Problem 48

/*

* Function multiplies a multiple-digit number (array of digits) by a fixed number,

* while a applying a shift (this is a base operation in the standard multiplocation

* algorithm)

* Additionally, there is a truncation of the result to a certain number of digits

*/

function truncatedMultiplyByNumber(array, number, shift, truncationThreshold) {

const newArray = [];

let uebertrag = 0;

for (let nullindex = 0; nullindex < shift; nullindex++) {

if (nullindex >= truncationThreshold) { return newArray }

newArray.push(0)

}

for (let index = 0; index < array.length; index++) {

if (index + shift >= truncationThreshold) {uebertrag = 0; break}

const wert = (uebertrag + array[index] * number)

newArray.push(wert % 10);

uebertrag = (wert - (wert % 10)) / 10;

}

while (uebertrag > 0) {

newArray.push(uebertrag % 10);

uebertrag = (uebertrag - (uebertrag % 10)) / 10;

}

return newArray;

}

/*

* Function inmplements a summation while truncating the result to a certain

* number of digits

*/

function truncatedAddition(array1, array2, truncationThreshold) {

const resultArray = [];

let i = 0;

uebertrag = 0;

while (array1[i] != undefined || array2[i] != undefined || uebertrag > 0) {

if (i >= truncationThreshold) {break}

const value = (array1[i] || 0) + (array2[i] || 0) + uebertrag;

resultArray.push(value % 10);

uebertrag = (value - value % 10) / 10

i += 1;

}

return resultArray;

}

/*

* Function implements the full multiplication of two multi-digit numbers (arrays)

* while truncating all the steps in the algorithm to be performed with truncated

* numbers

*/

function truncatedMultiplication(array1, array2, truncationThreshold) {

let result = [0]

array1.forEach((x, index) => { result = truncatedAddition(result, truncatedMultiplyByNumber(array2, x, index, truncationThreshold), truncationThreshold)})

return result;

}

/*

* Function implements a truncated version of the power function. All calculations

* are essentially carried out with numbers truncated to a certain number of digits

*/

function truncatedSelfPower(number, truncationThreshold,) {

const numberArr = number.toString().split('').map(x => parseInt(x)).reverse()

let resultArr = [...numberArr];

for (let i = 1; i < number; i++) {

resultArr = truncatedMultiplication(numberArr, resultArr, truncationThreshold )

}

return resultArr

}

function calculateSelfPowerSum(number, truncationThreshold) {

result = [0];

for (let i= 1; i <= number; i++) {

result = truncatedAddition(result, truncatedSelfPower(i, truncationThreshold), truncationThreshold)

}

return result

}

console.log(calculateSelfPowerSum(1000, 10).reduce((a,b,index) => a + b * 10 ** (index)))