[BZOJ 2656][ZJOI 2012] 数列

题目大意

给定这么一个数列:

给定 $n$,求 $a_n$。多组询问。

$1 \leqslant T \leqslant 20$

$0 \leqslant n \leqslant 1 \times 10^{100}$

题目链接

BZOJ 2656

题解

记忆化搜索 + 高精度。

代码

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#include <cstdio>
#include <cstring>
#include <map>
#include <vector>
#include <algorithm>
const int MAXN = 105;
struct BigInt {
std::vector<char> v;
BigInt(int x = 0) {
*this = x;
}
BigInt &operator=(int x) {
v.clear();
do v.push_back(x % 10); while (x /= 10);
return *this;
}
BigInt &operator=(const BigInt &x) {
v.resize(x.v.size());
for (int i = 0; i < v.size(); i++) v[i] = x.v[i];
return *this;
}
bool operator<(const BigInt &another) const {
if (v.size() != another.v.size()) return v.size() < another.v.size();
for (int i = v.size() - 1; ~i; i--) {
if (v[i] != another.v[i]) return v[i] < another.v[i];
}
return false;
}
BigInt read() {
static char s[MAXN];
scanf("%s", s);
v.clear();
int n = strlen(s);
for (int i = n - 1; ~i; i--) v.push_back(s[i] - '0');
return *this;
}
bool isOdd() const {
return v[0] & 1;
}
void print() const {
for (int i = v.size() - 1; ~i; i--) putchar(v[i] + '0');
}
};
BigInt operator+(const BigInt &a, const BigInt &b) {
BigInt res;
res.v.clear();
bool flag = false;
for (int i = 0; i < std::max(a.v.size(), b.v.size()); i++) {
int temp = 0;
if (i < a.v.size()) temp += a.v[i];
if (i < b.v.size()) temp += b.v[i];
if (flag) temp++, flag = false;
if (temp >= 10) temp -= 10, flag = true;
res.v.push_back(temp);
}
if (flag) res.v.push_back(1);
return res;
}
BigInt operator/(const BigInt &a, int b) {
BigInt res;
res.v.resize(a.v.size());
for (int i = a.v.size() - 1, temp = 0; ~i; i--) {
temp = a.v[i] + temp * 10;
res.v[i] = temp / b;
temp %= b;
}
int size = res.v.size();
while (size > 1 && res.v[size - 1] == 0) size--;
res.v.resize(size);
return res;
}
static std::map<BigInt, BigInt> f;
BigInt calc(const BigInt &x) {
if (f.find(x) != f.end()) return f[x];
BigInt res;
if (x.isOdd()) res = calc(x / 2) + calc(x / 2 + 1);
else res = calc(x / 2);
return f[x] = res;
}
int main() {
f[0] = 0;
f[1] = 1;
int T;
scanf("%d", &T);
while (T--) {
BigInt x;
x.read();
calc(x).print();
puts("");
}
return 0;
}