[CSAcademy]Sum of Powers 题目大意: 给定\(n,m,k(n,m,k\le4096)\).一个无序可重集\(A\)为合法的,当且仅当\(|A|=m\)且\(\sum A_i=n\).定义一个集合的贡献为\(\sum A_i^k\),求所有满足条件的集合的贡献之和. 思路: \(f[i][j]\)表示将\(j\)个数之和为\(i\)的方案数,有如下两种转移: \(f[i][j]+=f[i-1][j-1]\),表示新加入一个元素\(1\): \(f[i][j]+=f[i-j]…

转帖:Euler's Sum of Powers Conjecture 存不存在四个大于1的整数的五次幂恰好是另一个整数的五次幂? 暴搜:O(n^4) 用dictionary:O(n^3) import itertools def euler(m): """Yield tuples (a, b, c, d, e) such that a^5 + b^5 + c^5 + d^5 = e^5, where all are integers, and 1 < a ≤ b ≤…

题目链接: http://poj.org/problem?id=1707 Language: Default Sum of powers Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 735   Accepted: 354 Description A young schoolboy would like to calculate the sum   for some fixed natural k and differe…

Description A young schoolboy would like to calculate the sum for some fixed natural k and different natural n. He observed that calculating ik for all i (1<=i<=n) and summing up results is a too slow way to do it, because the number of required ari…

自然数幂和: (1) 伯努利数的递推式: B0 = 1 (要满足(1)式,求出Bn后将B1改为1 /2) 参考:https://en.wikipedia.org/wiki/Bernoulli_number http://blog.csdn.net/acdreamers/article/details/38929067 使用分数类,代入求解 #include<cstdio> #include<iostream> #include<cstdlib> #include<…

题目链接:http://poj.org/problem?id=1707 题意:给出n 在M为正整数且尽量小的前提下,使得n的系数均为整数. 思路: i64 Gcd(i64 x,i64 y) { if(y==0) return x; return Gcd(y,x%y); } i64 Lcm(i64 x,i64 y) { x=x/Gcd(x,y)*y; if(x<0) x=-x; return x; } struct fraction { i64 a,b; fraction() {} fractio…

题意: 考虑所有的可重集{a1,a2,a3....ak} 满足a1+a2+....+ak=n,求所有a1^m+a2^m+a3^m的和 n,m,k<=5000 题解: part1: 考虑f[i][j]表示前i个,总和为j 决策有两种1 1.之前的都加1 2.插入一个1 然后对于之前的都加一说是用斯特林数还原..以后再学.. part2: 满分做法..挺简单的 考虑单独的贡献 枚举每个出现的次数,然后乘以组合数就可以了…

题意: 求 ,要求M尽量小. 析:这其实就是一个伯努利数,伯努利数公式如下: 伯努利数满足条件B0 = 1,并且 也有 几乎就是本题,然后只要把 n 换成 n-1,然后后面就一样了,然后最后再加上一个即可. 代码如下: #pragma comment(linker, "/STACK:1024000000,1024000000") #include <cstdio> #include <string> #include <cstdlib> #inclu…

与UVA766 Sum of powers类似,见http://www.cnblogs.com/IMGavin/p/5948824.html 由于结果对MOD取模,使用逆元 #include<cstdio> #include<iostream> #include<cstdlib> #include<cstring> #include<string> #include<algorithm> #include<map> #in…

http://blogs.mathworks.com/loren/2007/03/01/creating-sparse-finite-element-matrices-in-matlab/ Loren on the Art of MATLAB March 1st, 2007 Creating Sparse Finite-Element Matrices in MATLAB I'm pleased to introduce Tim Davis as this week's guest blogge…