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1103_Integer Factorization (30).cpp
78 lines (73 loc) · 1.92 KB
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1103_Integer Factorization (30).cpp
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/*
dfs+回溯,
还有DP做法,类似于背包
*/
#include <bits/stdc++.h>
using namespace std;
vector<vector<int>> ans;
int n, p, k;
vector<int> power;
int pow(int x, int p) {
int res = 1;
while (p--) res *= x;
return res;
}
void printAnswer(vector<int> num) {
cout << n << " = ";
for (int i = power.size(); i >= 1; i--) {
if (num[i] != 0) {
cout << i << "^" << p;
num[i]--;
break;
}
}
for (int i = power.size(); i >= 1; i--) {
for (int j = 1; j <= num[i]; j++) {
cout << " + " << i << "^" << p;
}
}
cout << endl;
}
void solve(vector<int> &num, int val, int size, int start) {
if (size == k && val == 0) {
ans.push_back(num);
return;
}
if (start >= power.size() || size > k || val < 0) return;
for (int j = 0; (val >= j*power[start]) && (size+j <= k) && (ceil(val/(double)power[start])+j+size >= k); j++) {
num[start+1] = j;
val -= power[start]*j;
size += j;
solve(num, val, size, start+1);
size -= j;
val += power[start]*j;
num[start+1] = 0;
}
}
int main() {
vector<int> num;
scanf("%d %d %d", &n, &k, &p);
for (int i = 1; ; i++) {
int val = pow(i, p);
if (val <= n) power.push_back(val);
else break;
}
num.resize(power.size()+1);
solve(num, n, 0, 0);
sort(ans.begin(), ans.end(), [](const vector<int> &a, const vector<int> &b)
{
int na = 0, nb = 0;
for (int i = a.size()-1; i >= 1; i--) {na += i * a[i]; nb += i * b[i];}
if (na == nb) {
for (int i = a.size()-1; i >= 1; i--) {
if (a[i] > b[i]) return true;
else if (a[i] < b[i]) return false;
}
return true;
}
else return na > nb;
});
if (ans.empty()) cout << "Impossible" << endl;
else printAnswer(ans[0]);
return 0;
}