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Grokking the Coding Interview Patterns

Solution: Dungeon Game

Understand how to apply dynamic programming to solve the Dungeon Game problem by calculating the minimum initial health needed for a knight to safely reach the princess. Explore backward calculation and DP table construction for optimal path health management.

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Statement

A group of demons has captured a princess and locked her in the bottom-right corner of a dungeon. The dungeon is represented as a 2D grid of size m×nm × n, where each cell contains an integer value that affects the knight’s health.

The knight, starting in the top-left corner of the grid, must travel through the dungeon to rescue the princess.
He can move only to the right or downward at each step.

  • If a cell ...