Ways to evenly disperse values

I have a total of 10,000 units that I want to distribute among 99 points in a non-uniform manner following an increasing linear curve. The value assigned to each point will progressively increase from the first point to the last, where the final point might be allocated a higher value like 250 units. However, all the points must collectively add up to the full amount of 10,000 units. Is there a method to achieve this distribution effectively?

// Note: The examples of 10 and 250 units for the initial and final values are just placeholders; they can be any values. The total sum (10,000 units) should remain variable so it can be adjusted to a different figure, like 20,000 units in the future.

javascriptdistribution

Answer №1

Start by selecting 99 cells filled with numbers from [1,2,3,4,...,99]. Next, calculate each number by multiplying it with S/4950, where S represents the target sum (e.g. S=10,000).

Answer №2

From 3 to 199, spanning 99 intervals and summing up to 10,000. Could this possibly be a homework inquiry?

let totalSum = 0;
for (let j = 1; j < 100; j += 1) {
    totalSum += j * 2 + 1;
}
console.log(totalSum);

Answer №3

Although a bit vague, if we assign a value of X to the first point and Y as the gap between each successive points, the total of 99 such points can be calculated using the formula:

(99 * X) + (0.5 * 99 * 98 * Y)

This formula can help you determine appropriate values for X and Y in order to achieve a total of 10,000. You may start by fixing one variable and then solving for the other, but keep in mind that integer solutions may not always be possible. Your specific requirements may lead to non-integer results, so it's important to play around with different values until you find a suitable combination. This method should suffice until a more definitive answer is found.

Answer №4

Recently, I encountered a similar scenario where I needed to tackle a specific problem. While my solution may come a bit late for some, I believe it could still be beneficial to others facing a similar issue.

Here's what I came up with:

let totalSum = 10000;
let arrayLength = 99;
let pointsArray = [];
let nextNumber;
let sumCheck = 0;

for (let i = 0; i < arrayLength; i += 1) {
    nextNumber = ((1 - i / arrayLength) / (0.5 * arrayLength + 0.5)) * totalSum;
    pointsArray.push(nextNumber);
    sumCheck += nextNumber;
}

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