CodeForces-689C.Mike and Chocolate Thieves

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概述


C. Mike and Chocolate Thieves
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output

Bad news came to Mike’s village, some thieves stole a bunch of chocolates from the local factory! Horrible!

Aside from loving sweet things, thieves from this area are known to be very greedy. So after a thief takes his number of chocolates for himself, the next thief will take exactly k times more than the previous one. The value of k (k > 1) is a secret integer known only to them. It is also known that each thief’s bag can carry at most n chocolates (if they intend to take more, the deal is cancelled) and that there were exactly four thieves involved.

Sadly, only the thieves know the value of n, but rumours say that the numbers of ways they could have taken the chocolates (for a fixed n, but not fixed k) is m. Two ways are considered different if one of the thieves (they should be numbered in the order they take chocolates) took different number of chocolates in them.

Mike want to track the thieves down, so he wants to know what their bags are and value of n will help him in that. Please find the smallest possible value of n or tell him that the rumors are false and there is no such n.

Input
The single line of input contains the integer m (1 ≤ m ≤ 1015) — the number of ways the thieves might steal the chocolates, as rumours say.

Output
Print the only integer n — the maximum amount of chocolates that thieves’ bags can carry. If there are more than one n satisfying the rumors, print the smallest one.

If there is no such n for a false-rumoured m, print - 1.

Examples
input
1
output
8
input
8
output
54
input
10
output
-1
Note
In the first sample case the smallest n that leads to exactly one way of stealing chocolates is n = 8, whereas the amounts of stealed chocolates are (1, 2, 4, 8) (the number of chocolates stolen by each of the thieves).

In the second sample case the smallest n that leads to exactly 8 ways is n = 54 with the possibilities: (1, 2, 4, 8), (1, 3, 9, 27), (2, 4, 8, 16), (2, 6, 18, 54), (3, 6, 12, 24), (4, 8, 16, 32), (5, 10, 20, 40), (6, 12, 24, 48).

There is no n leading to exactly 10 ways of stealing chocolates in the third sample case.
题意：4个小偷偷东西，后一个偷的东西是前一个的k(k>1)倍，且他们的袋子的容量n是固定的，现在告诉你有m种偷的方式，求最小容量n.
题解：假设容量为x，那么偷的方式有way=x/(2*2*2)+x/(3*3*3)+x/(4*4*4)……直到加到0为止。可用二分求解，经测x最大不超过5e15。

#include<iostream>
using namespace std;
#define MAX 5000000000000000
long long Solve(long long n)
{
long long l = 0, r = MAX, solution, wayy;
while (l <= r)
{
long long mid = (l + r) / 2;
long long way = 0, i;
for (i = 2; mid / (i*i*i) != 0 && way <= n; i++)
{
way = way + mid / (i*i*i);
}
if (way >= n)
{
r = mid - 1;
solution = mid;
wayy = way;
}
else
l = mid + 1;
}
if (wayy == n)
return solution;
return -1;
}
int main()
{
long long m, Way;
scanf("%lld", &m);
Way = Solve(m);
printf("%lldn", Way);
return 0;
}