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 = [2]

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 = [0]

Output

0

Explanation

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



Solution :



title-img




                        Solution in C++ :

const int MOD = 1e9 + 7;
const int even[3] = {1, 2, 4};
const int odd[3] = {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][2];

        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
                    


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