//****************************************************************************************************////  求和为n的连续正整数序列 - C++ - by Chimomo////  题目： 输入一个正整数n，输出全部和为n的连续正整数序列。比如：输入15，因为1+2+3+4+5=4+5+6=7+8=15，所以输出3个连续序列1-5、4-6和7-8。

// // Answer: Suppose n = i+(i+1)+...+(j-1)+j, then n = (i+j)(j-i+1)/2 = (j*j-i*i+i+j)/2 => j^2+j+(i-i^2-2n) = 0 => j = (sqrt(1-4(i-i^2-2n))-1)/2 => j = (sqrt(4i^2+8n-4i+1)-1)/2. // We know 1 <= i < j <= n/2+1, so for each i in [1,n/2], do this arithmetic to check if there is a integer answer. // // Note: 二次函数 ax^2+bx+c=0 的求根公式为： x = (-b±sqrt(b^2-4ac)) / 2a。 // //**************************************************************************************************** #include <iostream> #include <cassert> #include <stack> #include <math.h> using namespace std ; int FindConsecutiveSequence(int n) { int count = 0; for (int i = 1; i <= n/2; i++) { double sqroot = sqrt(4*i*i + 8*n - 4*i + 1); int floor = sqroot; if(sqroot == floor) { cout << i << "-" << (sqroot - 1) / 2 << endl; count++; } } return count; } int main() { int count = FindConsecutiveSequence(15); cout << "Totally " << count << " sequences found." << endl; return 0; } // Output: /* 1-5 4-6 7-8 Totally 3 sequences found. */