题面 传送门 思路 首先,我们观察一下上升数的性质 可以发现,它一定可以表示为最多9个全是1的数字的和 那么我们设$N$可以被表示成$k$个上升数的和,同时我们设$p_i=\underbrace{111\cdots 11}_{i}$ 我们令$a_{i,j}$表示构成$N$的第$I$个上升数的第$j$个全1数的位数 那么可以写出这样的式子 $N=\sum_{i=1}^k\sum_{j=1}^9 p_{a[i][j]}$ 我们发现,$p_{i,j}$这样子摆在这里非常不好操作,那么我们继续观察$p_…

题意: 如果一个十进制非负整数的所有数位从高位到低位是不减的,我们称它为“上升数”,例如1558,11,3,0都是上升数,而10,20170312则不是: 给定整数N,求最小的k使得N能被表示为k个上升数之和. $1\leq N\leq 10^{500000}$ 题解: 一个结论:每个上升数必定能被分解为九个全一数的和: 所谓“全一数”就是指1,1111,11111111这种每一位数都为1的数(包括0),证明显然. 设N可以被分解成K个全一数之和,显然答案$k=\lceil\frac{K}{9}…

题意 给定一个数\(n\),\(n≤10^{500,000}\),问\(n\)最少可以拆分成几个不降数的和.一个不降数是在十进制位下,从高位往低位看,每个数都不会比高位的数更小的数 做法 不降数可以拆成若干个形似\(1111...111\)的数相加 位数为\(l\)的全\(1\)数可以写成\(\dfrac{10^{l+1}-1}{9}\) \(N=\sum\limits_{i=1}^k \dfrac{10^{a_i}-1}{9}\) 通过手玩可以进一步发现充分条件:\(9|k\) 写成\(N+9…

Colossal Fibonacci Numbers 想先说下最近的状态吧,已经考完试了,这个暑假也应该是最后刷题的暑假了,打完今年acm就应该会退了,但是还什么都不会呢? +_+ 所以这个暑假,一定要竭尽全力地去刷题,当然,也是能好好刷题的最后时间了. [题目链接]Colossal Fibonacci Numbers [题目类型]数学 &题意: 求Fi(f(a^b)%n) Fi()是斐波那契 &题解: 注意:unsigned时 要把%d全换成%u 数学大法好. 首先你要能看出来这是有循环…

Description The cows, as you know, have no fingers or thumbs and thus are unable to play Scissors, Paper, Stone' (also known as 'Rock, Paper, Scissors', 'Ro, Sham, Bo', and a host of other names) in order to make arbitrary decisions such as who gets…

2019 杭电多校 8 1003 题目链接:HDU 6659 比赛链接:2019 Multi-University Training Contest 8 Problem Description Acesrc is a famous mathematician at Nanjing University second to none. Playing with interesting numbers is his favorite. Today, he finds a manuscript whe…

Consider this sequence {1, 2, 3, . . . , N}, as a initial sequence of first N natural numbers. You canearrange this sequence in many ways. There will be N! different arrangements. You have to calculatethe number of arrangement of first N natural numbers…

A palindrome is a word, number, or phrase that reads the same forwards as backwards. For example,the name “anna” is a palindrome. Numbers can also be palindromes (e.g. 151 or 753357). Additionallynumbers can of course be ordered in size. The first few…

题意翻译 给你一串数列a.对于一个质数p,定义函数f(p)=a数列中能被p整除的数的个数.给出m组询问l,r,询问[l,r]区间内所有素数p的f(p)之和. 题目描述 Recently, the bear started studying data structures and faced the following problem. You are given a sequence of integers x1,x2,...,xn x_{1},x_{2},...,x_{n} x1​,x2​,.…

169.Numbers Let us call P(n) - the product of all digits of number n (in decimal notation). For example, P(1243)=1*2*4*3=24; P(198501243)=0. Let us call n to be a good number, if (p(n)<>0) and (n mod P(n)=0). Let us call n to be a perfect number, if…