SDE - 1

An expression is called the postfix expression if the operator appears in the expression after the operands.

Example :

Infix expression: A + B  *  C - D 

Postfix expression:  A B + C D - *

Given a postfix expression, the task is to evaluate the expression. The answer could be very large, output your answer modulo (10^9+7). Also, use modular division when required.

Note:

1. Operators will only include the basic arithmetic operators like '*', '/', '+', and '-'.

2. The operand can contain multiple digits. 

3. The operators and operands will have space as a separator between them.

4. There won’t be any brackets in the postfix expression.

You are given D dice, each having F faces numbered 1 to F, both inclusive. The task is to find the possible number of ways to roll the dice together such that the sum of face-up numbers equal the given target S.

Note :

As the answer can be large, return your answer modulo 10^9  + 7.

Follow Up :

Can you solve this using not more than O(S) extra space?

You are given a non-decreasing array 'arr' consisting of 'n' integers and an integer 'x'. You need to find the first and last position of 'x' in the array.

Note:

1. The array follows 0-based indexing, so you need to return 0-based indices.
2. If 'x' is not present in the array, return {-1 -1}.
3. If 'x' is only present once in the array, the first and last position of its occurrence will be the same.

Example:

Input:  arr = [1, 2, 4, 4, 5],  x = 4

Output: 2 3

Explanation: The given array’s 0-based indexing is as follows:
 1      2     4     4     5
 ↓      ↓     ↓     ↓     ↓
 0      1     2     3     4

So, the first occurrence of 4 is at index 2, and the last occurrence of 4 is at index 3.

You are given an 'N * N' 'MAZE' where some cells have a door while some do not and a key that can be used only once to open a door.

You need to find if there exists a path from the top-left cell to the bottom right cell of the maze provided only downward and rightward movements are allowed.

Note:

1. You have only one key. And a key once used is exhausted and no more available with you during the journey through that path in a maze.

2. A cell with value 1, means the door or path is closed. And you have to spend a key to open the door/ reach that cell.

3. A cell with value 0, means that the cell is free to move / door is always open.

4. Top left cell in the maze and bottom-right cell in the maze may also have a door.

5. Downwards movement: From cell (i, j) to (i, j+1).

6. Rightwards movement: From cell (i, j) to (i+1, j).

You have been given stock values/prices for N number of days. Every i-th day signifies the price of a stock on that day. Your task is to find the maximum profit which you can make by buying and selling the stocks.

 Note :

You may make as many transactions as you want but can not have more than one transaction at a time i.e, if you have the stock, you need to sell it first, and then only you can buy it again.

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You have been given a directed graph of 'V' vertices and 'E' edges.

Your task is to count the total number of ways to reach different nodes in the graph from the given source node ‘S’. A way is called as different from others if the destination node or used edges differ.

As the total number of such ways can be large, print the total ways modulo 10 ^ 9 + 7.

Note:

1. Include the source node as a destination also.
2. There are no cycles in the given graph.