# 中国(北方)大学生程序设计训练赛(第二周)(Problem C: A Water Problem-dp)

xiaoxiao2021-03-25  46

给一个数， +1 代价x，＊2代价y，问从0变成n 1e7 的最小代价

如果一个数翻倍后2次-1，不如先-1再翻倍。

在只考虑+1，*2的情况下计算代价，并不断用 f(x+1) 更新 f(x)

#include <iostream> #include <cmath> #include <algorithm> #include <cstdio> #include <cstring> #include <string> #include <vector> #include <map> #include <functional> #include <cstdlib> #include <queue> #include <stack> using namespace std; #define For(i,n) for(int i=1;i<=n;i++) #define Fork(i,k,n) for(int i=k;i<=n;i++) #define Rep(i,n) for(int i=0;i<n;i++) #define ForD(i,n) for(int i=n;i;i--) #define ForkD(i,k,n) for(int i=n;i>=k;i--) #define RepD(i,n) for(int i=n;i>=0;i--) #define Forp(x) for(int p=Pre[x];p;p=Next[p]) #define Forpiter(x) for(int &p=iter[x];p;p=Next[p]) #define Lson (o<<1) #define Rson ((o<<1)+1) #define MEM(a) memset(a,0,sizeof(a)); #define MEMI(a) memset(a,127,sizeof(a)); #define MEMi(a) memset(a,128,sizeof(a)); #define INF (2139062143) #define F (100000007) #define pb push_back #define mp make_pair #define fi first #define se second #define vi vector<int> #define pi pair<int,int> #define SI(a) ((a).size()) typedef long long ll; typedef unsigned long long ull; ll mul(ll a,ll b){return (a*b)%F;} ll add(ll a,ll b){return (a+b)%F;} ll sub(ll a,ll b){return (a-b+llabs(a-b)/F*F+F)%F;} void upd(ll &a,ll b){a=(a%F+b%F)%F;} int read() { int x=0,f=1; char ch=getchar(); while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();} while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();} return x*f; } #define MAXN (10000000+10) ll n,x,y,f[MAXN]; int main() { // freopen("C.in","r",stdin); while(scanf("%lld%lld%lld",&n,&x,&y)==3) { f[0]=0; For(i,n+1) { f[i]=f[i-1]+x; if (i%2==0) f[i]=min(f[i],f[i/2]+y); f[i-1]=min(f[i-1],f[i]+x); } printf("%lld\n",f[n]); } return 0; }