Split number into sum components

Question

Is there an efficient algorithm to split up a number into N subsections so that the sum of the numbers adds up to the original, with a base minimum? For example, if

Answer 1

I was working on something similar and here is what I came up with.

You can do this in O(N-1) using some calculations at each step. You begin by picking a random number between the minimum number and max number for each spot. For each spot, max number is calculated by subtracting (Min_Number * Remaining_Spots) from the Remaining Balance.

For example: for the first spot you pick a number between 2 and 38. You get this by subtracting (7-1)*2 from 50. i.e. 50 - 12 = 38.

Once you pick a number, let's say 19, then for the next spot the range is 2-21. i.e. 50-19-(5*2) = 21..

..and so on.

Here is the code snippet:

function splitNumIntoXRandomComponents(num, x, min_num) {

var components = [];    

var count = 1;
var cumulative = 0;
var balance = num;

for (var i = 0; i 0.5){ //0.5 can be tuned to your liking 
        max_num = Math.floor(max_num / 2) + min_num;
    }

    //generate the number for the spot at 'count'
    var c = Math.floor(Math.random()*(max_num-min_num+1)+min_num);

    //adjust balances
    cumulative += c;
    balance -= c;       
    count++;    

    //store this number
    components.push(c);                     

}

//push remaining balance into the last spot
components.push(balance);

//print numbers
console.log(components);

}

for (var i=0; i<10; i++) {
    splitNumIntoXRandomComponents(50, 7, 2);
}

Here is the sample output:

[34, 2, 4, 3, 3, 2, 2]
[14, 12, 8, 8, 4, 2, 2]
[7, 4, 26, 5, 2, 3, 3]
[8, 2, 16, 4, 4, 9, 7]
[20, 8, 4, 4, 7, 4, 3]
[3, 34, 4, 2, 2, 2, 3]
[10, 5, 15, 2, 7, 5, 6]
[6, 3, 10, 4, 10, 3, 14]
[31, 4, 2, 3, 5, 2, 3]
[7, 5, 2, 9, 9, 2, 16]

Here is the jsFiddle: http://jsfiddle.net/wj81kvsc/6/