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只做了 AEI 三题，还是太菜了…
Little Sub and Pascal’s Triangle
打表快乐找规律……发现的规律是，对于答案序列中每连续的1<<n个数，后一半序列是由前一半的序列乘二得到的。于是可以直接根据 k 的二进制得到答案。
#include <bits/stdc++.h>
using namespace std;
long long t, k, a;
int main()
{
for (scanf("%lld", &t); t--; printf("%lld\n", a))
{
scanf("%lld", &k);
for (k -= a = 1; k; k >>= 1)
if (k & 1)
a <<= 1;
}
}
Little Sub and his Geometry Problem
容易发现，对于某个固定的询问 C，符合要求的点一定是随着 X 增加 Y 减少，于是使用 X、Y 方向的双指针维护答案。
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 1e5 + 7;
int t, n, k, q, ans;
int main()
{
for (scanf("%d", &t); t--;)
{
scanf("%d%d", &n, &k);
vector<vector<int>> e(n + 1);
for (int i = 0, x, y; i < k; ++i)
scanf("%d%d", &x, &y), e[x].push_back(y);
for (scanf("%d", &q); q--; printf("%d%c", ans, q ? ' ' : '\n'))
{
ll c, x = 1, y = n, cnt = ans = 0, sum = 0;
vector<int> cnty(n + 1), sumy(n + 1);
for (scanf("%lld", &c); x <= n; ++x)
{
for (auto u : e[x])
if (u <= y)
++cnt, ++cnty[u], sum += x + u, sumy[u] += x + u;
for (; (x + y) * cnt - sum > c; --y)
cnt -= cnty[y], sum -= sumy[y];
if ((x + y) * cnt - sum == c)
++ans;
}
}
}
}
Little Sub and Mr.Potato’s Math Problem
十分不熟悉的数位 DP，现场做了很久……以后要多多练习。
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
struct POW : vector<ll>
{
POW(int x, int n) : vector<ll>(n, 1)
{
for (int i = 1; i < size(); ++i)
at(i) = at(i - 1) * x;
}
} POW10(10, 19);
struct DP
{
vector<ll> f;
ll sum;
DP(const vector<ll> &d) : f(d.size()), sum(0)
{
for (int i = 0; i < d.size(); ++i)
{
for (int j = f[i] = 0; j <= i; ++j)
f[i] += (d[j] - (j == 0)) * POW10[i - j];
sum += f[i] + 1;
}
}
};
ll cal(ll n, ll k, ll s, ll len)
{
if (n > s * POW10[len])
return cal(n - s * POW10[len], k, s, len + 1);
return (n / POW10[len] + POW10[ll(log10(k))]) * POW10[len] + n % POW10[len] - 1;
}
int main()
{
ll t, k, m;
for (scanf("%lld", &t); t--;)
{
scanf("%lld%lld", &k, &m);
vector<ll> d;
for (ll n = k; n; n /= 10)
d.push_back(n % 10);
reverse(d.begin(), d.end());
DP dp(d);
printf("%lld\n", m == dp.sum ? k : m < dp.sum || k == *lower_bound(POW10.begin(), POW10.end(), k) ? 0 : cal(m - dp.sum, k, dp.f.back(), 1));
}
}
Little Sub and Isomorphism Sequences
容易看出求最大的 k 就是求两个相同元素下标差的最大值，用一个 set 维护即可。为了求稳使用了离散化处理。
#include <bits/stdc++.h>
#define MP(i) make_pair(vs[i].size() < 2 ? -1 : *vs[i].rbegin() - *vs[i].begin(), i)
using namespace std;
typedef int ll;
struct Ranker : vector<ll>
{
void init()
{
sort(begin(), end()), resize(unique(begin(), end()) - begin());
}
int ask(ll x) const
{
return lower_bound(begin(), end(), x) - begin();
}
};
ll getll(FILE *in = stdin)
{
ll val = 0, sgn = 1, ch = getc(in);
for (; !isdigit(ch) && ch != EOF; ch = getc(in))
if (ch == '-')
sgn = -sgn;
for (; isdigit(ch); ch = getc(in))
val = val * 10 + ch - '0';
return ungetc(ch, in), sgn * val;
}
int main()
{
for (ll t = getll(); t--;)
{
ll n = getll(), m = getll();
Ranker input;
for (int i = 0; i < n; ++i)
input.push_back(getll());
for (int i = 0; i < m; ++i)
{
input.push_back(getll());
if (input.back() == 1)
{
input.push_back(getll());
input.push_back(getll());
}
}
Ranker::iterator it = input.begin();
Ranker rk(input), a;
rk.init();
vector<set<int>> vs(rk.size());
for (int i = 0; i < n; ++i)
{
a.push_back(rk.ask(*(it++)));
vs[a.back()].insert(i);
}
set<pair<int, int>> q;
for (int i = 0; i < vs.size(); ++i)
q.insert(MP(i));
for (int i = 0; i < m; ++i)
{
if (*(it++) == 1)
{
ll x = *(it++) - 1;
q.erase(MP(a[x]));
vs[a[x]].erase(x);
q.insert(MP(a[x]));
a[x] = rk.ask(*(it++));
q.erase(MP(a[x]));
vs[a[x]].insert(x);
q.insert(MP(a[x]));
}
else
printf("%d\n", q.rbegin()->first);
}
}
}