dynamic programming and maximum length of a sequence of rectangles that fit into each other

function maxNumberOfFittingRectangles(rectangles) {
     // Storage of optimal, intermediate results (DP principle), 
     //    keyed by the index of the first rectangle taken
    let memo = new Map;

    // Take a copy of rectangles, and sort it in order of decreasing width, 
    //    and if there are ties: by decreasing height
    rectangles = [...rectangles].sort( (a, b) => (b.width - a.width) 
                                              || (b.height - a.height) );
    
    function recurse(maxHeight, startIndex) {
        for (let i = startIndex; i < rectangles.length; i++) {
            if (rectangles[i].height <= maxHeight ) { // Can fit
                // Try a solution that includes rectangles[i]
                // - Only recurse when we did not do this before
                if (!(memo.has(i))) memo.set(i, recurse(rectangles[i].height, i+1)+1);
                // Also try a solution that excludes rectangles[i], and 
                // return best of both possibilities:
                return Math.max(memo.get(i), recurse(maxHeight, i+1));
            }
        }
        return 0; // recursion's base case
    }
    
    let result = recurse(Infinity, 0);
    // Display some information for understanding the solution:
    for (let i = 0; i < rectangles.length; i++) {
        console.log(JSON.stringify(rectangles[i]), 
                    'if taken as first: solution = ', memo.get(i));
    }
    
    return result;
}

// Sample data
let rectangles = [
    { width: 10, height:  8 },
    { width:  6, height: 12 },
    { width:  
                                                    

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