1109: [POI2007]堆积木Klo

1109: [POI2007]堆积木Klo

https://lydsy.com/JudgeOnline/problem.php?id=1109

分析：

　　首先是dp，f[i]表示到第i个的最优值，f[i]=f[j]+1，(j<i,a[j]<a[i],j-a[j]<i-a[i])，三维偏序，可以cdq+线段树转移。实际上由a[j]<a[i]和j-a[j]<i-a[i]可以推出j<i所以二维偏序，直接LIS。

代码：

 #include<cstdio>
 #include<algorithm>
 #include<cstring>
 #include<iostream>
 #include<cmath>
 #include<cctype>
 #include<set>
 #include<queue>
 #include<vector>
 #include<map>
 using namespace std;
 typedef long long LL;

 inline int read() {
     int x=,f=;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-;
     for(;isdigit(ch);ch=getchar())x=x*+ch-'';return x*f;
 }

 const int N = ;

 struct Node{
     int x, c;
     bool operator < (const Node &A) const {
         return x == A.x ? c > A.c : x < A.x;
     }
 }A[N];
 int f[N];

 int main() {
     int n = read(), cnt = ;
     for (int i = ; i <= n; ++i) {
         int x = read();
         if (i - x >= )
         A[++cnt].x = x, A[cnt].c = i - x;
     }
     if (cnt == ) {
         cout << ; return ;
     }
     int len = ;
     sort(A + , A + cnt + );
     f[] = A[].c;
     for (int i = ; i <= cnt; ++i) {
         if (A[i].x != A[i - ].x && A[i].c >= f[len]) f[++len] = A[i].c;
         else {
             int p = upper_bound(f + , f + len + , A[i].c) - f;
             f[p] = A[i].c;
         }
     }
     cout << len;
     return ;
 }
 

LIS

 #include<cstdio>
 #include<algorithm>
 #include<cstring>
 #include<iostream>
 #include<cmath>
 #include<cctype>
 #include<set>
 #include<queue>
 #include<vector>
 #include<map>
 using namespace std;
 typedef long long LL;

 inline int read() {
     int x=,f=;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-;
     for(;isdigit(ch);ch=getchar())x=x*+ch-'';return x*f;
 }

 const int N = ;

 struct Node{
     int id, x, c;
     bool operator < (const Node &A) const {
         return c == A.c ? x < A.x : c < A.c;
     }
 }A[N], B[N];
 int f[N], mx;

 #define Root 1, mx, 1
 #define lson l, mid, rt << 1
 #define rson mid + 1, r, rt << 1 | 1
 struct SegmentTree{
     int mx[N << ];
     SegmentTree() { for (int i = ; i <= ; ++i) mx[i] = -1e9; }
     void update(int l,int r,int rt,int p,int v) {
         if (l == r) { mx[rt] = v; return ; }
         int mid = (l + r) >> ;
         if (p <= mid) update(lson, p, v);
         else update(rson, p, v);
         mx[rt] = max(mx[rt << ], mx[rt <<  | ]);
     }
     int query(int l,int r,int rt,int p) {
         if (p < ) return -1e9;
         if (r <= p) return mx[rt];
         int mid = (l + r) >> ;
         if (p <= mid) return query(lson, p);
         else return max(mx[rt << ], query(rson, p));
     }
 }T;

 void cdq(int l,int r) {
     if (l >= r) return ;
     int mid = (l + r) >> ;
     cdq(l, mid);
     for (int i = mid + ; i <= r; ++i) B[i] = A[i];
     sort(B + mid + , B + r + );
     for (int p = l, j = mid + ; j <= r; ++j) {
         if (f[B[j].id] == -1e9) continue;
         while (p <= mid && A[p].c <= B[j].c) T.update(Root, A[p].x, f[A[p].id]), p ++;
         f[B[j].id] = max(f[B[j].id], T.query(Root, B[j].x - ) + );
     }
     for (int i = l; i <= mid; ++i) T.update(Root, A[i].x, ); // B[i].x!!!
     cdq(mid + , r);
     sort(A + l, A + r + );
 }

 int main() {
     int n = read();
     for (int i = ; i <= n; ++i) {
         A[i].x = read(), A[i].id = i, A[i].c = i - A[i].x;
         if (A[i].x <= i) f[i] = ;
         else f[i] = -1e9;
         mx = max(mx, A[i].x);
     }
     cdq(, n);
     int ans = ;
     for (int i = ; i <= n; ++i) ans = max(ans, f[i]);
     cout << ans;
     return ;
 }
 

CDQ