# Collecting Coins - Amazon Top Interview Questions

### Problem Statement :

```You are given a two-dimensional integer matrix where each cell represents number of coins in that cell. Assuming we start at matrix, and can only move right or down, find the maximum number of coins you can collect by the bottom right corner.

Constraints

n, m ≤ 100 where n and m are the number of rows and columns in matrix.

Example 1

Input

matrix = [
[0, 3, 1, 1],
[2, 0, 0, 4]
]

Output

9

Explanation

We take the following path: [0, 3, 1, 1, 4]

Example 2

Input

matrix = [
[0, 3, 1, 1],
[2, 0, 0, 4],
[1, 5, 3, 1]
]

Output

12

Explanation

We take the following path: [0, 2, 1, 5, 3, 1]

Example 3

Input

matrix = [
[0, 2, 1],
[2, 5, 0],
[4, 1, 3]
]

Output

11

Explanation

We take the following path: [0, 2, 5, 1, 3]```

### Solution :

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

int solve(vector<vector<int>>& matrix) {
vector<vector<int>> dp(int(matrix.size()), vector<int>(int(matrix.size()), 0));

dp = matrix;

for (int j = 0; j < int(matrix.size()); ++j) {
for (int i = 0; i < int(matrix.size()); ++i) {
if (i - 1 >= 0) dp[j][i] = max(dp[j][i - 1] + matrix[j][i], dp[j][i]);
if (j - 1 >= 0) dp[j][i] = max(dp[j - 1][i] + matrix[j][i], dp[j][i]);
}
}

return dp[int(matrix.size()) - 1][int(matrix.size()) - 1];
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, matrix):
for i in range(len(matrix)):
for j in range(len(matrix)):
fromLeft = matrix[i][j]
fromAbove = matrix[i][j]
if j > 0:
fromLeft = matrix[i][j] + matrix[i][j - 1]
if i > 0:
fromAbove = matrix[i][j] + matrix[i - 1][j]
matrix[i][j] = max(fromLeft, fromAbove)
return matrix[-1][-1]```
```

## 2D Array-DS

Given a 6*6 2D Array, arr: 1 1 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 An hourglass in A is a subset of values with indices falling in this pattern in arr's graphical representation: a b c d e f g There are 16 hourglasses in arr. An hourglass sum is the sum of an hourglass' values. Calculate the hourglass sum for every hourglass in arr, then print t

## Dynamic Array

Create a list, seqList, of n empty sequences, where each sequence is indexed from 0 to n-1. The elements within each of the n sequences also use 0-indexing. Create an integer, lastAnswer, and initialize it to 0. There are 2 types of queries that can be performed on the list of sequences: 1. Query: 1 x y a. Find the sequence, seq, at index ((x xor lastAnswer)%n) in seqList.

## Left Rotation

A left rotation operation on an array of size n shifts each of the array's elements 1 unit to the left. Given an integer, d, rotate the array that many steps left and return the result. Example: d=2 arr=[1,2,3,4,5] After 2 rotations, arr'=[3,4,5,1,2]. Function Description: Complete the rotateLeft function in the editor below. rotateLeft has the following parameters: 1. int d

## Sparse Arrays

There is a collection of input strings and a collection of query strings. For each query string, determine how many times it occurs in the list of input strings. Return an array of the results. Example: strings=['ab', 'ab', 'abc'] queries=['ab', 'abc', 'bc'] There are instances of 'ab', 1 of 'abc' and 0 of 'bc'. For each query, add an element to the return array, results=[2,1,0]. Fun

## Array Manipulation

Starting with a 1-indexed array of zeros and a list of operations, for each operation add a value to each of the array element between two given indices, inclusive. Once all operations have been performed, return the maximum value in the array. Example: n=10 queries=[[1,5,3], [4,8,7], [6,9,1]] Queries are interpreted as follows: a b k 1 5 3 4 8 7 6 9 1 Add the valu

## Print the Elements of a Linked List

This is an to practice traversing a linked list. Given a pointer to the head node of a linked list, print each node's data element, one per line. If the head pointer is null (indicating the list is empty), there is nothing to print. Function Description: Complete the printLinkedList function in the editor below. printLinkedList has the following parameter(s): 1.SinglyLinkedListNode