Count of numbers in given range [L, R] that is perfect square and digits are in wave form

Given two integers L and R, the task is to count the integers in the range [L, R] such that they satisfy the following two properties:

• The number must be a perfect square of any integer.
• In digits of the integer must be in the wave form i.e, let d1, d2, d3, d4, d5 be the digits in the current integer, then d1 < d2 > d3 < d4… must hold true.

Examples:

Input: L = 1, R = 64
Output: 7 
Explanation:
The special numbers in the range [1, 64] are 1, 4, 9, 16, 25, 36 and 49.

Input: L = 80, R = 82
Output: 0

Naive Approach: The simplest approach to solve the problem is to traverse in the range [L, R], and for each number in the range check for the above two conditions.
Time Complexity: O(N)
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach iterate over only perfect squares and check for the second condition. Follow the steps below for the approach:

• Initialize a variable say, count = 0, to count all the special numbers in the range [L, R].
• Iterate over all the perfect squares that are less than R.
• Define a function, say check(N), to check whether the number N satisfies the second condition by iterating over even and odd digits.
• Increase the count, if the number is greater than L and function check returns true for the given number.
• Finally, return the count.

Below is the implementation of the above approach:

C++

// C++ implementation for the above approach
#include <bits/stdc++.h>
using namespace std;

// Utility function to check if
// the digits of the current
// integer forms a wave pattern
bool check(int N)
{
    // Convert the number to a string
    string S = to_string(N);

    // Loop to iterate over digits
    for (int i = 0; i < S.size(); i++) {
        if (i == 0) {

            // Next character of
            // the number
            int next = i + 1;

            // Current character is
            // not a local minimum
            if (next < S.size()) {
                if (S[i] >= S[next]) {

                    return false;
                }
            }
        }

        else if (i == S.size() - 1) {

            // Previous character of
            // the number
            int prev = i - 1;
            if (prev >= 0) {

                // Character is a
                // local maximum
                if (i & 1) {

                    // Character is not
                    // a local maximum
                    if (S[i] <= S[prev]) {
                        return false;
                    }
                }
                else {
                    // Character is a
                    // local minimum
                    if (S[i] >= S[prev]) {
                        return false;
                    }
                }
            }
        }
        else {
            int prev = i - 1;
            int next = i + 1;
            if (i & 1) {

                // Character is a
                // local maximum
                if ((S[i] > S[prev])
                    && (S[i] > S[next])) {
                }
                else {
                    return false;
                }
            }
            else {
                // Character is a
                // local minimum
                if ((S[i] < S[prev])
                    && (S[i] < S[next])) {
                }
                else {
                    return false;
                }
            }
        }
    }
    return true;
}

// Function to calculate total
// integer in the given range
int totalUniqueNumber(int L, int R)
{
    // Base case
    if (R <= 0) {
        return 0;
    }

    // Current number
    int cur = 1;

    // Variable to store
    // total unique numbers
    int count = 0;

    // Iterating over perfect
    // squares
    while ((cur * cur) <= R) {
        int num = cur * cur;

        // If number is greater
        // than L and satisfies
        // required conditions
        if (num >= L && check(num)) {
            count++;
        }

        // Moving to the
        // next number
        cur++;
    }

    // Return Answer
    return count;
}

// Driver Code
int main()
{
    int L = 1, R = 64;
    cout << totalUniqueNumber(L, R);
}

Java

// Java  program for the above approach
import java.util.*;
public class GFG
{

  // Utility function to check if
  // the digits of the current
  // integer forms a wave pattern
  static boolean check(int N)
  {

    // Convert the number to a string
    String S = Integer.toString(N);

    // Loop to iterate over digits
    for (int i = 0; i < S.length(); i++) {
      if (i == 0) {

        // Next character of
        // the number
        int next = i + 1;

        // Current character is
        // not a local minimum
        if (next < S.length()) {
          if (S.charAt(i) >= S.charAt(next)) {

            return false;
          }
        }
      }

      else if (i == S.length() - 1) {

        // Previous character of
        // the number
        int prev = i - 1;
        if (prev >= 0) {

