hdu 4742 Pinball Game 3D（cdq分治）

题目链接：hdu 4742 Pinball Game 3D

三维的LIS，将元素按照x，y，z排序，这样确保了i 一定是从[1,i-1]中转移过来的。每次二分[l,r]区间，先处理[l,mid]，然后通过[l,mid]更新[mid+1,r]，更新的过程中，按照[l,r]中y值小的优先处理,树状数组维护第三维z。

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
#define lowbit(x) ((-x)&(x))
typedef long long ll;
const int maxn = 1e5 + 5;
const ll mod = 1 << 30;

struct Pi {
int x, y, z;
bool operator < (const Pi& u) const {
if (x != u.x)
return x < u.x;
if (y != u.y)
return y < u.y;
return z < u.z;
}
}P[maxn];

bool cmp (const int a, const int b) {
return P[a].y < P[b].y;
}

int N, ans, dp[maxn], sz[maxn], tz[maxn];
int bw, ty[maxn << 1], sy[maxn];
ll cans, num[maxn];

namespace Bit {
int n, fenw[maxn];
ll cnt[maxn];

void init (int k) {
n = k;
memset(fenw, 0, (n + 1) * sizeof(int));
}

void add (int x, int k, ll d) {
while (x <= n) {
if (fenw[x] == k)
cnt[x] = (cnt[x] + d) % mod;
else if (fenw[x] < k)
cnt[x] = d, fenw[x] = k;
x += lowbit(x);
}
}

void search (int x, int& ret, ll& sum) {
ret = sum = 0;
while (x) {
if (fenw[x] == ret)
sum += cnt[x];
else if (fenw[x] > ret)
ret = fenw[x], sum = cnt[x];
x -= lowbit(x);
}
}
};

void solve (int l, int r) {
if (l == r) {
if (dp[l] > ans) {
ans = dp[l];
cans = num[l];
} else if (dp[l] == ans)
cans = (cans + num[l]) % mod;
sz[l] = P[l].z;
return ;
}

int mid = (l + r) >> 1, len = r - l + 1;
int pl = l, pr = mid + 1, n = mid - l + 1;
memcpy(ty + bw, sy + l, len * sizeof(int));
for (int i = 0; i < len; i++) {
if (ty[bw+i] <= mid)
sy[pl++] = ty[bw + i];
else
sy[pr++] = ty[bw + i];
}
bw += len;
solve(l, mid);
int limt = bw, pos;
bw -= len;

Bit::init(n);
//printf("%d %d: n = %d\n", l, r, n);
for (int i = bw; i < limt; i++) {
if (ty[i] <= mid) {
pos = lower_bound(sz + l, sz + l + n, P[ty[i]].z) - (sz+l)+1;
Bit::add(pos, dp[ty[i]], num[ty[i]]);
// printf("add:%d %d\n", pos, dp[ty[i]]);
continue;
}
pos = lower_bound(sz + l, sz + l + n, P[ty[i]].z) - (sz+l);
// printf("check:%d\n", pos);

if (pos >= n || sz[l+pos] > P[ty[i]].z)
pos--;

if (pos >= 0) {
int ret;
ll sum;
Bit::search(pos + 1, ret, sum);
ret++;
// printf("check:%d %d\n", pos, ret);
if (ret > dp[ty[i]]) {
dp[ty[i]] = ret;
num[ty[i]] = sum;
} else if (ret == dp[ty[i]] && ret != 1)
num[ty[i]] = (num[ty[i]] + sum) % mod;
}

}

solve(mid + 1, r);
merge(sz + l, sz + l + n, sz + l + n, sz + l + len, tz);
memcpy(sz + l, tz, len * sizeof(int));
}

void init () {
memset(ty, 0, sizeof(ty));
memset(tz, 0, sizeof(tz));
memset(sz, 0, sizeof(sz));
ans = bw = cans = 0;
scanf("%d", &N);
for (int i = 1; i <= N; i++)
scanf("%d%d%d", &P[i].x, &P[i].y, &P[i].z);
sort(P + 1, P + N + 1);
for (int i = 1; i <= N; i++) {
sy[i] = i;
dp[i] = num[i] = 1;
}
sort(sy + 1, sy + N + 1, cmp);
}

int main () {
int cas;
scanf("%d", &cas);
while (cas--) {
init ();
solve (1, N);
// for (int i = 1; i <= N; i++)
// printf("%d %d %d %d %lld\n", P[i].x, P[i].y, P[i].z, dp[i], num[i]);
printf("%d %lld\n", ans, cans % mod);
}
return 0;
}