Dado un gran número positivo N . La tarea es dividir N en dos números ‘A’ y ‘B’ de manera que la diferencia entre ellos sea K (1 <= K <= 10 100 ), es decir, A – B = K.
Ejemplos:
Input : N = 10, K = 2 Output : A = 6 B = 4 Input : N = 20, K = 4 Output : A = 12 B = 8
Deje que los dos números requeridos sean ‘A’ y ‘B’. Entonces, sabemos que la suma de ‘A’ y ‘B’ terminará en N.
Entonces, una ecuación se convirtió en
A + B = N
Y también, queremos que la diferencia entre ‘A’ y ‘B’ sea igual a ‘K’.
Entonces, otra ecuación se convierte en
A – B = K
Al sumar ambas ecuaciones, obtenemos
2*A = N + K
Entonces, A = (N + K)/2
Entonces podemos encontrar B por, B = (N – A )
Ahora, para manejar el Big Integer, tenemos que almacenar Integers en una array de caracteres y definir una función para realizar la operación en ellos.
A continuación se muestra la implementación en C de este enfoque:
C++
// C++ program to Divide a Big
// Number into two parts
#include <bits/stdc++.h>
using namespace std;
#define MAX 100
// Function to adds two Numbers
// represented as array of character.
void add(char v1[], char v2[])
{
int i, d, c = 0;
// length of string
int l1 = strlen(v1);
int l2 = strlen(v2);
// initializing extra character
// position to 0
for (i = l1; i < l2; i++)
v1[i] = '0';
for (i = l2; i < l1; i++)
v2[i] = '0';
// Adding each element of character
// and storing the carry.
for (i = 0; i < l1 || i < l2; i++) {
d = (v1[i] - '0') + (v2[i] - '0') + c;
c = d / 10;
d %= 10;
v1[i] = '0' + d;
}
// If remainder remains.
while (c) {
v1[i] = '0' + (c % 10);
c /= 10;
i++;
}
v1[i] = '\0';
v2[l2] = '\0';
}
// Function to subtracts two numbers
// represented by string.
void subs(char v1[], char v2[])
{
int i, d, c = 0;
// Finding the length of the string.
int l1 = strlen(v1);
int l2 = strlen(v2);
// initializing extra character position to 0.
for (i = l2; i < l1; i++)
v2[i] = '0';
// Subtracting each element of character.
for (i = 0; i < l1; i++) {
d = (v1[i] - '0' - c) - (v2[i] - '0');
if (d < 0) {
d += 10;
c = 1;
}
else
c = 0;
v1[i] = '0' + d;
}
v2[l2] = '\0';
i = l1 - 1;
while (i > 0 && v1[i] == '0')
i--;
v1[i + 1] = '\0';
}
// Function divides a number represented by
// character array a constant.
int divi(char v[], int q)
{
int i, l = strlen(v);
int c = 0, d;
// Dividing each character element by constant.
for (i = l - 1; i >= 0; i--) {
d = c * 10 + (v[i] - '0');
c = d % q;
d /= q;
v[i] = '0' + d;
}
i = l - 1;
while (i > 0 && v[i] == '0')
i--;
v[i + 1] = '\0';
return c;
}
// Function to reverses the character array.
void rev(char v[])
{
int l = strlen(v);
int i;
char cc;
// Reversing the array.
for (i = 0; i < l - 1 - i; i++) {
cc = v[i];
v[i] = v[l - 1 - i];
v[l - i - 1] = cc;
}
}
// Wrapper Function
void divideWithDiffK(char a[], char k[])
{
// Reversing the character array.
rev(a);
rev(k);
// Adding the each element of both array
// and storing the sum in array a[].
add(a, k);
// Dividing the array a[] by 2.
divi(a, 2);
// Reversing the character array to get output.
rev(a);
cout <<" "<< a;
// Subtracting each element of array
// i.e calculating a = a - b
rev(a);
subs(a, k);
// Reversing the character array to get output.
rev(a);
cout <<" "<< a;
}
// Driven Program
int main()
{
char a[MAX] = "100", k[MAX] = "20";
divideWithDiffK(a, k);
return 0;
}
// this code is contributed by shivanisinghss2110
C
// C program to Divide a Big
// Number into two parts
#include <stdio.h>
#include <string.h>
#define MAX 100
// Function to adds two Numbers
// represented as array of character.
void add(char v1[], char v2[])
{
int i, d, c = 0;
// length of string
int l1 = strlen(v1);
int l2 = strlen(v2);
// initializing extra character
// position to 0
for (i = l1; i < l2; i++)
v1[i] = '0';
for (i = l2; i < l1; i++)
v2[i] = '0';
// Adding each element of character
// and storing the carry.
for (i = 0; i < l1 || i < l2; i++) {
d = (v1[i] - '0') + (v2[i] - '0') + c;
c = d / 10;
d %= 10;
v1[i] = '0' + d;
}
// If remainder remains.
while (c) {
v1[i] = '0' + (c % 10);
c /= 10;
i++;
}
v1[i] = '\0';
v2[l2] = '\0';
}
// Function to subtracts two numbers
// represented by string.
