# Drop a Ball Down the Stairs - Google Top Interview Questions

### Problem Statement :

```You are given an integer height and a list of integers blacklist.
You are currently standing at height height and you are playing a game to move a small ball down to height 0.

In even rounds (0, 2, 4, 6 etc.) you can move the ball down 1, 2, or 4 stairs down.
In odd rounds, you can move the ball down 1, 3, or 4 stairs.
There are some levels of the stairs where if the ball lands there, it will die as labelled in blacklist.
Return number of ways you can move the ball down to height 0. Mod the result by 10 ** 9 + 7.

Constraints

1 ≤ height ≤ 100,000

0 ≤ b ≤ 100,000 where b is the length of blacklist
Example 1

Input

height = 4

blacklist = 

Output

2

Explanation
We can move 4 stairs down on round 0.

We can move 1 stair down on round 0 and then 3 stairs down on round 1.

Example 2

Input

height = 5

blacklist = 

Output

0

Explanation

There's no way to reach height 0 since it's on the blacklist.```

### Solution :

```                        ```Solution in C++ :

const int MOD = 1e9 + 7;
const int even = {1, 2, 4};
const int odd = {1, 3, 4};
unordered_set<int> s;
vector<vector<int>> dp;

int f(int h, int round) {
// base case
if (h < 0 or s.count(h)) return 0;

// found a way
if (h == 0) return 1;

// memoization
int& ans = dp[round][h];
if (ans != -1) return ans;
ans = 0;

// even round
if (!round) {
for (auto x : even) {
ans = (ans + f(h - x, round ^ 1)) % MOD;
}
}
// odd round
else {
for (auto x : odd) {
ans = (ans + f(h - x, round ^ 1)) % MOD;
}
}
return ans;
}

int solve(int height, vector<int>& blacklist) {
s.clear();
dp.clear();
dp.resize(2, vector<int>(height + 1, -1));
for (auto x : blacklist) s.insert(x);
return f(height, 0);
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
long MOD = 1000000007;
public int solve(int height, int[] bList) {
DP = new Long[height + 1];

Set<Integer> set = new HashSet<>();
for (int num : bList) set.add(num);

return (int) dp(set, height, 0);
}
Long[][] DP;
private long dp(Set<Integer> bList, int curr, int odd) {
if (bList.contains(curr) || curr < 0)
return 0;
if (curr == 0)
return 1;
if (DP[curr][odd] != null)
return DP[curr][odd];
if (odd == 1)
return DP[curr][odd] =
(dp(bList, curr - 1, 0) + dp(bList, curr - 3, 0) + dp(bList, curr - 4, 0))
% MOD;

return DP[curr][odd] =
(dp(bList, curr - 1, 1) + dp(bList, curr - 2, 1) + dp(bList, curr - 4, 1)) % MOD;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, height, blacklist):
MOD = 10 ** 9 + 7
found = set(blacklist)

if 0 in found:
return 0

@lru_cache(None)
def dp(h, rnd):
if h < 0 or h in found:
return 0

if h == 0:
return 1

ans = 0

if rnd % 2 == 0:
ans += dp(h - 2, rnd ^ 1)
else:
ans += dp(h - 3, rnd ^ 1)

ans += dp(h - 1, rnd ^ 1)
ans += dp(h - 4, rnd ^ 1)

return ans

return dp(height, 0) % MOD```
```

## Delete a Node

Delete the node at a given position in a linked list and return a reference to the head node. The head is at position 0. The list may be empty after you delete the node. In that case, return a null value. Example: list=0->1->2->3 position=2 After removing the node at position 2, list'= 0->1->-3. Function Description: Complete the deleteNode function in the editor below. deleteNo

## Print in Reverse

Given a pointer to the head of a singly-linked list, print each data value from the reversed list. If the given list is empty, do not print anything. Example head* refers to the linked list with data values 1->2->3->Null Print the following: 3 2 1 Function Description: Complete the reversePrint function in the editor below. reversePrint has the following parameters: Sing

Given the pointer to the head node of a linked list, change the next pointers of the nodes so that their order is reversed. The head pointer given may be null meaning that the initial list is empty. Example: head references the list 1->2->3->Null. Manipulate the next pointers of each node in place and return head, now referencing the head of the list 3->2->1->Null. Function Descriptio