bzoj3209 花神的数论题

Posted 2020-08-31 MashiroSky

http://www.lydsy.com/JudgeOnline/problem.php?id=3209 (题目链接)

题意

　　${sum(i)}$表示${i}$的二进制表示中${1}$的个数。求${\prod^n sum(i)}$

Solution

　　${f_{i,s}}$表示dp到第${i}$位，已经有${s}$个${1}$时的乘积。然后一路dfs就可以了。

细节

　　LL，返回值要与1取个max

代码

// bzoj3598
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<ctime>
#define LL long long
#define inf (1ll<<30)
#define MOD 10000007
#define Pi acos(-1.0)
#define free(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout);
using namespace std;

LL f[60][60],m;
int n,t[60];

LL dfs(int pos,LL s,int lim) {
	if (!pos) return s;
	if (!lim && f[pos][s]!=-1) return f[pos][s];
	int end=lim ? t[pos] : 1;
	LL res=1;
	for (int i=0;i<=end;i++)
		(res*=max(1ll,dfs(pos-1,s+i,lim && i==end)))%=MOD;
	if (!lim) f[pos][s]=res;
	return res;
}
int main() {
	memset(f,-1,sizeof(f));
	scanf("%lld",&m);
	for (n=0;m;m>>=1) t[++n]=m&1;
	printf("%lld",dfs(n,0,1));
	return 0;
}