1103. Integer Factorization (30)
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 2Sample Output 1:
169 = 6^2 + 6^2 + 6^2 + 6^2 + 5^2Sample Input 2:
169 167 3Sample Output 2:
Impossible
#include <iostream>
#include<vector>
#include <math.h>
#include<stdio.h>
#pragma warning(disable:4996)
using namespace std;
int n, p, k;
vector<int> num,numtemp;
void Calc(int i, int sum, int level,vector<int> temp) {
sum += pow(i, k);
temp.push_back(i);
if (p - temp.size() > n - sum)
return;
if (sum > n)
return;
if (level == 0) {
if (sum == n) {
int flag = false;
if (num.size() == 0)
flag = true;
else {
for (int j = p-1; j >=0; j--) {
if (num[j] > temp[j]) {
flag = false;
break;
}
else if (num[j] < temp[j]) {
flag = true;
break;
}
}
}
if (flag == true) {
num.clear();
for (int j = 0; j < p; j++)
num.push_back(temp[j]);
}
}
return;
}
else {
for (int j = 1; j <= i; j++) {
Calc(j, sum, level - 1, temp);
}
}
}
int main(void) {
cin >> n >> p >> k;
int breakpoint = pow(n, 1.0 / k);
/*if (p > breakpoint) {
if (n == p) {
cout << n << " =";
for (int i = 0; i < p; i++) {
cout << " " << "1" << "^" << k;
if (i != p - 1)
cout << " +";
}
}
else {
cout << "Impossible";
}
return 0;
}*/
int cnt = 0;
for (int i = 1; i <= breakpoint; i++) {
if (cnt == 2)
break;
if (!num.empty())
cnt++;//奇技淫巧。。。。
numtemp.clear();
Calc(i, 0, p-1, numtemp);
}
if (num.size() == 0) {
cout << "Impossible";
}
else {
cout << n << " =";
for (int i = 0; i < num.size(); i++) {
// cout << " " << num[i] << "^" << k;
printf(" %d^%d", num[i], k);
if (i != num.size() - 1)
printf(" +");
//cout << " +";
}
}
return 0;
}