          // Character is a
          // local maximum
          if ((i & 1) == 1) {

            // Character is not
            // a local maximum
            if (S.charAt(i) <= S.charAt(prev)) {
              return false;
            }
          }
          else
          {

            // Character is a
            // local minimum
            if (S.charAt(i) >= S.charAt(prev)) {
              return false;
            }
          }
        }
      }
      else {
        int prev = i - 1;
        int next = i + 1;
        if ((i & 1) == 1) {

          // Character is a
          // local maximum
          if ((S.charAt(i) > S.charAt(prev))
              && (S.charAt(i) > S.charAt(next))) {
          }
          else {
            return false;
          }
        }
        else
        {

          // Character is a
          // local minimum
          if ((S.charAt(i) < S.charAt(prev))
              && (S.charAt(i) < S.charAt(next))) {
          }
          else {
            return false;
          }
        }
      }
    }
    return true;
  }

  // Function to calculate total
  // integer in the given range
  static int totalUniqueNumber(int L, int R)
  {

    // Base case
    if (R <= 0) {
      return 0;
    }

    // Current number
    int cur = 1;

    // Variable to store
    // total unique numbers
    int count = 0;

    // Iterating over perfect
    // squares
    while ((cur * cur) <= R) {
      int num = cur * cur;

      // If number is greater
      // than L and satisfies
      // required conditions
      if (num >= L && check(num)) {
        count++;
      }

      // Moving to the
      // next number
      cur++;
    }

    // Return Answer
    return count;
  }

  // Driver Code
  public static void main(String args[])
  {
      int L = 1, R = 64;

      // Function call
      System.out.println(totalUniqueNumber(L, R));
  }
}
// This code is contributed by Samim Hossain Mondal.

Python3

# Python  program for the above approach

# Utility function to check if
# the digits of the current
# integer forms a wave pattern
def check(N):

    # Convert the number to a string
    S = str(N);

    # Loop to iterate over digits
    for i in range(len(S)):
        if (i == 0):

            # Next character of
            # the number
            next = i + 1;

            # Current character is
            # not a local minimum
            if (next < len(S)):
                if (S[i] >= S[next]):

                    return False;

        elif(i == len(S) - 1):

            # Previous character of
            # the number
            prev = i - 1;
            if (prev >= 0):

                # Character is a
                # local maximum
                if ((i & 1) == 1):

                    # Character is not
                    # a local maximum
                    if (S[i] <= S[prev]):
                        return False;
                else:

                    # Character is a
                    # local minimum
                    if (S[i] >= S[prev]):
                        return False;

        else:
            prev = i - 1;
            next = i + 1;
            if ((i & 1) == 1):

                # Character is a
                # local maximum
                if ((S[i] > S[prev]) and (S[i] > S[next])):
                    return True;
                else:
                    return False;

            else:

                # Character is a
                # local minimum
                if ((S[i] < S[prev]) and (S[i] < S[next])):
                    return True;
                else:
                    return False;

    return True;

# Function to calculate total
# integer in the given range
def totalUniqueNumber(L, R):

    # Base case
    if (R <= 0):
        return 0;

    # Current number
    cur = 1;

    # Variable to store
    # total unique numbers
    count = 0;

    # Iterating over perfect
    # squares
    while ((cur * cur) <= R):
        num = cur * cur;

        # If number is greater
        # than L and satisfies
        # required conditions
        if (num >= L and check(num)):
            count += 1;

        # Moving to the
        # next number
        cur += 1;

    # Return Answer
    return count;

# Driver Code
if __name__ == '__main__':
    L = 1;
    R = 64;

    # Function call
    print(totalUniqueNumber(L, R));

# This code is contributed by gauravrajput1

C#

// C# program for the above approach
using System;
using System.Collections;

class GFG
{

  // Utility function to check if
  // the digits of the current
  // integer forms a wave pattern
  static bool check(int N)
  {
    // Convert the number to a string
    string S = N.ToString();

    // Loop to iterate over digits
    for (int i = 0; i < S.Length; i++) {
      if (i == 0) {

        // Next character of
        // the number
        int next = i + 1;

