Least Greater number with same digit sum
Last Updated :
05 Apr, 2022
Given a number represented in the form of an array such that each element of the array stores a single digit of the number. That is, array for the number 1234 will be arr[] = {1,2,3,4}. The task is to find the least number greater than the given number but having the sum of digits equal to the given number. For simplicity: Consider the length of number can be 20 at maximum. Examples:
Input : arr[] = {0, 0, 0, 0, 0, 0, 0, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 8 }; Output : 00000004799999999999 Explanation : Sum of digits = 110 Input : arr[] = {0, 0, 0, 0, 0, 0, 0, 3, 9, 7, 0, 0, 2, 9, 8, 9, 5, 9, 9, 0}; Output : 00000003970029896089 Explanation : Sum of digits = 70
A Brute Force Approach is to:
- Start from that number and increment the number by one.
- Check the sum. If the sum is same the return the number.
- Else return to step one.
A Better Approach is to jump to the next number in O(n) time complexity, where n is the length of string.
We divide the number into 4 regions : 1st: Trailing zeros . 2nd: The lowest digit not in Region 1. 3rd: Consecutive 9s starting with the digit above Region 2. 4th: All remaining digits. Then the next number is : [Region 4+1] [Region 1] [Region 2-1] [Region 3] . Example: Input Number = 548995000 Region 1 : 000 Region 2 : 5 Region 3 : 99 Region 4 : 548 Next number = 549000499
Below is the implementation of the above approach:
C++
// CPP program to find next greater number with
// same sum of digits.
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
void getnext(int arr[], int n)
{
// for storing 4 regions
vector<int> a1, a2, a3, a4;
// trailing zeros region1
int i = n - 1; // last index
while (arr[i] == 0)
{
a1.pb(0);
i--;
}
// lowest region(region 2) not in region 1
a2.pb(arr[i--]);
// Consecutive 9's (region 3)
while (arr[i] == 9)
{
a3.pb(9);
i--;
}
int j = 0;
while (arr[j] == 0)
j++; // Starting zeros
while (j <= i) // 4th region
{
a4.pb(arr[j]);
j++;
}
// Calculation of result
j = a4.size() - 1;
a4[j]++; // Region4 + 1
a2[0]--; // Region2 -1
int l = a1.size() + a2.size() + a3.size() + a4.size();
// Calculating the result
j = n-1;
i = a3.size() - 1;
// Copying the third region
while (i >= 0)
{
arr[j--] = a3[i--];
}
// Copying the 2nd region
i = a2.size() - 1;
while (i >= 0)
{
arr[j--] = a2[i--];
}
// Copying the 1st region
i = a1.size() - 1;
while (i >= 0)
{
arr[j--] = a1[i--];
}
// Copying the 4th region
i = a4.size() - 1;
while (i >= 0)
{
arr[j--] = a4[i--];
}
while (j >= 0)
arr[j--] = 0;
}
int main()
{
int arr[] = { 0, 0, 0, 0, 0, 0, 0, 3, 9, 7,
0, 0, 2, 9, 8, 9, 5, 9, 9, 0 };
int n = sizeof(arr)/sizeof(arr[0]);
getnext(arr, n); // Calling the function
for (int i = 0; i < n; i++)
cout << arr[i];
return 0;
}
// Java program to find next greater number with
// same sum of digits.