void subs(char v1[], char v2[])
{
int i, d, c = 0;
// Finding the length of the string.
int l1 = strlen(v1);
int l2 = strlen(v2);
// initializing extra character position to 0.
for (i = l2; i < l1; i++)
v2[i] = '0';
// Subtracting each element of character.
for (i = 0; i < l1; i++) {
d = (v1[i] - '0' - c) - (v2[i] - '0');
if (d < 0) {
d += 10;
c = 1;
}
else
c = 0;
v1[i] = '0' + d;
}
v2[l2] = '\0';
i = l1 - 1;
while (i > 0 && v1[i] == '0')
i--;
v1[i + 1] = '\0';
}
// Function divides a number represented by
// character array a constant.
int divi(char v[], int q)
{
int i, l = strlen(v);
int c = 0, d;
// Dividing each character element by constant.
for (i = l - 1; i >= 0; i--) {
d = c * 10 + (v[i] - '0');
c = d % q;
d /= q;
v[i] = '0' + d;
}
i = l - 1;
while (i > 0 && v[i] == '0')
i--;
v[i + 1] = '\0';
return c;
}
// Function to reverses the character array.
void rev(char v[])
{
int l = strlen(v);
int i;
char cc;
// Reversing the array.
for (i = 0; i < l - 1 - i; i++) {
cc = v[i];
v[i] = v[l - 1 - i];
v[l - i - 1] = cc;
}
}
// Wrapper Function
void divideWithDiffK(char a[], char k[])
{
// Reversing the character array.
rev(a);
rev(k);
// Adding the each element of both array
// and storing the sum in array a[].
add(a, k);
// Dividing the array a[] by 2.
divi(a, 2);
// Reversing the character array to get output.
rev(a);
printf("%s ", a);
// Subtracting each element of array
// i.e calculating a = a - b
rev(a);
subs(a, k);
// Reversing the character array to get output.
rev(a);
printf("%s", a);
}
// Driven Program
int main()
{
char a[MAX] = "100", k[MAX] = "20";
divideWithDiffK(a, k);
return 0;
}
Javascript
// JavaScript program to Divide a Big
// Number into two parts
let MAX = 100;
// Function to adds two Numbers
// represented as array of character.
function add(v1, v2)
{
let i, d, c = 0;
// length of string
let l1 = v1.length;
let l2 = v2.length;
// initializing extra character
// position to 0
for (i = l1; i < l2; i++)
v1[i] = '0';
for (i = l2; i < l1; i++)
v2[i] = '0';
// Adding each element of character
// and storing the carry.
for (i = 0; i < l1 || i < l2; i++) {
d = parseInt(v1[i] ) + parseInt(v2[i] ) + c;
c = Math.floor(d / 10);
d %= 10;
v1[i] = d.toString();
}
// If remainder remains.
while (c) {
v1[i] = (c % 10).toString();
c = Math.floor(c / 10);
i++;
}
return v1;
}
// Function to subtracts two numbers
// represented by string.
function subs(v1, v2)
{
let i, d, c = 0;
// Finding the length of the string.
let l1 = v1.length;
let l2 = v2.length;
// initializing extra character position to 0.
for (i = l2; i < l1; i++)
v2[i] = '0';
// Subtracting each element of character.
for (i = 0; i < l1; i++) {
d = parseInt(v1[i]) - c - parseInt(v2[i]);
if (d < 0) {
d += 10;
c = 1;
}
else
c = 0;
v1[i] = d.toString();
}
i = l1 - 1;
while (i > 0 && v1[i] == '0')
i--;
return v1;
}
// Function divides a number represented by
// character array a constant.
function divi(v, q)
{
let i, l = v.length;
let c = 0, d;
// Dividing each character element by constant.
for (i = l - 1; i >= 0; i--) {
d = c * 10 + parseInt(v[i]);
c = d % q;
d = Math.floor(d / q);
v[i] = d.toString();
}
i = l - 1;
while (i > 0 && v[i] == '0')
i--;
return v;
// return c;
}
// Function to reverses the character array.
function rev(v)
{
let l = v.length;
let i;
let cc;
// Reversing the array.
for (i = 0; i < l - 1 - i; i++) {
cc = v[i];
v[i] = v[l - 1 - i];
v[l - i - 1] = cc;
}
return v;
}
// Wrapper Function
function divideWithDiffK(a, k)
{
// Reversing the character array.
a = rev(a);
k = rev(k);
// Adding the each element of both array
// and storing the sum in array a[].
a = add(a, k);
// Dividing the array a[] by 2.
a = divi(a, 2);
// Reversing the character array to get output.
a = rev(a);
process.stdout.write(" " + parseInt(a.join("")));
// Subtracting each element of array
// i.e calculating a = a - b
a = rev(a);
a = subs(a, k);
// Reversing the character array to get output.
a = rev(a);
process.stdout.write(" " + parseInt(a.join("")));
}
// Driven Program
let a = "100".split("");
let k = "20".split("");
divideWithDiffK(a, k);
// This code is contributed by phasing17
Producción:
60 40