https://leetcode.com/problems/dungeon-game/submissions/

dungeonGame.js

// recursive
var calculateMinimumHP = function(dungeon) {
    
    const [m, n] = [dungeon.length, dungeon[0].length];
    const dp = new Array(m).fill(0).map(() => new Array(n).fill(null));
    
    const traverse = (i, j) => {
        
        if(i === m) return Infinity;
        if(j === n) return Infinity;
        if(i === m-1 && j === n-1){
            const squareCost = dungeon[m-1][n-1];
            return squareCost <= 0 ? Math.abs(squareCost) + 1 : 1;
        }
        
        if(dp[i][j] !== null) return dp[i][j];
        
        return dp[i][j] = Math.max(
            Math.min(
                traverse(i, j+1) - dungeon[i][j], // health requirement to get from right to here
                traverse(i+1, j) - dungeon[i][j] // health requirement to get from down to here
            ),
            1 // because our health can never be below 1
        );
    };
    
    return traverse(0, 0);
};

// bottom-up
var calculateMinimumHP = function(dungeon) {
  
    const [m, n] = [dungeon.length, dungeon[0].length];
    const dp = new Array(m).fill(0).map(() => new Array(n).fill(null));
    
    const squareCost = dungeon[m-1][n-1];
    dp[m-1][n-1] = squareCost <= 0 ? Math.abs(squareCost) + 1 : 1;
    
    for(let i=m-2; i>=0; i--){
        const lastCol = n-1;
        dp[i][lastCol] = Math.max(dp[i+1][lastCol] - dungeon[i][lastCol], 1);
    }
    
    for(let i=n-2; i>=0; i--){
        const lastRow = m-1;
        dp[lastRow][i] = Math.max(dp[lastRow][i+1] - dungeon[lastRow][i], 1);
    }
    
    for(let i=m-2; i>=0; i--){
        for(let j=n-2; j>=0; j--){
            dp[i][j] = Math.max(Math.min(dp[i+1][j], dp[i][j+1]) - dungeon[i][j], 1);
        }
    }
    
    return dp[0][0];
};