HDU 6156 回文 数位DP（2017CCPC）
Palindrome Function
Time Limit: 8000/4000 MS (Java/Others) Memory Limit: 256000/256000 K (Java/Others)
Total Submission(s): 559 Accepted Submission(s): 299
Problem Description
As we all know,a palindrome number is the number which reads the same backward as forward,such as 666 or 747.Some numbers are not the palindrome numbers in decimal form,but in other base,they may become the palindrome number.Like 288,it’s not a palindrome number under 10-base.But if we convert it to 17-base number,it’s GG,which becomes a palindrome number.So we define an interesting function f(n,k) as follow:
f(n,k)=k if n is a palindrome number under k-base.
Otherwise f(n,k)=1.
Now given you 4 integers L,R,l,r,you need to caluclate the mathematics expression ∑Ri=L∑rj=lf(i,j) .
When representing the k-base(k>10) number,we need to use A to represent 10,B to represent 11,C to repesent 12 and so on.The biggest number is Z(35),so we only discuss about the situation at most 36-base number.
f(n,k)=k if n is a palindrome number under k-base.
Otherwise f(n,k)=1.
Now given you 4 integers L,R,l,r,you need to caluclate the mathematics expression ∑Ri=L∑rj=lf(i,j) .
When representing the k-base(k>10) number,we need to use A to represent 10,B to represent 11,C to repesent 12 and so on.The biggest number is Z(35),so we only discuss about the situation at most 36-base number.
Input
The first line consists of an integer T,which denotes the number of test cases.
In the following T lines,each line consists of 4 integers L,R,l,r.
(1≤T≤105,1≤L≤R≤109,2≤l≤r≤36)
In the following T lines,each line consists of 4 integers L,R,l,r.
(1≤T≤105,1≤L≤R≤109,2≤l≤r≤36)
Output
For each test case, output the answer in the form of “Case #i: ans” in a seperate line.
Sample Input
3
1 1
2 36
1 982180
10 10
496690841 524639270
5 20
Sample Output
Case #1: 665
Case#2: 1000000
Case #3: 447525746
Source
思路：枚举进制计算结果即可。
代码：
1 #include <bits/stdc++.h> 2 using namespace std; 3 4 typedef long long LL; 5 const int maxn = 1010; 6 const int maxm = 55; 7 const LL mod = 1e9+7; 8 int digit[maxn], revert[maxn]; 9 LL L, R, l, r; 10 LL dp[maxm][maxm][maxn][2]; 11 12 LL dfs(int k, int s, int l, bool ok, bool lim) { 13 if(l < 0) { 14 if(ok) return k; 15 return 1; 16 } 17 if(!lim && ~dp[k][s][l][ok]) return dp[k][s][l][ok]; 18 int pos = lim ? digit[l] : k - 1; 19 LL ret = 0; 20 for(int i = 0; i <= pos; i++) { 21 revert[l] = i; 22 if(i == 0 && s == l) { 23 ret += dfs(k, s-1, l-1, ok, lim&&(i==pos)); 24 } 25 else if(ok && l < (s + 1) / 2) { 26 ret += dfs(k, s, l-1, i==revert[s-l], lim&&(i==pos)); 27 } 28 else { 29 ret += dfs(k, s, l-1, ok, lim&&(i==pos)); 30 } 31 } 32 if(!lim) dp[k][s][l][ok] = ret; 33 return ret; 34 } 35 36 LL f(LL n, LL k) { 37 if(n == 0) return k; 38 int pos = 0; 39 while(n) { 40 digit[pos++] = n % k; 41 n /= k; 42 } 43 return dfs(k, pos-1, pos-1, 1, 1); 44 } 45 46 47 signed main() { 48 int T, tt = 1; 49 scanf("%d", &T); 50 memset(dp, -1, sizeof(dp)); 51 while(T--) { 52 scanf("%lld%lld%lld%lld",&L,&R,&l,&r); 53 LL ret = 0; 54 for(int i = l; i <= r; i++) { 55 ret += f(R, i) - f(L-1, i); 56 } 57 printf("Case #%d: %lld\n", tt++, ret); 58 } 59 return 0; 60 }
