CF622F The Sum of the k-th Powers 题意:给\(n\)和\(k\),让你求\(\sum\limits_{i = 1} ^ n i^k \ mod \ 10^9 + 7\).\((1 \le n \le 10^9,0 \le k \le 10^6)\) 好,我们先不看题,来补一些数学. 考虑这样一个序列 \[ h_0,h_1,\dots,h_n,\dots \] 我们定义它的一个差分序列(一阶) \[ \Delta h_0, \Delta h_1, \dots ,…

题目大意:给你$n,k(n\leqslant10^9,k\leqslant10^6)$,求:$$\sum\limits_{i=1}^ni^k\pmod{10^9+7}$$ 题解:可以猜测是一个$k+1$次的多项式,可以求出$x$在$0,1,2,3,\dots,k+1$时的值,设为$s_0,s_1,\dots,s_{k+1}$,根据拉格朗日插值公式: $$\begin{align*}f_n&=\sum\limits_{i=0}^{k+1}y_i\prod\limits_{j=0,j\not=i}^…

Return the length of the shortest, non-empty, contiguous subarray of A with sum at least K. If there is no non-empty subarray with sum at least K, return -1. Example 1: Input: A = [1], K = 1 Output: 1 Example 2: Input: A = [1,2], K = 4 Output: -1 Exa…

题面 TJOI2018出CF原题弱化版是不是有点太过分了?对,就是 TJOI2018 教科书般的亵渎 然而我这个问题只会那个题的范围的m^3做法 回忆一下1到n求和是二次的,平方求和公式是三次的,立方求和公式是四次的,那m次方求和公式一定是个m+1次多项式 直接扔m+2个值进去把它插出来,因为是连续的可以做到线性(不算逆元) #include<cstdio> ,mod=1e9+; int n,k,ans,sum,fac[N],pre[N],suf[N]; int Qpow(int x,int…

Return the length of the shortest, non-empty, contiguous subarray of A with sum at least K. If there is no non-empty subarray with sum at least K, return -1. Example 1: Input: A = [1], K = 1 Output: 1 Example 2: Input: A = [1,2], K = 4 Output: -1 Exa…

https://leetcode.com/problems/shortest-subarray-with-sum-at-least-k/ 首先回顾一下求max子数组的值的方法是:记录一个前缀min值,然后扫一遍sum数组. 1.首先这里不需要最大,因为刚好够k就好了 2.这里需要距离最短.就是数组的长度最短. 这里的思路也一样,不过保存很多个min值,就是用一个队列,保存前缀的min值,不需要最min,只不过有更小的就更好. 也就是如果sum数组的值是: ..... 60, 40.....Y..…

Return the length of the shortest, non-empty, contiguous subarray of A with sum at least K. If there is no non-empty subarray with sum at least K, return -1. Example 1: Input: A = [1], K = 1 Output: 1 Example 2: Input: A = [1,2], K = 4 Output: -1 Exa…

Return the length of the shortest, non-empty, contiguous subarray of A with sum at least K. If there is no non-empty subarray with sum at least K, return -1. Example 1: Input: A = [1], K = 1 Output: 1 Example 2: Input: A = [1,2], K = 4 Output: -1 Exa…

作者: 负雪明烛 id: fuxuemingzhu 个人博客:http://fuxuemingzhu.cn/ 目录 题目描述 题目大意 解题方法 暴力求解 日期 题目地址:https://leetcode-cn.com/problems/two-sum-less-than-k/ 题目描述 Given an array A of integers and integer K, return the maximum S such that there exists i < j with A[i] +…

作者: 负雪明烛 id: fuxuemingzhu 个人博客: http://fuxuemingzhu.cn/ 目录 题目描述 题目大意 解题方法 队列 日期 题目地址:https://leetcode.com/problems/shortest-subarray-with-sum-at-least-k/ 题目描述 Return the length of the shortest, non-empty, contiguous subarray of A with sum at least K.…