1103. Integer Factorization (30)搜索+剪枝——PAT (Advanced Level) Practise
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题目信息
1103. Integer Factorization (30)
时间限制1200 ms
内存限制65536 kB
代码长度限制16000 B
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
解题思路
搜索加剪枝
AC代码
#include <cstdio>
#include <cstring>
#include <cmath>
#include <functional>
#include <algorithm>
using namespace std;
int rmx = -1, rs[405], trs[405], pw[22];
int n, k, p, has = 0;
void find(int t, int lit, int loc, int sum)
if (t == 0 && loc > k)
if (sum > rmx)
rmx = sum;
memcpy(rs, trs, sizeof(rs));
has = 1;
if (loc > k) return;
for (int i = lit; i >= 1; --i)
if (pw[i] <= t - (k - loc) && pw[i] * (k - loc + 1) >= t) //剪枝
trs[loc] = i;
find(t - pw[i], i, loc + 1, sum + i);
int main()
scanf("%d%d%d", &n, &k, &p);
for (int i = 0; i < 21; ++i)
pw[i] = (int)(pow(i, p) + 0.1);
find(n, 20, 1, 0);
if (has)
printf("%d = %d^%d", n, rs[1], p);
for (int i = 2; i <= k; ++i)
printf(" + %d^%d", rs[i], p);
printf("\\n");
else
printf("Impossible\\n");
return 0;
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