import java.util.*;
class GFG
{
static void getnext(int []arr, int n)
{
// for storing 4 regions
ArrayList<Integer> a1 = new ArrayList<Integer>();
ArrayList<Integer> a2 = new ArrayList<Integer>();
ArrayList<Integer> a3 = new ArrayList<Integer>();
ArrayList<Integer> a4 = new ArrayList<Integer>();
// trailing zeros region1
int i = n - 1; // last index
while (arr[i] == 0)
{
a1.add(0);
i--;
}
// lowest region(region 2) not in region 1
a2.add(arr[i--]);
// Consecutive 9's (region 3)
while (arr[i] == 9)
{
a3.add(9);
i--;
}
int j = 0;
while (arr[j] == 0)
j++; // Starting zeros
while (j <= i) // 4th region
{
a4.add(arr[j]);
j++;
}
// Calculation of result
j = a4.size() - 1;
a4.set(j,a4.get(j) + 1); // Region4 + 1
a2.set(0,a2.get(0) - 1); // Region2 -1
//int l = a1.size() + a2.size() + a3.size() + a4.size();
// Calculating the result
j = n - 1;
i = a3.size() - 1;
// Copying the third region
while (i >= 0)
{
arr[j--] = (int)a3.get(i);
i--;
}
// Copying the 2nd region
i = a2.size() - 1;
while (i >= 0)
{
arr[j--] = (int)a2.get(i);
i--;
}
// Copying the 1st region
i = a1.size() - 1;
while (i >= 0)
{
arr[j--] = a1.get(i);
i--;
}
// Copying the 4th region
i = a4.size() - 1;
while (i >= 0)
{
arr[j--] = a4.get(i);
i--;
}
while (j >= 0)
arr[j--] = 0;
}
// Driver code
public static void main (String[] args)
{
int []arr = { 0, 0, 0, 0, 0, 0, 0, 3, 9, 7,
0, 0, 2, 9, 8, 9, 5, 9, 9, 0 };
int n = arr.length;
getnext(arr, n); // Calling the function
for (int i = 0; i < n; i++)
System.out.print(arr[i]);
}
}
// This code is contributed by mits
# Python3 program to find next greater number with
# same sum of digits.
def getnext(arr, n):
# for storing 4 regions
a1=[];
a2=[];
a3=[];
a4=[];
# trailing zeros region1
i = n - 1; # last index
while (arr[i] == 0):
a1.append(0);
i-=1;
# lowest region(region 2) not in region 1
a2.append(arr[i]);
i-=1;
# Consecutive 9's (region 3)
while (arr[i] == 9):
a3.append(9);
i-=1;
j = 0;
while (arr[j] == 0):
j+=1; # Starting zeros
while (j <= i): # 4th region
a4.append(arr[j]);
j+=1;
# Calculation of result
j = len(a4) - 1;
a4[j]+=1; # Region4 + 1
a2[0]-=1; # Region2 -1
l = len(a1) + len(a2) + len(a3) + len(a4);
# Calculating the result
j = n-1;
i = len(a3) - 1;
# Copying the third region
while (i >= 0):
arr[j] = a3[i];
j-=1;
i-=1;
# Copying the 2nd region
i = len(a2) - 1;
while (i >= 0):
arr[j] = a2[i];
j-=1;
i-=1;
# Copying the 1st region
i = len(a1) - 1;
while (i >= 0):
arr[j] = a1[i];
j-=1;
i-=1;
# Copying the 4th region
i = len(a4) - 1;
while (i >= 0):
arr[j] = a4[i];
j-=1;
i-=1;
while (j >= 0):
arr[j] = 0;
j-=1;
# Driver code
arr = [ 0, 0, 0, 0, 0, 0, 0, 3, 9, 7, 0,
0, 2, 9, 8, 9, 5, 9, 9, 0 ];
n = len(arr);
getnext(arr, n); # Calling the function
for i in range(0,n):
print(arr[i],end="");
# This code is contributed by mits
// C# program to find next greater number with
// same sum of digits.
using System;
using System.Collections;
class GFG
{
static void getnext(int []arr, int n)
{
// for storing 4 regions
ArrayList a1 = new ArrayList();
ArrayList a2 = new ArrayList();
ArrayList a3 = new ArrayList();
ArrayList a4 = new ArrayList();
// trailing zeros region1
int i = n - 1; // last index
while (arr[i] == 0)
{
a1.Add(0);
i--;
}
// lowest region(region 2) not in region 1
a2.Add(arr[i--]);
// Consecutive 9's (region 3)
while (arr[i] == 9)
{
a3.Add(9);
i--;
}
int j = 0;
while (arr[j] == 0)
j++; // Starting zeros
while (j <= i) // 4th region
{
a4.Add(arr[j]);
j++;
}
// Calculation of result
j = a4.Count - 1;
a4[j] = (int)a4[j] + 1; // Region4 + 1
a2[0] = (int)a2[0] - 1; // Region2 -1
//int l = a1.Count + a2.Count + a3.Count + a4.Count;
// Calculating the result
j = n - 1;
i = a3.Count - 1;
// Copying the third region
while (i >= 0)
{
arr[j--] = (int)a3[i];
i--;
}
// Copying the 2nd region
i = a2.Count - 1;
while (i >= 0)
{
arr[j--] = (int)a2[i];
i--;
}
// Copying the 1st region
i = a1.Count - 1;
while (i >= 0)
{
arr[j--] = (int)a1[i];
i--;
}
// Copying the 4th region
i = a4.Count - 1;
while (i >= 0)
{
arr[j--] = (int)a4[i];
i--;
}
while (j >= 0)
arr[j--] = 0;
}
// Driver code
static void Main()
{
int []arr = { 0, 0, 0, 0, 0, 0, 0, 3, 9, 7,
0, 0, 2, 9, 8, 9, 5, 9, 9, 0 };
int n = arr.Length;
getnext(arr, n); // Calling the function
for (int i = 0; i < n; i++)
Console.Write(arr[i]);
}
}
// This code is contributed by mits
<?php
// PHP program to find next greater number with
// same sum of digits.
