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// 1269. Number of Ways to Stay in the Same Place After Some Steps
#include "leetcode.h"
/*
* you have a pointer at index 0 in an array of size 'arr_len'. at each step,
* you can move 1 position to the left, 1 position to the right in the array, or
* stay in the same plae. given two integers 'steps' and 'arr_len' return the
* number of ways such that your pointer is still at index 0 after exactly
* 'steps' steps. since the answer may be too large, return it modulo 10e9+7
*/
class Solution {
public:
int numWays(int steps, int arr_len) {
int n = min(steps / 2 + 1, arr_len);
vector<int> v1(n + 2), v2(n + 2);
v1[1] = 1;
while (steps--) {
for (auto i = 1; i <= n; ++i)
v2[i] = ((long)v1[i] + v1[i - 1] + v1[i + 1]) % 1000000007;
swap(v1, v2);
}
return v1[1];
}
};
int main() {
Solution obj;
printf("%d\n", obj.numWays(3, 2)); // expect: 4
printf("%d\n", obj.numWays(2, 4)); // expect: 2
printf("%d\n", obj.numWays(4, 2)); // expect: 8
}
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