### Problem

This problem was asked by Amazon.

There exists a staircase with N steps, and you can climb up either 1 or 2 steps at a time. Given N, write a function that returns the number of unique ways you can climb the staircase. The order of the steps matters.

For example, if N is 4, then there are 5 unique ways:

1, 1, 1, 1 2, 1, 1 1, 2, 1 1, 1, 2 2, 2 What if, instead of being able to climb 1 or 2 steps at a time, you could climb any number from a set of positive integers X? For example, if X = {1, 3, 5}, you could climb 1, 3, or 5 steps at a time.

### Solution

\[F(n) = \sum{F(n-i)} \forall i\]```
#include <iostream>
#include <vector>
int ways(const std::vector<int>& steps, int target) {
std::vector<int> positions(target + 1, 0);
positions[0] = 1;
for (int i = 1; i <= target; ++i) {
for (auto step : steps) {
if (i - step >= 0) {
positions[i] += positions[i-step];
}
}
std::cout << "pos[" << i << "] = " << positions[i] << std::endl;
}
return positions[target];
}
int main() {
std::cout << ways({1,2}, 4) << std::endl;
return EXIT_SUCCESS;
}
```