P7868 [COCI2015-2016#2] VUDU
将所有的数减去 $P$ ，转化为区间和大于 $0$ 。
在前缀和数组中，即
$$
s _ r - s _ {l - 1} \ge 0
\Longrightarrow s _ r \ge s _ {l - 1}
$$
即求非逆序对数。
树状数组版本，因为要离散化，所以较慢。
查看代码
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| #include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
typedef long long LL;
template <class Type>
void read(Type &x)
{
char c;
bool flag = false;
while ((c = getchar()) < '0' || c > '9')
c == '-' && (flag = true);
x = c - '0';
while ((c = getchar()) >= '0' && c <= '9')
x = (x << 3) + (x << 1) + c - '0';
flag && (x = ~x + 1);
}
template <class Type>
void write(Type x)
{
x < 0 && (putchar('-'), x = ~x + 1);
x > 9 && (write(x / 10), 0);
putchar(x % 10 + '0');
}
const int N = 1e6 + 10;
int n, m, k, w[N], tr[N];
LL s[N];
void modify(int x)
{
for (; x <= m; x += x & -x)
tr[x]++;
}
int query(int x)
{
int res = 0;
for (; x; x -= x & -x)
res += tr[x];
return res;
}
int main()
{
read(n);
for (int i = 1; i <= n; i++)
read(w[i]);
read(k);
for (int i = 1; i <= n; i++)
s[i] = s[i - 1] + w[i] - k;
vector<LL> ws;
for (int i = 0; i <= n; i++)
ws.push_back(s[i]);
sort(ws.begin(), ws.end());
m = ws.erase(unique(ws.begin(), ws.end()), ws.end()) - ws.begin();
for (int i = 0; i <= n; i++)
s[i] = lower_bound(ws.begin(), ws.end(), s[i]) - ws.begin() + 1;
modify(s[0]);
LL res = 0;
for (int i = 1; i <= n; i++)
{
res += query(s[i]);
modify(s[i]);
}
write(res);
return 0;
}
|
cdq分治版本。
查看代码
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| #include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
typedef long long LL;
template <class Type>
void read(Type &x)
{
char c;
bool flag = false;
while ((c = getchar()) < '0' || c > '9')
c == '-' && (flag = true);
x = c - '0';
while ((c = getchar()) >= '0' && c <= '9')
x = (x << 3) + (x << 1) + c - '0';
flag && (x = ~x + 1);
}
template <class Type>
void write(Type x)
{
x < 0 && (putchar('-'), x = ~x + 1);
x > 9 && (write(x / 10), 0);
putchar(x % 10 + '0');
}
const int N = 1e6 + 10;
int n, m, k, w[N];
LL s[N], tmp[N];
LL cdq(int l, int r)
{
if (l == r)
return 0;
int mid = l + r >> 1;
LL res = cdq(l, mid) + cdq(mid + 1, r);
int i = l, j = mid + 1, t = 0;
while (i <= mid && j <= r)
if (s[i] <= s[j])
tmp[t++] = s[i++];
else
{
res += i - l;
tmp[t++] = s[j++];
}
while (i <= mid)
tmp[t++] = s[i++];
while (j <= r)
{
res += mid - l + 1;
tmp[t++] = s[j++];
}
for (int i = l; i <= r; i++)
s[i] = tmp[i - l];
return res;
}
int main()
{
read(n);
for (int i = 1; i <= n; i++)
read(w[i]);
read(k);
for (int i = 1; i <= n; i++)
s[i] = s[i - 1] + w[i] - k;
write(cdq(0, n));
return 0;
}
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