hdu2227---Find the nondecreasing subsequences(dp+树状数组)

Problem Description
How many nondecreasing subsequences can you find in the sequence S = {s1, s2, s3, …., sn} ? For example, we assume that S = {1, 2, 3}, and you can find seven nondecreasing subsequences, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}.

Input
The input consists of multiple test cases. Each case begins with a line containing a positive integer n that is the length of the sequence S, the next line contains n integers {s1, s2, s3, …., sn}, 1 <= n <= 100000, 0 <= si <= 2^31.

Output
For each test case, output one line containing the number of nondecreasing subsequences you can find from the sequence S, the answer should % 1000000007.

Sample Input

3
1 2 3

Sample Output

7

Author
8600

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dp[i]表示以第i个元素结尾的不下降序列个数
dp[i]=∑i−1j=1 dp[j] +1
n达10万,所以用树状数组来优化

/*************************************************************************    > File Name: hdu2227.cpp    > Author: ALex    > Mail: [e-mail]     > Created Time: 2015年06月02日 星期二 18时33分24秒 ************************************************************************/#include <functional>#include <algorithm>#include <iostream>#include <fstream>#include <cstring>#include <cstdio>#include <cmath>#include <cstdlib>#include <queue>#include <stack>#include <map>#include <bitset>#include <set>#include <vector>using namespace std;const double pi = acos(-1.0);const int inf = 0x3f3f3f3f;const double eps = 1e-15;typedef long long LL;typedef pair <int, int> PLL;static const int N = 100010;static const int mod = 1000000007;LL tree[N];int lowbit(int x) {    return x & (-x);}void add(int n, int x, LL val) {    for (int i = x; i <= n; i += lowbit(i)) {        tree[i] += val;        tree[i] %= mod;    }}LL sum(int x) {    LL ans = 0;    for (int i = x; i; i -= lowbit(i)) {        ans += tree[i];        ans %= mod;    }    return ans;}LL dp[N];int Arr[N];int xis[N];int cnt;int search(int val) {    int l = 1, r = cnt;    int mid;    while (l <= r) {        mid = (l + r) >> 1;        if (xis[mid] == val) {            break;        }        if (xis[mid] > val) {            r = mid - 1;        }        else {            l = mid + 1;        }    }    return mid;}int main() {    int n;    while (~scanf("%d", &n)) {        cnt = 0;        memset(tree, 0, sizeof(tree));        for (int i = 1; i <= n; ++i) {            scanf("%d", &Arr[i]);            xis[++cnt] = Arr[i];        }        sort(xis + 1, xis + cnt + 1);        cnt = unique(xis + 1, xis + cnt + 1) - xis - 1;        memset(dp, 0, sizeof(dp));        LL ans = 0;        for (int i = 1; i <= n; ++i) {            int val = search(Arr[i]);            LL Sum = sum(val);            dp[i] = 1 + Sum;            dp[i] %= mod;            add(n, val, dp[i]);            ans += dp[i];            ans %= mod;        }        printf("%lld\n", ans);    }    return 0;}