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[HDOJ4734]F(x)(数位dp)

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=4734

题意:给定了一个函数,求[0,B]内的数的个数,使得他们换算出来的结果小于F(A)。

数位dp,dp(l,s)表示l位数的值,s为被F(A)减后还剩下的值。如果s<0说明此时的F(x)比F(A)大了,要剪枝掉。直到位数被枚举完全,判断s是否大于等于0。由于这个s最大为9*(∑i=0,9 2^i)≈5120,所以s这一维可以开5120。

 1 #include <bits/stdc++.h> 2 using namespace std; 3 #define fr first 4 #define sc second 5 #define cl clear 6 #define BUG puts("here!!!") 7 #define W(a) while(a--) 8 #define pb(a) push_back(a) 9 #define Rint(a) scanf("%d", &a)10 #define Rll(a) scanf("%I64d", &a)11 #define Rs(a) scanf("%s", a)12 #define Cin(a) cin >> a13 #define FRead() freopen("in", "r", stdin)14 #define FWrite() freopen("out", "w", stdout)15 #define Rep(i, len) for(int i = 0; i < (len); i++)16 #define For(i, a, len) for(int i = (a); i < (len); i++)17 #define Cls(a) memset((a), 0, sizeof(a))18 #define Clr(a, x) memset((a), (x), sizeof(a))19 #define Full(a) memset((a), 0x7f7f7f, sizeof(a))20 #define lrt rt << 121 #define rrt rt << 1 | 122 #define pi 3.1415926535923 #define RT return24 #define lowbit(x) x & (-x)25 #define onecnt(x) __builtin_popcount(x)26 typedef long long LL;27 typedef long double LD;28 typedef unsigned long long ULL;29 typedef pair<int, int> pii;30 typedef pair<string, int> psi;31 typedef pair<LL, LL> pll;32 typedef map<string, int> msi;33 typedef vector<int> vi;34 typedef vector<LL> vl;35 typedef vector<vl> vvl;36 typedef vector<bool> vb;37 38 const int maxn = 10;39 const int maxm = 5120;40 int digit[maxn];41 int dp[maxn][maxm];42 43 int f(int x) {44   int ret = 0, cnt = 0;45   while(x) {46     ret += (x % 10) * (1<<cnt++);47     x /= 10;48   }49   return ret;50 }51 52 int dfs(int l, int s, bool flag) {53   if(l == 0) return s >= 0;54   if(s < 0) return 0;55   if(!flag && ~dp[l][s]) return dp[l][s];56   int ret = 0;57   int pos = flag ? digit[l] : 9;58   Rep(i, pos+1) {59     ret += dfs(l-1, s-i*(1<<(l-1)), flag&&(i==pos));60   }61   if(!flag) dp[l][s] = ret;62   return ret;63 }64 65 int solve(int x, int y) {66   int pos = 0;67   while(x) {68     digit[++pos] = x % 10;69     x /=10;70   }71   return dfs(pos, y, true);72 }73 74 int a, b;75 76 signed main() {77   //FRead();78   int T, _ = 1;79   Rint(T);80   Clr(dp, -1);81   W(T) {82     Rint(a); Rint(b);83     a = f(a);84     printf("Case #%d: %d\n", _++, solve(b, a));85   }86   RT 0;87 }

 

[HDOJ4734]F(x)(数位dp)