >Dp[i][j]) { -DP[I][J] =T; -VIS[I][J] =1; -                 } in             } -         } to     } +printf"%d\n", Dp[n][m]); - } the  * intMain () { $scanf"%d", &T);Panax Notoginseng      while(t--){ -scanf"%d%d", &m, &n); the          for(inti =1; I <= N; i + +) scanf ("%d%d%d", p + I, A + I, B +i); + Work (); A     } the     return 0; +}

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Complete Backpack Variant (hdu5410)