6kyu Build a pile of Cubes

題目背景：

Task:

Your task is to construct a building which will be a pile of n cubes. The cube at the bottom will have a volume of n^3, the cube above will have volume of (n-1)^3 and so on until the top which will have a volume of 1^3.

You are given the total volume m of the building. Being given m can you find the number n of cubes you will have to build?

The parameter of the function findNb (find_nb, find-nb, findNb) will be an integer m and you have to return the integer n such as n^3 + (n-1)^3 + … + 1^3 = m if such a n exists or -1 if there is no such n.

題目分析：

此處有一個數學公式需要記憶： 1^3 +…+ n^3 = (1+2+…+n)^2，依據這個性質，可以在O(1)時間復雜度上完成此道題的求解。

AC代碼：

#include<math.h> class ASum {public:static long long findNb(long long m); }; // hint: 1^3 +...+ n^3 = (1+2+...+n)^2 long long ASum::findNb(long long m) {long long sqrt1 = sqrt(m);if (sqrt1 * sqrt1 == m ) {long long n = floor(sqrt(2 * sqrt1));if ( n * ( n + 1 ) == 2 * sqrt1 ) return n;else return -1;}else return -1; }

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