AtCoder Beginner Contest 340C - Divide and Divide

problem link

Naively, a brute force recursion solution be implemented with O ( n ) \mathcal O (n) O(n) complexity.

int work(int x)
{
	if(x==1)return 0;
	return x+work(x>>1)+work((x>>1)+(x&1))
}

However, since all possible x x x can be represented as n ⋅ 2 − k + 0 / 1 n\cdot 2^{-k}+0/1 n⋅2−k+0/1, the number of possible x x x does not exceed 2 ⋅ log ⁡ 2 ( n ) 2\cdot \log_2(n) 2⋅log2(n)

Then, we can intuitively implement a memorization search with map.

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<map>
using namespace std;
map <long long,long long> f;
long long n,ans;
long long work(long long x)
{
	if(x==1)return 0;
	if(f[x])return f[x];
	return f[x]=x+work(x>>1)+work((x>>1)+(x&1));
}
int main()
{
	cin>>n;
	cout<<work(n)<<endl;
	return 0;
}