题目链接:https://vjudge.net/contest/365059#problem/B
题目大意:求区间L到R之间的数A满足A的的数位的最长递增序列的长度为K的数的个数。
想法:
需要用 nlogn 的求最长上升子序列的算法去解决这道题,但是不能直接硬套,需要对状态进行压缩一下。
state状态维护的是前面上升子序列中出现的数字(二进制状态压缩),前面设状态为167(state为001100001),假设此时i=2,维护上升序列长度为3,应该把6变为2(此时state为001000011)
127,最长上升子序列长度不变,但能让后面更多的数加进来。
#pragma GCC optimize(3,"Ofast","inline")//O3优化 #pragma GCC optimize(2)//O2优化 #include <algorithm> #include <string> #include <string.h> #include <vector> #include <map> #include <stack> #include <set> #include <queue> #include <math.h> #include <cstdio> #include <iomanip> #include <time.h> #include <bitset> #include <cmath> #include <sstream> #include <iostream> #include <cstring> #define LL long long #define ls nod<<1 #define rs (nod<<1)+1 #define pii pair<int,int> #define mp make_pair #define pb push_back #define INF 0x3f3f3f3f #define max(a,b) (a>b?a:b) #define min(a,b) (a<b?a:b) const double eps = 1e-10; const int maxn = 2e5 + 10; const int mod = 1e9 + 7; int sgn(double a){return a < -eps ? -1 : a < eps ? 0 : 1;} using namespace std; LL L,R,k; int b[20]; int len; LL mem[20][1100][15]; int cal(int x) { int ans = 0; while (x) { ans += (x & 1); x >>= 1; } return ans; } int new_st(int st,int x) { for (int i = x;i <= 9;i++) { if (st & (1 << i)) { return (st ^ (1 << i)) | (1 << x); } } return st | (1 << x); } LL dfs(int cur,int st,bool f,bool g) { if (cur < 0) return cal(st) == k; if (!f && mem[cur][st][k] != -1) return mem[cur][st][k]; int v = 9; if (f) v = b[cur]; LL ans = 0; for (int i = 0;i <= v;i++) { ans += dfs(cur-1,(g && i == 0)?0:new_st(st,i),f && (i==v),g && (i == 0)); } if (!f) mem[cur][st][k] = ans; return ans; } LL solve(LL x) { len = 0; while (x) { b[len++] = x % 10; x /= 10; } return dfs(len-1,0,1,1); } int main() { ios::sync_with_stdio(0); int T; cin >> T; int t = 1; memset(mem,-1, sizeof(mem)); while (T--) { cin >> L >> R >> k; printf("Case #%d: %lld\n",t++,solve(R)-solve(L-1)); } return 0; }
原文:https://www.cnblogs.com/-Ackerman/p/12615277.html