Dp+bit (optimization complexity) UESTC 1217 the Battle of Chibi

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Test instructions: Ask n-length sequence to find out the scheme number of the ascending sub-sequence of length m.

Analysis: This question is asked: dp[i][j] = SUM (Dp[i-1][k]) (1 <= k <= N, A[k] < a[j]), the current length I one layer, the last subscript J layer, before the last subscript K layer, this is the complexity of n^3. Then the tree array can optimize the complexity of the j,k, that is, J-Scan the same time, the A[j] information updated to the tree, then the scan can use Logn time to count the information of K, before this first to a[] discretization.

/************************************************* author:running_time* Created time:2015/10/21 Wednesday 13:20:36* Fi Le name:c.cpp ************************************************/#include <cstdio> #include <algorithm># Include <iostream> #include <sstream> #include <cstring> #include <cmath> #include <string > #include <vector> #include <queue> #include <deque> #include <stack> #include <list># Include <map> #include <set> #include <bitset> #include <cstdlib> #include <ctime>using namespace std; #define Lson L, Mid, RT << 1#define Rson mid + 1, R, RT << 1 | 1typedef long ll;const int N = 1e3 + 10;const int INF = 0x3f3f3f3f;const int MOD = 1e9 + 7;const Double EPS = 1e-8;st    ruct BIT {int c[n], SZ;        void Add (int &a, int b) {A + = B;    while (a >= mod) A-= mod;        } void init (int n) {memset (c, 0, sizeof (c));    SZ = n; } void updata (int i, int x) {while (I <= SZ) {Add (C[i], x);        i + = i & (-i);        }} int query (int i) {int ret = 0;    while (i) {Add (ret, c[i]);        I-= i & (-i);    } return ret;    }}bit;int A[n], a[n];int dp[n][n];void compress (int N) {sort (A, a+n);    int nn = unique (A, a+n)-A;    for (int i=0; i<n; ++i) {A[i] = Lower_bound (A, a+n, A[i])-A + 1;    }}int Main (void) {int T, cas = 0; scanf ("%d", &t);  while (t--) {int n, m;        scanf ("%d%d", &n, &m);        Bit.init (n);            for (int i=0; i<n; ++i) {scanf ("%d", &a[i]);        A[i] = A[i];        } compress (n);        memset (DP, 0, sizeof (DP));        for (int i=0; i<n; ++i) dp[1][i] = 1;        int ans = 0;            for (int i=2; i<=m; ++i) {bit.init (n);      for (int j=0; j<n; ++j) {Dp[i][j] = Bit.query (A[j]-1);          Bit.updata (A[j], dp[i-1][j]);        }} for (int i=0; i<n; ++i) bit.add (ans, dp[m][i]);    printf ("Case #%d:%d\n", ++cas, ans); } return 0;}

　　

Dp+bit (optimization complexity) UESTC 1217 the Battle of Chibi