1103. Integer Factorization (30)

时间限制

1200 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

The K-P factorization of a positive integer N is to write N as the sum of the P-th power of K positive integers. You are supposed to write a program to find the K-P factorization of N for any positive integers N, K and P.

Input Specification:

Each input file contains one test case which gives in a line the three positive integers N (<=400), K (<=N) and P (1<P<=7). The numbers in a line are separated by a space.

Output Specification:

For each case, if the solution exists, output in the format:

N = n1^P + ... nK^P

where ni (i=1, ... K) is the i-th factor. All the factors must be printed in non-increasing order.

Note: the solution may not be unique. For example, the 5-2 factorization of 169 has 9 solutions, such as 122 + 42 + 22 + 22 + 12, or 112+ 62 + 22 + 22 + 22, or more. You must output the one with the maximum sum of the factors. If there is a tie, the largest factor sequence must be chosen -- sequence { a1, a2, ... aK } is said to be larger than { b1, b2, ... bK } if there exists 1<=L<=K such that ai=bi for i<L and aL>bL

If there is no solution, simple output "Impossible".

Sample Input 1:

169 5 2

Sample Output 1:

169 = 6^2 + 6^2 + 6^2 + 6^2 + 5^2

Sample Input 2:

169 167 3

Sample Output 2:

Impossible

C++：

/*@Date    : 2018-02-22 19:04:55@Author  : 酸饺子 (changzheng300@foxmail.com)@Link    : https://github.com/SourDumplings@Version : $Id$
*//*
https://www.patest.cn/contests/pat-a-practise/1103*/#include <iostream>
#include <cstdio>
#include <string>
#include <vector>
#include <algorithm>using namespace std;static const int MAXN = 401;
static vector<int> powerData(401);
static vector<int> thisFactors, resFactors;
static int thisFactorSum = 0, maxFactorSum = 0;
static int lastFactor; // 后一个因子不能大于前一个因子void DFS(int N, int K, int P)
{if (K == 0){if (N == 0){if (thisFactorSum > maxFactorSum){maxFactorSum = thisFactorSum;resFactors = thisFactors;}else if (thisFactorSum == maxFactorSum && thisFactors > resFactors)resFactors = thisFactors;}}else if (N != 0){int tempLastFactor = lastFactor;for (int i = 1; i <= lastFactor; ++i){if (powerData[i] > N) break;thisFactorSum += i;thisFactors.push_back(i);lastFactor = i;DFS(N - powerData[i], K - 1, P);lastFactor = tempLastFactor;thisFactorSum -= i;thisFactors.pop_back();}}return;
}int my_power(int x, int e)
{int res = x;for (int i = 2; i != e + 1; ++i)res *= x;return res;
}int main(int argc, char const *argv[])
{int N, K, P;scanf("%d %d %d", &N, &K, &P);for (int i = 1; i <= N; ++i)powerData[i] = my_power(i, P);lastFactor = N;DFS(N, K, P);if (!resFactors.empty()){int output = 0;printf("%d =", N);for (int f : resFactors){if (output++) printf(" +");printf(" %d^%d", f, P);}putchar('\n');}elseprintf("Impossible\n");return 0;
}

1103. Integer Factorization (30)相关推荐

PAT甲级1103 Integer Factorization (30 分)：[C++题解]背包问题，DP解法
文章目录题目分析题目链接题目分析分析把N(样例中N=169)看成背包的体积:把k(样例中k=5)看成背包能承的重量.把这道题转化为二维完全背包问题.由于数据范围给出的次幂P∈[2,7],那么 ...
PAT甲级 -- 1103 Integer Factorization (30 分)
The K−P factorization of a positive integer N is to write N as the sum of the P-th power of K positi ...
1103 Integer Factorization (30 分)【难度: 中 / 爆搜】
https://pintia.cn/problem-sets/994805342720868352/problems/994805364711604224 爆搜的做法,动态规划也可以做,有时间也一个动 ...
1103 Integer Factorization (30分)
第一个深度优先搜索的题目. 很显然这个就是分情况讨论,每次选和不选某值,最终将满足结果的序列筛选出来,我自己写的一个dfs遍历,我比较喜欢对每一个元素进行遍历,用循环控制,这样的好处是避免递归层数太多 ...
1103 Integer Factorization 需再做
本题是典型的DFS+剪枝我对DFS有了更深的认识:整个过程就是一片森林(根节点不唯一)的生长,到了界限就得到结果并返回或者得不到结果也返回,DFS的参数存放的是所有需要积累的变量. 提示: 1. 最 ...
PAT1103 Integer Factorization (30)（DFS：回溯）
题意: 给三个正整数N.K.P,将N表示成K个正整数(可以相同,递减排列)的P次方和,如果有多种方案,选择底数n1+-+nk最大的方案,如果还有多种方案,选择底数序列的字典序最大的方案思路: 这题看 ...
PAT A1103 Integer Factorization整数分解（经典DFS优化）
题目分析题意给定正整数N.K.P,将N表示成K个正整数(可以相同,递减排列)的P次方的和,即N=nP+-nkP.如果有多种方案,那么选择底数和n1+-+nK最大的方案,如果还有多种方案,那么选择 ...
PAT甲级题目翻译+答案 AcWing（数学）
1059 Prime Factors (25 分) 题意 : 给一正整数,要求分解质因数思路 : 使用is_first,来完成除了第一个质因数前都有*的效果如果n=1,要特判最后如果n>1 ...
dev调试时无法进入下一步_【问题解决方案】Dev C++ 无法调试的问题与解决
浅谈ARP协议以及应用 0. 前言本章主要简单的介绍ARP的协议格式,主机如何发送和处理ARP报文,以及免费ARP. 1. ARP协议原理 ARP,全称Address Resolution Prot ...

1103. Integer Factorization (30)

1103. Integer Factorization (30)相关推荐

最新文章

热门文章