题意及思路：https://blog.****.net/bossup/article/details/37076965
代码：
#include <bits/stdc++.h>
#define LL long long
#define INF 1e18
using namespace std;
int lcm(int x, int y) {
return x * y / __gcd(x, y);
}
const int maxn = 500010;
LL a, b, k;
LL dp[maxn];
unordered_map<LL, bool> v;
queue<pair<LL, LL> > q;
LL bfs(LL x, LL y) {
q.push(make_pair(x, 0));
while(!q.empty()) {
pair<LL, LL> tmp = q.front();
q.pop();
if(v[tmp.first]) continue;
v[tmp.first] = true;
if(tmp.first == y) return tmp.second;
for (int i = 2; i <= k; i++) {
if(tmp.first % i != 0) {
q.push(make_pair(tmp.first - tmp.first % i, tmp.second + 1));
}
}
q.push(make_pair(tmp.first - 1, tmp.second + 1));
}
}
LL dfs(LL x) {
if(dp[x] != -1) return dp[x];
LL tmp = INF;
for (int i = 2; i <= k; i++) {
if(x % i != 0)
tmp = min(tmp, dfs(x - x % i));
}
tmp = min(tmp, dfs(x - 1));
return dp[x] = tmp + 1;
}
int main() {
int LCM = 1;
scanf("%lld%lld%d", &a, &b, &k);
for (int i = 2; i <= k; i++) {
LCM = lcm(LCM, i);
}
memset(dp, -1, sizeof(dp));
dp[0] = 0;
for (int i = 1; i < LCM; i++) {
dfs(i);
}
LL ans = 0;
if(a - a % LCM >= b) {
ans += dp[a % LCM];
a -= a % LCM;
}
LL del = a - b;
LL tmp = del / LCM;
a -= tmp * LCM;
ans += tmp * (dp[LCM - 1] + 1);
if(a > b) {
LL tmp = bfs(a, b);
ans += tmp;
}
printf("%lld\n", ans);
}