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[ACM] HDU 5086 Revenge of Segment Tree(所有连续区间的和)

时间:2014-11-02 10:50:48      阅读:232      评论:0      收藏:0      [点我收藏+]

标签:acm   bestcoder round#16   

Revenge of Segment Tree



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
2 1 2 3 1 2 3
 

Sample Output
2 20
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.
 

Source


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:

bubuko.com,布布扣

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。

代码:

#include <iostream>
#include <stdio.h>
using namespace std;
#define ll long long
const ll mod=1000000007;
ll n;

int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%I64d",&n);
        ll x;
        ll ans=0;
        for(ll i=1;i<=n;i++)
        {
            scanf("%I64d",&x);
            ans=(ans+i*(n-i+1)%mod*x%mod)%mod;
        }
        printf("%I64d\n",ans);
    }
    return 0;
}

注意输出 I64

[ACM] HDU 5086 Revenge of Segment Tree(所有连续区间的和)

标签:acm   bestcoder round#16   

原文地址:http://blog.csdn.net/sr_19930829/article/details/40707173

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