Welcome to our blog, where we reveal the solutions to two algorithm challenges from the JP Morgan Chase & Co. NAMR Software Engineer Program's campus hiring process. These tasks, designed to be completed in 60 minutes, test your skills in resource optimization and problem-solving.

We'll explore the Meeting Scheduler problem, which requires scheduling multiple meetings without conflicts, and the Reduction 3 problem, which involves reducing an array to a single element through strategic operations. Join us as we break down these challenges and provide clear, efficient solutions to help you ace your coding interviews!

### Reduction 3

Given an array `arr`

of nnn integers, a sequence of n−1 operations must be performed on the array.

In each operation:

- Remove the minimum and maximum elements from the current array and add their sum back to the array.
- The cost of an operation,
`cost = ceil((minimum_element + maximum_element) / (maximum_element - minimum_element + 1))`

Find the total cost to reduce the array to a single element.

**Example:** Given `arr = [2, 3, 4, 5, 7]`

. The possible sequence of operations are:

- Choose 2 and 7, the cost = ceil((2 + 7) / (7 - 2 + 1)) = ceil(9 / 6) = 2. Remove 2 and 7, append 9,
`arr = [3, 4, 5, 9]`

, total_cost = 2. - Choose 3 and 9, the cost = ceil((3 + 9) / (9 - 3 + 1)) = ceil(12 / 7) = 2,
`arr = [4, 5, 12]`

, total_cost = 2 + 2 = 4. - Choose 4 and 12, the cost = ceil((4 + 12) / (12 - 4 + 1)) = ceil(16 / 9) = 2,
`arr = [5, 16]`

, total_cost = 4 + 2 = 6. - Choose 5 and 16, the cost = ceil((5 + 16) / (16 - 5 + 1)) = ceil(21 / 12) = 2,
`arr = [21]`

, total_cost = 6 + 2 = 8.

Return the total cost, 8.

**Function Description:** Complete the function `findTotalCost`

in the editor below.

`findTotalCost`

has the following parameter:

`int arr[n]`

: the array to be reduced.

**Returns:**

`int`

: the total cost to reduce the array to 1 element.

**Constraints:**

### Sample Case 0

**Sample Input for Custom Testing:**

STDIN | FUNCTION |
---|---|

6 | `arr[]` size n=6 |

3 | `arr = [3, 5, 2, 1, 9, 6]` |

5 | |

2 | |

1 | |

9 | |

6 |

**Sample Output:** 10

**Explanation:** The possible sequence of operations are:

- Choose 1 and 9, the cost = ceil((1 + 9) / (9 - 1 + 1)) = ceil(10 / 9) = 2. Remove 1 and 9, append 10,
`arr = [3, 5, 2, 6, 10]`

, total_cost = 2. - Choose 2 and 10, the cost = ceil((2 + 10) / (10 - 2 + 1)) = ceil(12 / 9) = 2,
`arr = [3, 5, 6, 12]`

, total_cost = 2 + 2 = 4. - Choose 3 and 12, the cost = ceil((3 + 12) / (12 - 3 + 1)) = ceil(15 / 10) = 2,
`arr = [5, 6, 15]`

, total_cost = 4 + 2 = 6. - Choose 5 and 15, the cost = ceil((5 + 15) / (15 - 5 + 1)) = ceil(20 / 11) = 2,
`arr = [6, 20]`

, total_cost = 6 + 2 = 8. - Choose 6 and 20, the cost = ceil((6 + 20) / (20 - 6 + 1)) = ceil(26 / 15) = 2,
`arr = [26]`

, total_cost = 8 + 2 = 10.

### Meeting Scheduler

On a given day, there are n meetings scheduled. There is a list of the meetings given as a 2D array, `meetingTimings`

, of size n×mn \times mn×m, that contains the start and end times of the meetings. Determine the minimum number of meeting rooms needed to conduct all the meetings so that no meetings overlap in a meeting room.

**Note:** Meetings can end and begin at the same time in one room. For example, meetings at times [10, 15], and [15, 20] can be held in the same room.

**Example:** Suppose n=5, `meetingTimings = [[1, 4], [1, 5], [5, 6], [6, 10], [7, 9]]`

.

Time | Event | Meetings Running |
---|---|---|

1 | meetings 1 and 2 start | 1, 2 |

2 | 1, 2 | |

3 | 1, 2 | |

4 | meeting 1 ends | 2 |

5 | meeting 2 ends, meeting 3 starts | 3 |

6 | meeting 3 ends, meeting 4 starts | 4 |

7 | meeting 5 starts | 4, 5 |

8 | 4, 5 | |

9 | meeting 5 ends | 4 |

Compiled successfully. All available test cases passed.

**Function Description:** Complete the function `getMinRooms`

in the editor below.

`getMinRooms`

has the following parameter:

`int meetingTimings[n][2]`

: the start and end times of the meetings.

**Returns:**

`int`

: the minimum number of meeting rooms required.

**Constraints:**

### Sample Case 0

**Sample Input for Custom Testing:**

STDIN | FUNCTION |
---|---|

6 | `meetingTimings[]` size, n=6n = 6n=6 |

2 | constant integer, 2 |

2 8 | `meetingTimings = [[2, 8],` |

3 9 | `[3, 9],` |

5 11 | `[5, 11],` |

3 4 | `[3, 4],` |

11 15 | `[11, 15],` |

8 20 | `[8, 20]]` |

**Sample Output:** 3

**Explanation:** An optimal way to assign rooms for meetings is:

- Room 1: [2, 8], [8, 20]
- Room 2: [3, 4], [5, 11], [11, 15]
- Room 3: [3, 9]

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