P16267 [GeeksforGeeks] Number of compositions of a natural number4627
普及-
题目描述

Given a natural number N, find the number of ways in which N can be expressed as a sum of natural numbers when order is taken into consideration. Two sequences that differ in the order of their terms define different compositions of their sum.

Example 1:
Input: N = 2
Output: 2
Explanation: All 2 compositions are
{1 + 1} and {2}.
Example 2:
Input: N = 4
Output: 8
Explanation: All 8 compositions are:
{1 + 1 + 1 + 1}, {1 + 1 + 2}, {1 + 2 + 1},
{2 + 1 + 1}, {2 + 2}, {1 + 3}, {3 + 1}, {4}.

Your Task:
You don't need to read or print anything. Your task is to complete the function no_of_ways() which takes n as the input parameter and returns the total no. of ways modulo 10^{9} + 7.

Expected Time Complexity: O(log(N))
Expected Space Complexity: O(1)
Constraints:
1 <= N <= 10^{9}

输入格式

见题面

输出格式

见题面

样例输入
N = 2
样例输出
2