bzoj3312: [Usaco2013 Nov]No Change

題意:php

K個硬幣,要買N個物品。K<=16,N<=1e5git

給定買的順序,即按順序必須是一路買過去,當選定買的東西物品序列後,付出錢後,貨主是不會找零錢的。現但願買完所須要的東西后,留下的錢越多越好,若是不能完成購買任務,輸出-1this

=>K那麼小。。。那麼咱們能夠想到二進制枚舉狀態。。。而後轉移。。。好像算不上狀壓dp吧。。。時間複雜度O(K2^Klogn)spa

#include<cstdio>
#include<cstring>
#include<cctype>
#include<algorithm>
using namespace std;
#define rep(i,s,t) for(int i=s;i<=t;i++)
#define dwn(i,s,t) for(int i=s;i>=t;i--)
#define clr(x,c) memset(x,c,sizeof(x))
int read(){
	int x=0;char c=getchar();
	while(!isdigit(c)) c=getchar();
	while(isdigit(c)) x=x*10+c-'0',c=getchar();
	return x;
}
const int nmax=20;
const int maxn=1e5+5;
const int inf=0x7f7f7f7f;
int a[nmax],b[maxn],dp[maxn],n,m,sm;
int find(int x,int eo){
	if(x==m) return 0;
	int l=x,r=m,ans=0,mid;
	while(l<=r){
		mid=(l+r)>>1;
		if(b[mid]-b[x]<=eo) ans=mid,l=mid+1;
		else r=mid-1;
	}
	return ans-x;
}
int main(){
	n=read(),m=read(),sm=0;
	rep(i,1,n) a[i]=read(),sm+=a[i];
	rep(i,1,m) b[i]=read()+b[i-1];
	int se=(1<<n)-1,tm=0,ans=-1;
	rep(i,1,se){
		tm=0;
		rep(j,1,n) if(i&(1<<(j-1))) dp[i]=max(dp[i],dp[i-(1<<(j-1))]+find(dp[i-(1<<j-1)],a[j])),tm+=a[j];
		if(dp[i]==m) ans=max(ans,sm-tm);
		//printf("%d:%d\n",i,dp[i]);
	}
	printf("%d\n",ans);return 0;
}

  

3312: [Usaco2013 Nov]No Change

Time Limit: 10 Sec  Memory Limit: 128 MB
Submit: 177  Solved: 113
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Description

Farmer John is at the market to purchase supplies for his farm. He has in his pocket K coins (1 <= K <= 16), each with value in the range 1..100,000,000. FJ would like to make a sequence of N purchases (1 <= N <= 100,000), where the ith purchase costs c(i) units of money (1 <= c(i) <= 10,000). As he makes this sequence of purchases, he can periodically stop and pay, with a single coin, for all the purchases made since his last payment (of course, the single coin he uses must be large enough to pay for all of these). Unfortunately, the vendors at the market are completely out of change, so whenever FJ uses a coin that is larger than the amount of money he owes, he sadly receives no changes in return! Please compute the maximum amount of money FJ can end up with after making his N purchases in sequence. Output -1 if it is impossible for FJ to make all of his purchases.blog

 

K個硬幣,要買N個物品。ip

給定買的順序,即按順序必須是一路買過去,當選定買的東西物品序列後,付出錢後,貨主是不會找零錢的。現但願買完所須要的東西后,留下的錢越多越好,若是不能完成購買任務,輸出-1rem

Input

Line 1: Two integers, K and N.get

* Lines 2..1+K: Each line contains the amount of money of one of FJ's coins.string

* Lines 2+K..1+N+K: These N lines contain the costs of FJ's intended purchases. it

Output

* Line 1: The maximum amount of money FJ can end up with, or -1 if FJ cannot complete all of his purchases.

Sample Input

3 6
12
15
10
6
3
3
2
3
7

INPUT DETAILS: FJ has 3 coins of values 12, 15, and 10. He must make purchases in sequence of value 6, 3, 3, 2, 3, and 7.

Sample Output

12
OUTPUT DETAILS: FJ spends his 10-unit coin on the first two purchases, then the 15-unit coin on the remaining purchases. This leaves him with the 12-unit coin.

HINT

 

Source

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