JavaScript version to the solution of Throwing Eggs from a Building problem. https://medium.freecodecamp.org/how-to-solve-the-google-recruiters-puzzle-about-throwing-eggs-from-a-building-de6e7ef1755d

throw-eggs-problem.js

const bestNextStepCache = {};
function bestNextStep(floors) {
    if (!bestNextStepCache[floors]){
        if (floors <= 2) {
            bestNextStepCache[floors] = 1;
        }
        else {
            let min = Infinity;
            let nextStep;

            for (let i = 1; i <= floors; i++) {
                const throws = maxThrows(floors, i);
                if (throws < min) {
                    min = throws;
                    nextStep = i;
                }
            }

            bestNextStepCache[floors] = nextStep;
        }
    }

    return bestNextStepCache[floors];
}

function maxThrows(floors, next) {
    if (floors <= 2) {
        return floors;
    }
    else {
        return Math.max(next, 1 + bestMaxThrows(floors - next));
    }
}

const bestMaxThrowsCache = {};
function bestMaxThrows(floors) {
    if (!bestMaxThrowsCache[floors]) {
        bestMaxThrowsCache[floors] = maxThrows(floors, bestNextStep(floors));
    }

    return bestMaxThrowsCache[floors];
}

function findSteps(floors) {
    const steps = [];
    let accumulatedFloors = 0;

    while (floors > 0) {
        const nextStep = bestNextStep(floors);

        accumulatedFloors += nextStep;
        steps.push(accumulatedFloors);

        floors = floors - nextStep;
    }

    return steps;
}

console.log(findSteps(100));
console.log(bestMaxThrows(100));