# Sudoku Validator - Amazon Top Interview Questions

### Problem Statement :

```Sudoku is a puzzle where you're given a 9 by 9 grid with digits. The objective is to fill the grid with the constraint that every row, column, and box (3 by 3 subgrid) must contain all of the digits from 1 to 9, and numbers shouldn't repeat within a row, column, or box.

Given a filled out sudoku board, return whether it's valid.

Constraints

n = 9 where n is number of rows and columns in matrix

Example 1

Input

matrix = [
[4, 2, 6, 5, 7, 1, 3, 9, 8],
[8, 5, 7, 2, 9, 3, 1, 4, 6],
[1, 3, 9, 4, 6, 8, 2, 7, 5],
[9, 7, 1, 3, 8, 5, 6, 2, 4],
[5, 4, 3, 7, 2, 6, 8, 1, 9],
[6, 8, 2, 1, 4, 9, 7, 5, 3],
[7, 9, 4, 6, 3, 2, 5, 8, 1],
[2, 6, 5, 8, 1, 4, 9, 3, 7],
[3, 1, 8, 9, 5, 7, 4, 6, 2]
]

Output

True```

### Solution :

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

bool solve(vector<vector<int>>& matrix) {
vector<map<int, int>> rows(9);
vector<map<int, int>> columns(9);
vector<map<int, int>> squares(9);

for (int i = 0; i < matrix.size(); i++) {
for (int j = 0; j < matrix[i].size(); j++) {
if (!(0 < matrix[i][j] && matrix[i][j] < 10)) {
return false;
}
if (rows[i][matrix[i][j]]) {
cout << "repeated in row, number: " << matrix[i][j];
return false;
}
rows[i][matrix[i][j]]++;
if (columns[j][matrix[i][j]]) {
cout << "repeated in column, number: " << matrix[i][j];
return false;
}
columns[j][matrix[i][j]]++;
int square = (i / 3 * 3) + (j / 3);
if (squares[square][matrix[i][j]]) {
cout << "repeated in square, number: " << matrix[i][j];
return false;
}
squares[square][matrix[i][j]]++;
}
}
return true;
}```
```

```                        ```Solution in Java :

import java.util.*;

class Solution {
public boolean solve(int[][] matrix) {
// Build a set of nums 1-9
Set<Integer> allNums = new HashSet<>();
for (int i = 1; i < 10; i++) {
allNums.add(i);
}
for (int i = 0; i < matrix.length; i++) {
Set<Integer> row = new HashSet<>(allNums);
Set<Integer> col = new HashSet<>(allNums);
for (int j = 0; j < matrix.length; j++) {
// Check row
if (!row.remove(matrix[i][j]))
return false;

// Check column
if (!col.remove(matrix[j][i]))
return false;
}
}
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
Set<Integer> box = new HashSet<>(allNums);
for (int k = 0; k < 3; k++) {
for (int l = 0; l < 3; l++) {
// Check box
if (!box.remove(matrix[i * 3 + k][j * 3 + l]))
return false;
}
}
}
}
// We validated all numbers 1-9 from all 9*9*9 cases
return true;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, matrix):
row = defaultdict(set)
col = defaultdict(set)
box = defaultdict(set)
# box = r // 3 * 3 + c // 3
for i in range(9):
for j in range(9):
if matrix[i][j] < 1 or matrix[i][j] > 9:
return False
row[i].add(matrix[i][j])
col[j].add(matrix[i][j])
box[i // 3 * 3 + j // 3].add(matrix[i][j])

for i in range(9):
if len(row[i]) != 9 or len(col[i]) != 9 or len(box[i]) != 9:
return False

return True```
```

## Tree Coordinates

We consider metric space to be a pair, , where is a set and such that the following conditions hold: where is the distance between points and . Let's define the product of two metric spaces, , to be such that: , where , . So, it follows logically that is also a metric space. We then define squared metric space, , to be the product of a metric space multiplied with itself: . For

## Array Pairs

Consider an array of n integers, A = [ a1, a2, . . . . an] . Find and print the total number of (i , j) pairs such that ai * aj <= max(ai, ai+1, . . . aj) where i < j. Input Format The first line contains an integer, n , denoting the number of elements in the array. The second line consists of n space-separated integers describing the respective values of a1, a2 , . . . an .

## Self Balancing Tree

An AVL tree (Georgy Adelson-Velsky and Landis' tree, named after the inventors) is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. We define balance factor for each node as : balanceFactor = height(left subtree) - height(righ

## Array and simple queries

Given two numbers N and M. N indicates the number of elements in the array A[](1-indexed) and M indicates number of queries. You need to perform two types of queries on the array A[] . You are given queries. Queries can be of two types, type 1 and type 2. Type 1 queries are represented as 1 i j : Modify the given array by removing elements from i to j and adding them to the front. Ty

## Median Updates

The median M of numbers is defined as the middle number after sorting them in order if M is odd. Or it is the average of the middle two numbers if M is even. You start with an empty number list. Then, you can add numbers to the list, or remove existing numbers from it. After each add or remove operation, output the median. Input: The first line is an integer, N , that indicates the number o

## Maximum Element

You have an empty sequence, and you will be given N queries. Each query is one of these three types: 1 x -Push the element x into the stack. 2 -Delete the element present at the top of the stack. 3 -Print the maximum element in the stack. Input Format The first line of input contains an integer, N . The next N lines each contain an above mentioned query. (It is guaranteed that each