        // Current character is
        // not a local minimum
        if (next < S.Length) {
          if (S[i] >= S[next]) {

            return false;
          }
        }
      }

      else if (i == S.Length - 1) {

        // Previous character of
        // the number
        int prev = i - 1;
        if (prev >= 0) {

          // Character is a
          // local maximum
          if ((i & 1) == 1) {

            // Character is not
            // a local maximum
            if (S[i] <= S[prev]) {
              return false;
            }
          }
          else {
            // Character is a
            // local minimum
            if (S[i] >= S[prev]) {
              return false;
            }
          }
        }
      }
      else {
        int prev = i - 1;
        int next = i + 1;
        if ((i & 1) == 1) {

          // Character is a
          // local maximum
          if ((S[i] > S[prev])
              && (S[i] > S[next])) {
          }
          else {
            return false;
          }
        }
        else {
          // Character is a
          // local minimum
          if ((S[i] < S[prev])
              && (S[i] < S[next])) {
          }
          else {
            return false;
          }
        }
      }
    }
    return true;
  }

  // Function to calculate total
  // integer in the given range
  static int totalUniqueNumber(int L, int R)
  {
    // Base case
    if (R <= 0) {
      return 0;
    }

    // Current number
    int cur = 1;

    // Variable to store
    // total unique numbers
    int count = 0;

    // Iterating over perfect
    // squares
    while ((cur * cur) <= R) {
      int num = cur * cur;

      // If number is greater
      // than L and satisfies
      // required conditions
      if (num >= L && check(num)) {
        count++;
      }

      // Moving to the
      // next number
      cur++;
    }

    // Return Answer
    return count;
  }


  // Driver Code
  public static void Main()
  {
    int L = 1, R = 64;

    // Function call
    Console.Write(totalUniqueNumber(L, R));

  }
}
// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
       // JavaScript code for the above approach

       // Utility function to check if
       // the digits of the current
       // integer forms a wave pattern
       function check(N)
       {

           // Convert the number to a string
           let S = N.toString();

           // Loop to iterate over digits
           for (let i = 0; i < S.length; i++) {
               if (i == 0) {

                   // Next character of
                   // the number
                   let next = i + 1;

                   // Current character is
                   // not a local minimum
                   if (next < S.length) {
                       if (S[i] >= S[next]) {

                           return false;
                       }
                   }
               }

               else if (i == S.length - 1) {

                   // Previous character of
                   // the number
                   let prev = i - 1;
                   if (prev >= 0) {

                       // Character is a
                       // local maximum
                       if (i & 1) {

                           // Character is not
                           // a local maximum
                           if (S[i] <= S[prev]) {
                               return false;
                           }
                       }
                       else {
                           // Character is a
                           // local minimum
                           if (S[i] >= S[prev]) {
                               return false;
                           }
                       }
                   }
               }
               else {
                   let prev = i - 1;
                   let next = i + 1;
                   if (i & 1) {

                       // Character is a
                       // local maximum
                       if ((S[i] > S[prev])
                           && (S[i] > S[next])) {
                       }
                       else {
                           return false;
                       }
                   }
                   else {
                       // Character is a
                       // local minimum
                       if ((S[i] < S[prev])
                           && (S[i] < S[next])) {
                       }
                       else {
                           return false;
                       }
                   }
               }
           }
           return true;
       }

       // Function to calculate total
       // integer in the given range
       function totalUniqueNumber(L, R) {
           // Base case
           if (R <= 0) {
               return 0;
           }

           // Current number
           let cur = 1;

           // Variable to store
           // total unique numbers
           let count = 0;

           // Iterating over perfect
           // squares
           while ((cur * cur) <= R) {
               let num = cur * cur;

               // If number is greater
               // than L and satisfies
               // required conditions
               if (num >= L && check(num)) {
                   count++;
               }

               // Moving to the
               // next number
               cur++;
           }

           // Return Answer
           return count;
       }

       // Driver Code
       let L = 1, R = 64;
       document.write(totalUniqueNumber(L, R));

 // This code is contributed by Potta Lokesh
   </script>

Output

7

Time Complexity: O(sqrt(N))
Auxiliary Space: O(1)