思路

很明显的最短路，建完图后，直接跑dijkstra即可，细节见代码。

答案：10266837

Code

#include<iostream>
#include<queue>
#include<memory.h>
using namespace std;
typedef long long ll;

const int Max = 1e6 + 5;

int u[Max], v[Max], w[Max];
int g = 0, first[Max], nex[Max];

struct node
{
	int n, w;
	bool operator<(const node& a)const
	{
		return w > a.w;
	}
	node(int a, int b)
	{
		n = a;
		w = b;
	}
};

ll dis[Max], b[Max];
priority_queue<node> que;

void add(int a, int b,int c)
{
	u[++g] = a;
	v[g] = b;
	w[g] = c;
	nex[g] = first[a];
	first[a] = g;
}

ll gcd(ll a, ll b)
{
	if (a == 0)return b;
	return gcd(b%a, a);
}

ll lcm(ll a, ll b)
{
	return a * b / gcd(a, b);
}

int main()
{

	memset(first, -1, sizeof(first));
	memset(dis, 0x7f, sizeof(dis));
	for (int i = 1;i <= 2021;i++)
	{
		for (int j = i + 1;j - i <= 21 && j <= 2021;j++)
		{
			add(i, j, lcm(i, j));
			add(j, i, lcm(i, j));
		}
	}
	que.push(node(1,0));
	dis[1] = 0;
	while(!que.empty())
	{
		node no = que.top();
		que.pop();
		if (b[no.n])continue;
		dis[no.n] = no.w;
		b[no.n] = 1;
		for (int i = first[no.n];i != -1;i = nex[i])
		{
			if (b[v[i]])continue;
			if (dis[u[i]] + w[i] < dis[v[i]])
			{	
				dis[v[i]] = dis[u[i]] + w[i];
				que.push(node(v[i],dis[u[i]]+w[i]));
			}
		}
	}
	cout << dis[2021];
}