Greater And Least

CONCEPTS USED:

Searching

DIFFICULTY LEVEL:

Hard

PROBLEM STATEMENT(SIMPLIFIED):

Given a number N, find the smallest number that has same set-of-digits as N and is greater than N. If N is the greatest possible number with its set-of-digits, then print the same number N.

See original problem statement here

For Example:

Input  : "12345"

Output : "12354"
Input  : "54321"

Output : "54321"

Explanation : No number is greater than 54321 with same set of digits, thats why print same number.
Input  : "12321"

Output : "13122"

OBSERVATIONS:

  1. If the digits are all sorted in strictly descending order, then the number itself would be our answer as there is no bigger number than that.
    For example, 54321.

  2. If the digits are all sorted in strictly increasing order, then just swap the last two digits. For example, 12345 will change to 12354.

  3. For all other cases, we need to process all the digits in the number from right to left as we need to find the smallest of the greater numbers.

SOLVING APPROACH:

  1. Start traversing the given number from rightmost digit till you reach a digit that is just smaller than its right digit, say index of this digit be i.
    For example:
    N = 125321, here if we scan from right to left, 2 is the first digit that is less than 5 so 2 is our ithindex digit.

  2. Now again traverse to the right of this index i and find the smallest digit that is just greater than the digit at ith index. Let's say the found index is j at the right of i. Now if we traverse right of 2, the smallest digit that is greater than 2 is 3 (not 5).

  3. Swap digits at ith and jth index. After swapping 125321 becomes 135221.

  4. Sort digits from (i+1) to the rightmost index in increasing order. After sorting, 135221 becomes 131225, which is our required solution.

OPTIMIZATIONS:

  1. A few optimizations can be made in this approach and significantly improve the Time Complexity of the approach according to the data structures and algorithms in c++.

  2. The Linear Search used in Step-2 can be replaced with Binary Search as the right digits are already sorted. This reduces Time Complexity from O(n) to O(logn).

  3. The Sorting used in Step-4 can be done in O(n) instead of O(nlogn) as only one digit needs to be repositioned else all are already sorted.

  4. This Optimization would improve our solution from O(n+n+nlogn) to O(n+logn+n) giving overall time complexity of O(n), where
    n = number-of-digits-of-a-given-number.

SOLUTIONS:

#include <stdio.h>

//function for swapping two values
void swap(int arr[], int i, int j)
{
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}

//sorting a subarray in increasing order
void sortSubarray(int number[], int i, int j)
{
    while (i < j)
    {
        swap(number, i, j);
        i += 1;
        j -= 1;
    }
}

void findNextGreaterNumber(int arr[], int n)
{
    int lastDigitSeen = arr[n - 1], i, j;
    for (i = n - 2; i >= 0; i--)
    {
        if (lastDigitSeen > arr[i])
            break;
        lastDigitSeen = arr[i];
    }
    if (i >= 0)
    {
        for (j = n - 1; j > i; j--)
        {
            if (arr[j] > arr[i])
                break;
        }

        swap(arr, i, j);
        sortSubarray(arr, i + 1, n - 1);
    }
}
int main()
{
    int t;
    scanf("%d", &t);
    while (t--)
    {
        long long n;
        scanf("%lld", &n);
        int count = 0;
        long long num = n;

        //count the number of digits in n
        while (num > 0)
        {
            num /= 10;
            count++;
        }

        //storing all digits of n into an array
        int arr[count];
        int i = count - 1;
        while (n > 0)
        {
            arr[i--] = n % 10;
            n /= 10;
        }

        findNextGreaterNumber(arr, count);

        //printing all digits of the resultant number
        for (int j = 0; j < count; j++)
          printf("%d", arr[j]);
        printf("\n");
    }
    return 0;
}

#include <bits/stdc++.h>
using namespace std;

//function for swapping two values
void swap(int arr[], int i, int j)
{
    int temp = arr[i];
    arr[i] = arr[j];
    arr[j] = temp;
}

//sorting a subarray in increasing order
void sortSubarray(int number[], int i, int j)
{
    while (i < j)
    {
        swap(number, i, j);
        i += 1;
        j -= 1;
    }
}

void findNextGreaterNumber(int arr[], int n)
{
    int lastDigitSeen = arr[n - 1], i, j;
    for (i = n - 2; i >= 0; i--)
    {
        if (lastDigitSeen > arr[i])
            break;
        lastDigitSeen = arr[i];
    }
    if (i >= 0)
    {
        for (j = n - 1; j > i; j--)
        {
            if (arr[j] > arr[i])
                break;
        }

        swap(arr, i, j);
        sortSubarray(arr, i + 1, n - 1);
    }
}
int main()
{
    int t;
    cin >> t;
    while (t--)
    {
        long long n;
        cin >> n;
        int count = 0;
        long long num = n;

        //count the number of digits in n
        while (num > 0)
        {
            num /= 10;
            count++;
        }

        //storing all digits of n into an array
        int arr[count];
        int i = count - 1;
        while (n > 0)
        {
            arr[i--] = n % 10;
            n /= 10;
        }

        findNextGreaterNumber(arr, count);

        //printing all digits of the resultant number
        for (int j = 0; j < count; j++)
            cout << arr[j];
        cout << "\n";
    }
    return 0;
}
#include <bits/stdc++.h>
using namespace std;

string NextGreater(string str){
  int n = str.size();
  for(int i=n-2; i>=0; i--){
      if(str[i] < str[i+1]){
        sort(str.begin() + i + 1, str.end());
        auto it = upper_bound(str.begin() + i + 1, str.end(), str[i]);
        int index = it - str.begin();
        swap(str[index], str[i]);
        break;
      }
    }
  return str;
}
int main()
{
  int t; cin>>t;
  while(t--){
    string str; cin>>str;
    cout<<"\n"<<NextGreater(str);  
  }
  return 0;
}



import java.util.*;
import java.io.*;

public class Main {
  static void swap(long []arr, int i, int j)
  {
      long temp = arr[i];
      arr[i] = arr[j];
      arr[j] = temp;
  }

  //sorting a subarray in increasing order
  static void sortSubarray(long []number, int i, int j)
  {
      while (i < j)
      {
          swap(number, i, j);
          i += 1;
          j -= 1;
      }
  }

  static void findNextGreaterNumber(long []arr, int n)
  {
      long lastDigitSeen = arr[n - 1];
      int i, j;
      for (i = n - 2; i >= 0; i--)
      {
          if (lastDigitSeen > arr[i])
              break;
          lastDigitSeen = arr[i];
      }
      if (i >= 0)
      {
          for (j = n - 1; j > i; j--)
          {
              if (arr[j] > arr[i])
                  break;
          }

          swap(arr, i, j);
          sortSubarray(arr, i + 1, n - 1);
      }
  }
  public static void main(String args[]) throws IOException {

    Scanner sc = new Scanner(System.in);
    int t = sc.nextInt();
    while (t != 0)
    {
      long n = sc.nextLong();
      int count = 0;
      long num = n;

      //count the number of digits in n
      while (num > 0)
      {
          num /= 10;
          count++;
      }

      //storing all digits of n into an array
      long arr[] = new long[count];
      int i = count - 1;
      while (n > 0)
      {
          arr[i--] = n % 10;
          n /= 10;
      }

      findNextGreaterNumber(arr, count);

      //printing all digits of the resultant number
      for (int j = 0; j < count; j++)
          System.out.print(arr[j]);
      System.out.println();
      t--;
    }

  }
}



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