# Maximize the total profit of all the persons

There is a hierarchical structure in an organization. A party is to be organized. No two immediate subordinates can come to the party. A profit is associated with every person. You have to maximize the total profit of all the persons who come to the party.

**Hierarchical Structure**

In a hierarchical organization, all employees(except the one at the head) are subordinates of some other employee.

Employees only directly report to their immediate superior. This allows for a flexible and efficient structure.

For purposes of this problem, this structure may be imagined as a tree, with each employee as its node.

Examples:

Input: 15 / \ 10 12 / \ / \ 26 4 7 9 Output: The Maximum Profit would be 15+12+26+9 = 62 The Parent 15 chooses sub-ordinate 12, 10 chooses 26 and 12 chooses 9. Input: 12 / | \ 9 25 16 / / \ 13 13 9 Output: 12+25+13+13 = 63

**Approach:**

Given the profit from each employee, we have to find the maximum sum such that no two employees(Nodes) with the same superior(Parent) are invited. This can be achieved if each employee selects the subordinate with the maximum contribution to go.

In the program, the hierarchy of the company is implemented in the form of a dictionary, with the key being a unique employee ID, and data being an array of the form [Profit associated with this employ, [List of immediate Sub-ordinates]].

For each Employee, the subordinate with the highest profit associated is added to the total profit. Further, the Employee at the head is always invited.

`def` `getMaxProfit(hier): ` ` ` `# The head has no competition and therefore invited ` ` ` `totSum ` `=` `hier[` `1` `][` `0` `] ` ` ` `for` `i ` `in` `hier: ` ` ` `currentSuperior ` `=` `hier[i] ` ` ` `selectedSub ` `=` `0` ` ` `# select the subordinate with maximum ` ` ` `# value of each superior ` ` ` `for` `j ` `in` `currentSuperior[` `1` `]: ` ` ` `if` `(hier[j][` `0` `] > selectedSub): ` ` ` `selectedSub ` `=` `hier[j][` `0` `] ` ` ` `totSum ` `+` `=` `selectedSub ` ` ` `return` `totSum ` ` ` `# driver function ` `def` `main(): ` ` ` `# Define the Organization as a Dictionary ` ` ` `# Index : [Profit, List of Employees] ` ` ` `# Same as example 1 given above ` `# 1:15 ` `# / \ ` `# 2:10 3:12 ` `# / \ / \ ` `# 4:26 5:4 6:7 7:9 ` ` ` ` ` `organization ` `=` `{` `1` `:[` `15` `, [` `2` `, ` `3` `]], ` ` ` `2` `:[` `10` `, [` `4` `, ` `5` `]], ` `3` `:[` `12` `, [` `6` `, ` `7` `]], ` ` ` `4` `:[` `26` `, []], ` `5` `:[` `4` `, []], ` `6` `:[` `7` `, []], ` `7` `:[` `9` `, []]} ` ` ` `maxProfit ` `=` `getMaxProfit(organization) ` ` ` `print` `(maxProfit) ` ` ` `main() ` |

*chevron_right*

*filter_none*

**Output:**

62

## Recommended Posts:

- Stock Buy Sell to Maximize Profit
- Maximize profit when divisibility by two numbers have associated profits
- Probability that two persons will meet
- Maximum number of teams that can be formed with given persons
- Minimum cost to buy N kilograms of sweet for M persons
- Maximize the value of x + y + z such that ax + by + cz = n
- Maximize the number of subarrays with XOR as zero
- Maximize the bitwise OR of an array
- Maximize big when both big and small can be exchanged
- Maximize the number of segments of length p, q and r
- Maximize the number of sum pairs which are divisible by K
- Maximize the product of four factors of a Number
- Burst Balloon to maximize coins
- Maximize the happiness of the groups on the Trip
- Select numbers in such way to maximize the amount of money

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.