【CUGBACM15级BC第16场 A】Revenge of Segment Tree

Revenge of Segment Tree

Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1708    Accepted Submission(s): 635

Problem Description

In computer science, a segment tree is a tree data structure for storing intervals, or segments. It allows querying which of the stored segments contain a given point. It is, in principle, a static structure; that is, its content cannot be modified once the structure is built. A similar data structure is the interval tree.
A segment tree for a set I of n intervals uses O(n log n) storage and can be built in O(n log n) time. Segment trees support searching for all the intervals that contain a query point in O(log n + k), k being the number of retrieved intervals or segments.
---Wikipedia

Today, Segment Tree takes revenge on you. As Segment Tree can answer the sum query of a interval sequence easily, your task is calculating the sum of the sum of all continuous sub-sequences of a given number sequence.

 

Input

The first line contains a single integer T, indicating the number of test cases.

Each test case begins with an integer N, indicating the length of the sequence. Then N integer Ai follows, indicating the sequence.

[Technical Specification]
1. 1 <= T <= 10
2. 1 <= N <= 447 000
3. 0 <= Ai <= 1 000 000 000

 

Output

For each test case, output the answer mod 1 000 000 007.

 

Sample Input

21231 2 3

 

Sample Output

220
Hint
For the second test case, all continuous sub-sequences are [1], [2], [3], [1, 2], [2, 3] and [1, 2, 3]. So the sum of the sum of the sub-sequences is 1 + 2 + 3 + 3 + 5 + 6 = 20.Huge input, faster I/O method is recommended. And as N is rather big, too straightforward algorithm (for example, O(N^2)) will lead Time Limit Exceeded.And one more little helpful hint, be careful about the overflow of int.
 

 

解题思路：

给定n个数的数列，求所有连续区间的和。。最简单的一道题，智商捉急啊，没想到。。。。

对于当前第i个数（i>=1），我们只要知道有多少个区间包含a[i]就可以了，答案是 i*(n-i+1)， i代表第i个数前面有多少个数，包括它自己，(n-i+1)代表第i个数后面有多少个数，包括它自己，然后相乘，代表前面的标号和后边的标号两两配对。

如图：

上图数列取得不恰当，标号和数正好相等，比如数列1，4，2，4，5，图也是和上图一样的。关键的是标号，而不是具体的数

#include <bits/stdc++.h>#define _ ios_base::sync_with_stdio(0);cin.tie(0);using namespace std;#define ll long longconst ll mod = 1000000007;ll n;int main(){    _    int t;    cin >> t;    while (t--)    {        cin >> n;        ll x, ans = 0;        for (ll i = 1; i <= n; i++)        {            cin >> x;            ans = (ans + i * (n - i + 1) % mod * x % mod) % mod;        }        cout << ans << endl;    }    return 0;}