Maximize Grid Happiness - Problem
Imagine you're a city planner tasked with arranging residents in an m x n residential grid to maximize overall community happiness! 🏘️
You have two personality types to work with:
- Introverts: Start with
120happiness but lose30points for each neighbor - Extroverts: Start with
40happiness but gain20points for each neighbor
Given introvertsCount introverts and extrovertsCount extroverts, you need to strategically place them (or leave some out) to achieve the maximum possible grid happiness.
Neighbors are those living in directly adjacent cells (north, south, east, west). The total happiness is the sum of all residents' individual happiness scores.
Input & Output
example_1.py — Basic Grid
$
Input:
m = 2, n = 3, introvertsCount = 1, extrovertsCount = 2
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Output:
240
💡 Note:
Place 1 introvert and 2 extroverts optimally. Extroverts gain happiness from neighbors while introvert should be isolated.
example_2.py — Small Grid
$
Input:
m = 3, n = 1, introvertsCount = 2, extrovertsCount = 1
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Output:
260
💡 Note:
In a 3×1 grid, place extrovert in middle (gains from 2 neighbors) and introverts on ends (each loses from 1 neighbor).
example_3.py — Edge Case
$
Input:
m = 2, n = 2, introvertsCount = 4, extrovertsCount = 0
›
Output:
240
💡 Note:
With only introverts available, place them to minimize neighbor interactions (diagonal arrangement gives 60×4 = 240).
Constraints
- 1 ≤ m, n ≤ 5
- 0 ≤ introvertsCount ≤ min(6, m × n)
- 0 ≤ extrovertsCount ≤ min(6, m × n)
- Grid size is small enough for DP with bitmask approach
Visualization
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Explanation
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// Output will appear here after running code