function getnext(&$arr, $n)
{
// for storing 4 regions
$a1=array();
$a2=array();
$a3=array();
$a4=array();
// trailing zeros region1
$i = $n - 1; // last index
while ($arr[$i] == 0)
{
array_push($a1,0);
$i--;
}
// lowest region(region 2) not in region 1
array_push($a2,$arr[$i--]);
// Consecutive 9's (region 3)
while ($arr[$i] == 9)
{
array_push($a3,9);
$i--;
}
$j = 0;
while ($arr[$j] == 0)
$j++; // Starting zeros
while ($j <= $i) // 4th region
{
array_push($a4,$arr[$j]);
$j++;
}
// Calculation of result
$j = count($a4) - 1;
$a4[$j]++; // Region4 + 1
$a2[0]--; // Region2 -1
$l = count($a1) + count($a2) + count($a3) + count($a4);
// Calculating the result
$j = $n-1;
$i = count($a3) - 1;
// Copying the third region
while ($i >= 0)
{
$arr[$j--] = $a3[$i--];
}
// Copying the 2nd region
$i = count($a2) - 1;
while ($i >= 0)
{
$arr[$j--] = $a2[$i--];
}
// Copying the 1st region
$i = count($a1) - 1;
while ($i >= 0)
{
$arr[$j--] = $a1[$i--];
}
// Copying the 4th region
$i = count($a4) - 1;
while ($i >= 0)
{
$arr[$j--] = $a4[$i--];
}
while ($j >= 0)
$arr[$j--] = 0;
}
// Driver code
$arr = array( 0, 0, 0, 0, 0, 0, 0, 3, 9, 7,
0, 0, 2, 9, 8, 9, 5, 9, 9, 0 );
$n = count($arr);
getnext($arr, $n); // Calling the function
for ($i = 0; $i < $n; $i++)
echo $arr[$i];
// This code is contributed by mits
?>
<script>
// JavaScript program to find next greater number with
// same sum of digits.
function getnext(arr, n)
{
// for storing 4 regions
let a1 = [], a2 = [], a3 = [], a4 = [];
// trailing zeros region1
let i = n - 1; // last index
while (arr[i] == 0)
{
a1.push(0);
i--;
}
// lowest region(region 2) not in region 1
a2.push(arr[i--]);
// Consecutive 9's (region 3)
while (arr[i] == 9)
{
a3.push(9);
i--;
}
let j = 0;
while (arr[j] == 0)
j++; // Starting zeros
while (j <= i) // 4th region
{
a4.push(arr[j]);
j++;
}
// Calculation of result
j = a4.length - 1;
a4[j]++; // Region4 + 1
a2[0]--; // Region2 -1
let l = a1.length + a2.length + a3.length + a4.length;
// Calculating the result
j = n-1;
i = a3.length - 1;
// Copying the third region
while (i >= 0)
{
arr[j--] = a3[i--];
}
// Copying the 2nd region
i = a2.length - 1;
while (i >= 0)
{
arr[j--] = a2[i--];
}
// Copying the 1st region
i = a1.length - 1;
while (i >= 0)
{
arr[j--] = a1[i--];
}
// Copying the 4th region
i = a4.length - 1;
while (i >= 0)
{
arr[j--] = a4[i--];
}
while (j >= 0)
arr[j--] = 0;
}
// driver code
let arr = [ 0, 0, 0, 0, 0, 0, 0, 3, 9, 7,
0, 0, 2, 9, 8, 9, 5, 9, 9, 0 ];
let n = arr.length;
getnext(arr, n); // Calling the function
for (let i = 0; i < n; i++)
document.write(arr[i]);
// code is contributed by shinjanpatra
</script>
Output:00000003970029896089
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