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Maximum time such that absolute difference between hour and minute lies in given range
• Last Updated : 07 Jan, 2021

Given a 24-hour time value, where on some numbers are question marks( ‘?’ ), and two integers L and R. The question mark can be replaced with any number. The task is to find the maximum time such that the absolute difference between hour value and minute value lies in the interval [L, R]. If no possible value of time exists, then print -1.

Examples:

Input : time = “2?:03”, L = 5, R = 18
Output : 21:03
Explanation : Since, the difference is 21 – 3 = 18 and the time value 21:03 is the largest possible value whose difference lies in the range [5, 18]

Input : time = “??:??”, L = 60, R = 69
Output : -1
Explanation : Since maximum possible difference between hour value and minute value is 59. So, no time value is possible.

Approach :
We will run two nested loops, one to represent ‘hour’ value from 23 to 0 and another to represent ‘minute’ value from 59 to 0. We keep decreasing ‘hour’ and ‘minute’ value until we get the desired time value.

1. Since the maximum time value is desired, so we decrease the ‘hour’ value from 23 to 0 and similarly ‘minute’ value from 59 to 0.
2. After decreasing the ‘hour’ and ‘minute’ value, we need to check if the ‘hour’ and ‘minute’ value is valid or not.
3. Change in value of ‘hour’ and ‘minute’ is allowed only at those positions which have ‘?’. Changes at other positions will make time value invalid. To ensure this we will call function isValid().
4. Keep on decreasing ‘hour’ and ‘minute’ value until a valid time is found whose difference lies in the range [ L, R ].
5. If no valid time is found, then print “-1”.

Below is the implementation of the above approach:

## C++

 // C++ program for the above approach#include using namespace std; // Function checks whether// given time is correctbool isValid(char a1, char a2,             string str, int flag){     char v1, v2;    // To check minute value of time    if (flag == 0) {        v1 = str[4];        v2 = str[3];    }    else {        // To check hour value of time        v1 = str[1];        v2 = str[0];    }     // Changes in value is not allowed    // at position where '?' is not    // present    if (v1 != a1 && v1 != '?')        return false;    if (v2 != a2 && v2 != '?')        return false;     return true;} // Function checks whether// the absolute difference// between hour and minute// value is within [L, R]bool inRange(int hh,             int mm, int L, int R){    int a = abs(hh - mm);     // Checks if the difference is outside    // the give range    if (a < L || a > R)        return false;     return true;} // Displays time in proper// 24-hour formatvoid displayTime(int hh, int mm){    if (hh > 10)        cout << hh << ":";    else if (hh < 10)        cout << "0" << hh << ":";     if (mm > 10)        cout << mm << endl;    else if (mm < 10)        cout << "0" << mm << endl;} // Function find the desired// value of time whose difference// lies in the range [L, R]void maximumTimeWithDifferenceInRange(    string str,    int L, int R){    int i, j;    int h1, h2, m1, m2;     // Decrease hour value from 23 to 0    for (i = 23; i >= 0; i--) {        h1 = i % 10;        h2 = i / 10;         // Check if the hour value is valid        // if not valid then no need to change        // minute value, since time will still        // remain in valid, to check hour value        // flag is set to 1.        if (!isValid(h1 + '0', h2 + '0', str, 1)) {            continue;        }         // Decrease minute value from 59 to 0        for (j = 59; j >= 0; j--) {            m1 = j % 10;            m2 = j / 10;             // Check if the minute value is valid,            // if not valid then skip the current            // iteration, to check 'minute' value            // flag is set to 0.            if (!isValid(m1 + '0', m2 + '0', str, 0)) {                continue;            }             if (inRange(i, j, L, R)) {                displayTime(i, j);                return;            }        }    }    if (inRange(i, j, L, R))        displayTime(i, j);    else        cout << "-1" << endl;} // Driver codeint main(){    // Input time    string timeValue = "??:??";     // Difference range    int L = 20, R = 39;    maximumTimeWithDifferenceInRange(        timeValue,        L, R);    return 0;}

## Java

 // Java program for// the above approachimport java.util.*;class GFG {   // Function checks whether// given time is correctstatic boolean isValid(char a1, char a2,                       String str, int flag){  char v1, v2;     // To check minute value of time  if (flag == 0)  {    v1 = str.charAt(4);    v2 = str.charAt(3);  }  else  {    // To check hour value of time    v1 = str.charAt(1);    v2 = str.charAt(0);  }   // Changes in value is not allowed  // at position where '?' is not  // present  if (v1 != a1 && v1 != '?')    return false;  if (v2 != a2 && v2 != '?')    return false;   return true;} // Function checks whether// the absolute difference// between hour and minute// value is within [L, R]static boolean inRange(int hh, int mm,                       int L, int R){  int a = Math.abs(hh - mm);   // Checks if the difference  // is outside the give range  if (a < L || a > R)    return false;   return true;} // Displays time in proper// 24-hour formatstatic void displayTime(int hh, int mm){  if (hh > 10)    System.out.print(hh + ":");  else if (hh < 10)    System.out.print("0" + hh + ":");   if (mm > 10)    System.out.println(mm);  else if (mm < 10)    System.out.println("0" + mm);} // Function find the desired// value of time whose difference// lies in the range [L, R]static void maximumTimeWithDifferenceInRange(String str,                                             int L,                                             int R){  int i = 0, j = 0;  int h1, h2, m1, m2;   // Decrease hour value  // from 23 to 0  for (i = 23; i >= 0; i--)  {    h1 = i % 10;    h2 = i / 10;     // Check if the hour value    // is valid if not valid    // then no need to change    // minute value, since time    // will still remain in valid,    // to check hour value    // flag is set to 1.    if (!isValid((char)h1,                 (char)h2, str, 1))    {      continue;    }     // Decrease minute value    // from 59 to 0    for (j = 59; j >= 0; j--)    {      m1 = j % 10;      m2 = j / 10;       // Check if the minute value      // is valid, if not valid      // then skip the current      // iteration, to check      // 'minute' value      // flag is set to 0.      if (!isValid((char)m1,                   (char)m2, str, 0))      {        continue;      }       if (inRange(i, j, L, R))      {        displayTime(i, j);        return;      }    }  }  if (inRange(i, j, L, R))    displayTime(i, j);  else    System.out.println("-1");} // Driver codepublic static void main(String[] args){  // Input time  String timeValue = "??:??";   // Difference range  int L = 20, R = 39;  maximumTimeWithDifferenceInRange(timeValue, L, R);}} // This code is contributed by Chitranayal

