【HDU4991】树状数组

http://acm.hdu.edu.cn/showproblem.php?pid=4991

用f[i][j] 表示 前i个数以第i个数结尾的合法子序列的个数，则递推式不难写出：

f[i][j] = sum(f[k][j - 1]); 其中 k < i, 且a[k] < a[i]; 边界：f[i][1] = 1; 显然需要用数据结构来优化查询

如果不考虑离散的话，用一个数据结构，记录节点为a[i]的f值，同时维护一个区间f值之和，那么f[i][j] = query(0, a[i] - 1)；然后考虑特定的顺序用f值更新数据结构中的信息

具体见代码（树状数组）：

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <map>
 #include <stack>
 #include <string>
 #define mem0(a) memset(a, 0, sizeof(a))
 #define mem(a, b) memset(a, b, sizeof(a))
 #define lson l, m, rt << 1
 #define rson m + 1, r, rt << 1 | 1
 #define lr rt << 1
 #define rr rt << 1 | 1
 #define eps 0.0001
 #define lowbit(x) ((x) & -(x))
 #define memc(a, b) memcpy(a, b, sizeof(b))
 typedef char Str[];
 using namespace std;
 #define LL long long
 #define DL double

 map<int, int> Hash;
 int mol = ;
 int a[], f[][], b[], R[], c[], N, n, m;

 void init()
 {
         sort(a + , a +  + n);
         N = ;
         for(int i = ; i <= n; i++) {
                 if(a[i] == a[i - ] && i > ) continue;
                 Hash[a[i]] =  ++N;
         }
 }
 int query(int p)
 {
         int ans = ;
         while(p) {
                 ans += c[p];
                 if(ans >= mol) ans -= mol;
                 p -= lowbit(p);
         }
         return ans;
 }
 void update(int p, int x)
 {
         while(p <= N) {
                 c[p] += x;
                 if(c[p] >= mol) c[p] -= mol;
                 p += lowbit(p);
         }
 }
 int main()
 {
         //freopen("input.txt", "r", stdin);
         //freopen("output.txt", "w", stdout);
         while(~scanf("%d%d", &n, &m)) {
                 for(int i = ; i <= n; i++) {
                         scanf("%d", a + i);
                 }
                 memc(b, a);
                 init();
                 mem0(f);
                 //puts("d");
                 for(int i = ; i <= n; i++) f[i][] = ;
                 for(int i = ; i <= n; i++) R[i] = Hash[b[i]];
                 for(int j = ; j <= m; j++) {
                         mem0(c);
                         for(int i = ; i <= n; i++) {
                                 f[i][j] = query(R[i] - );
                                 update(R[i], f[i][j - ]);
                                 //cout<< i<< " "<< j<< " "<< f[i][j]<< endl;
                         }
                 }
                 int ans = ;
                 for(int i = m; i <= n; i++) {
                         ans += f[i][m];
                         if(ans >= mol) ans -= mol;
                 }
                 cout<< ans<< endl;
         }
         return ;
 }

另外用线段树写了一下， 不过超时（2000+ms）了，线段树才不到500ms，由此可见能用树状数组决不用线段树，递归线段树常数太大了

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <map>
 #include <stack>
 #include <string>
 #define mem0(a) memset(a, 0, sizeof(a))
 #define mem(a, b) memset(a, b, sizeof(a))
 #define lson l, m, rt << 1
 #define rson m + 1, r, rt << 1 | 1
 #define lr rt << 1
 #define rr rt << 1 | 1
 #define eps 0.0001
 #define lowbit(x) ((x) & -(x))
 #define memc(a, b) memcpy(a, b, sizeof(b))
 typedef char Str[];
 using namespace std;
 #define LL long long
 #define DL double
 struct seg{
         int sum;
 }tree[ << ];
 map<int, int> Hash;
 int mol = ;
 int a[], f[][], b[], R[], N, n, m;

 void init()
 {
         sort(a + , a +  + n);
         N = ;
         for(int i = ; i <= n; i++) {
                 if(a[i] == a[i - ] && i > ) continue;
                 Hash[a[i]] =  ++N;
         }
 }
 void build(int l, int r, int rt)
 {
         tree[rt].sum = ;
         if(l == r) return;
         int m = (l + r) >> ;
         build(lson);
         build(rson);
 }
 void pushUP(int rt)
 {
         tree[rt].sum = tree[rt << ].sum + tree[rt<<  | ].sum;
         if(tree[rt].sum >= mol) tree[rt].sum -= mol;
 }
 void update(int p, int x, int l, int r, int rt)
 {
         if(l == r) {
                 tree[rt].sum += x;
                 if(tree[rt].sum >= mol) tree[rt].sum -= mol;
                 return;
         }
         int m = (l + r) >> ;
         if(p <= m) update(p, x, lson);
         else update(p, x, rson);
         pushUP(rt);
 }
 int query(int L, int R, int l, int r, int rt)
 {
         if(L <= l && r <= R) {
                 return tree[rt].sum;
         }
         int m = (l + r) >> , res = ;
         if(L <= m) res+= query(L, R, lson);
         if(R > m) res += query(L, R, rson);
         if(res >= mol) res -= mol;
         return res;
 }
 int main()
 {
         //freopen("input.txt", "r", stdin);
         //freopen("output.txt", "w", stdout);
         while(~scanf("%d%d", &n, &m)) {
                 for(int i = ; i <= n; i++) {
                         scanf("%d", a + i);
                 }
                 memc(b, a);
                 init();
                 mem0(f);
                 //puts("d");
                 for(int i = ; i <= n; i++) f[i][] = ;
                 for(int i = ; i <= n; i++) R[i] = Hash[b[i]];
                 for(int j = ; j <= m; j++) {
                         build(, N, );
                         for(int i = ; i <= n; i++) {
                                 if(R[i] > ) f[i][j] = query(, R[i] - , , N, );
                                 update(R[i], f[i][j - ], , N, );
                         }
                 }
                 int ans = ;
                 for(int i = m; i <= n; i++) {
                         ans += f[i][m];
                         if(ans >= mol) ans -= mol;
                 }
                 cout<< ans<< endl;
         }
         return ;
 }