## Python3

 # Python3 program for the above approach # Function checks whether# given time is correctdef isValid(a1, a2, strr, flag):     v1, v2 = 0, 0         # To check minute value of time    if (flag == 0):        v1 = strr[4]        v2 = strr[3]    else:                 # To check hour value of time        v1 = strr[1]        v2 = strr[0]     # Changes in value is not allowed    # at position where '?' is not    # present    if (v1 != a1 and v1 != '?'):        return False    if (v2 != a2 and v2 != '?'):        return False     return True # Function checks whether# the absolute difference# between hour and minute# value is within [L, R]def inRange(hh, mm, L, R):    a = abs(hh - mm)     # Checks if the difference is    # outside the give range    if (a < L or a > R):        return False     return True # Displays time in proper# 24-hour formatdef displayTime(hh, mm):     if (hh > 10):        print(hh, end = ":")    elif (hh < 10):        print("0", hh, end = ":")     if (mm > 10):        print(mm)    elif (mm < 10):        print("0", mm) # Function find the desired# value of time whose difference# lies in the range [L, R]def maximumTimeWithDifferenceInRange(strr, L, R):         i, j = 0, 0    h1, h2, m1, m2 = 0, 0, 0, 0     # Decrease hour value from 23 to 0    for i in range(23, -1, -1):        h1 = i % 10        h2 = i // 10         # Check if the hour value is valid        # if not valid then no need to change        # minute value, since time will still        # remain in valid, to check hour value        # flag is set to 1.        if (not isValid(chr(h1), chr(h2), strr, 1)):            continue         # Decrease minute value from 59 to 0        for j in range(59, -1, -1):            m1 = j % 10            m2 = j // 10             # Check if the minute value is valid,            # if not valid then skip the current            # iteration, to check 'minute' value            # flag is set to 0.            if (not isValid(chr(m1), chr(m2),                            strr, 0)):                continue             if (inRange(i, j, L, R)):                displayTime(i, j)                return                      if (inRange(i, j, L, R)):        displayTime(i, j)    else:        print(-1) # Driver code # Input timetimeValue = "??:??" # Difference rangeL = 20R = 39     maximumTimeWithDifferenceInRange(timeValue, L, R) # This code is contributed by mohit kumar 29

## C#

 // C# program for the above approachusing System; class GFG{     // Function checks whether// given time is correctstatic bool isValid(char a1, char a2,                    string str, int flag){    char v1, v2;         // To check minute value of time    if (flag == 0)    {        v1 = str[4];        v2 = str[3];    }    else    {                 // To check hour value of time        v1 = str[1];        v2 = str[0];    }         // Changes in value is not allowed    // at position where '?' is not    // present    if (v1 != a1 && v1 != '?')    {        return false;    }    if (v2 != a2 && v2 != '?')    {        return false;    }    return true;} // Function checks whether// the absolute difference// between hour and minute// value is within [L, R]static bool inRange(int hh, int mm,                    int L, int R){    int a = Math.Abs(hh - mm);         // Checks if the difference    // is outside the give range    if (a < L || a > R)    {        return false;    }    return true;} // Displays time in proper// 24-hour formatstatic void displayTime(int hh, int mm){    if (hh > 10)    {        Console.Write(hh + ":");    }    else if (hh < 10)    {        Console.Write("0" + hh + ":");    }    if (mm > 10)    {        Console.Write(mm);    }    else if (mm < 10)    {        Console.Write("0" + mm);    }} // Function find the desired// value of time whose difference// lies in the range [L, R]static void maximumTimeWithDifferenceInRange(    string str, int L, int R){    int i = 0, j = 0;    int h1, h2, m1, m2;         // Decrease hour value    // from 23 to 0    for(i = 23; i >= 0; i--)    {        h1 = i % 10;        h2 = i / 10;                 // Check if the hour value        // is valid if not valid        // then no need to change        // minute value, since time        // will still remain in valid,        // to check hour value        // flag is set to 1.           if (!isValid((char)h1, (char)h2, str, 1))        {            continue;        }                 // Decrease minute value        // from 59 to 0        for(j = 59; j >= 0; j--)        {            m1 = j % 10;            m2 = j / 10;                         // Check if the minute value            // is valid, if not valid            // then skip the current            // iteration, to check            // 'minute' value            // flag is set to 0.            if (!isValid((char)m1, (char)m2, str, 0))            {                continue;            }            if (inRange(i, j, L, R))            {                displayTime(i, j);                return;            }        }    }    if (inRange(i, j, L, R))    {        displayTime(i, j);    }    else    {        Console.WriteLine("-1");    }} // Driver codestatic public void Main(){         // Input time    string timeValue = "??:??";         // Difference range    int L = 20, R = 39;         maximumTimeWithDifferenceInRange(timeValue, L, R);}} // This code is contributed by avanitrachhadiya2155
Output:
23:59

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

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