# Maximum possible time that can be formed from four digits

Given an array arr[] having 4 integer digits only. The task is to return the maximum 24 hour time that can be formed using the digits from the array.

Note that the minimum time in 24 hour format is 00:00, and the maximum is 23:59. If a valid time cannot be formed then return -1.

Examples:

Input: arr[] = {1, 2, 3, 4}
Output: 23:41

Input: arr[] = {5, 5, 6, 6}
Output: -1

Approach: Create a HashMap and store the frequency of each digit in the map which can be used to know how many of such digits are available.

Now, in order to generate a valid time following conditions must be satisfied:

• First digit of hours must be from the range [0, 2]. Start checking in decreasing order in order to maximize the time i.e. from 2 to 0. Once the digit is chosen, decrement its occurrence in the map by 1.
• Second digit of hours must be from the range [0, 3] if first digit was chosen as 2 else [0, 9]. Update the HashMap accordingly after choosing the digit.
• First digit of minutes must be from the range [0, 5] and second digit of minutes must be from the range [0, 9].

If any of the above condition fails i.e. no digit could be chosen at any point then print -1 else print the time.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function to return the updated frequency map` `// for the array passed as argument` `map<``int``, ``int``> getFrequencyMap(``int` `arr[], ``int` `n)` `{` `    ``map<``int``, ``int``> hashMap;` `    ``for` `(``int` `i = 0; i < n; i++) {`   `        ``hashMap[arr[i]]++;` `    ``}` `    ``return` `hashMap;` `}`   `// Function that returns true if the passed digit is present` `// in the map after decrementing it's frequency by 1` `bool` `hasDigit(map<``int``, ``int``>* hashMap, ``int` `digit)` `{`   `    ``// If map contains the digit` `    ``if` `((*hashMap)[digit]) {`   `        ``// Decrement the frequency of the digit by 1` `        ``(*hashMap)[digit]--;`   `        ``// True here indicates that the digit was found in the map` `        ``return` `true``;` `    ``}`   `    ``// Digit not found` `    ``return` `false``;` `}`   `// Function to return the maximum possible time_value in 24-Hours format` `string getMaxtime_value(``int` `arr[], ``int` `n)` `{` `    ``map<``int``, ``int``> hashMap = getFrequencyMap(arr, n);` `    ``int` `i;` `    ``bool` `flag;` `    ``string time_value = ``""``;`   `    ``flag = ``false``;`   `    ``// First digit of hours can be from the range [0, 2]` `    ``for` `(i = 2; i >= 0; i--) {` `        ``if` `(hasDigit(&hashMap, i)) {` `            ``flag = ``true``;` `            ``time_value += (``char``)i + 48;` `            ``break``;` `        ``}` `    ``}`   `    ``// If no valid digit found` `    ``if` `(!flag)` `        ``return` `"-1"``;`   `    ``flag = ``false``;`   `    ``// If first digit of hours was chosen as 2 then` `    ``// the second digit of hours can be` `    ``// from the range [0, 3]` `    ``if` `(time_value[0] == ``'2'``) {` `        ``for` `(i = 3; i >= 0; i--) {` `            ``if` `(hasDigit(&hashMap, i)) {` `                ``flag = ``true``;` `                ``time_value += (``char``)i + 48;` `                ``break``;` `            ``}` `        ``}` `    ``}`   `    ``// Else it can be from the range [0, 9]` `    ``else` `{` `        ``for` `(i = 9; i >= 0; i--) {` `            ``if` `(hasDigit(&hashMap, i)) {` `                ``flag = ``true``;` `                ``time_value += (``char``)i + 48;` `                ``break``;` `            ``}` `        ``}` `    ``}` `    ``if` `(!flag)` `        ``return` `"-1"``;`   `    ``// Hours and minutes separator` `    ``time_value += ``":"``;`   `    ``flag = ``false``;`   `    ``// First digit of minutes can be from the range [0, 5]` `    ``for` `(i = 5; i >= 0; i--) {` `        ``if` `(hasDigit(&hashMap, i)) {` `            ``flag = ``true``;` `            ``time_value += (``char``)i + 48;` `            ``break``;` `        ``}` `    ``}` `    ``if` `(!flag)` `        ``return` `"-1"``;`   `    ``flag = ``false``;`   `    ``// Second digit of minutes can be from the range [0, 9]` `    ``for` `(i = 9; i >= 0; i--) {` `        ``if` `(hasDigit(&hashMap, i)) {` `            ``flag = ``true``;` `            ``time_value += (``char``)i + 48;` `            ``break``;` `        ``}` `    ``}` `    ``if` `(!flag)` `        ``return` `"-1"``;`   `    ``// Return the maximum possible time_value` `    ``return` `time_value;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { 0, 0, 0, 9 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);` `    ``cout << (getMaxtime_value(arr, n));` `    ``return` `0;` `}` `// contributed by Arnab Kundu`

## Java

 `// Java implementation of the approach`   `import` `java.util.*;`   `public` `class` `GFG {`   `    ``// Function to return the updated frequency map` `    ``// for the array passed as argument` `    ``static` `HashMap getFrequencyMap(``int` `arr[])` `    ``{` `        ``HashMap hashMap = ``new` `HashMap<>();` `        ``for` `(``int` `i = ``0``; i < arr.length; i++) {` `            ``if` `(hashMap.containsKey(arr[i])) {` `                ``hashMap.put(arr[i], hashMap.get(arr[i]) + ``1``);` `            ``}` `            ``else` `{` `                ``hashMap.put(arr[i], ``1``);` `            ``}` `        ``}` `        ``return` `hashMap;` `    ``}`   `    ``// Function that returns true if the passed digit is present` `    ``// in the map after decrementing it's frequency by 1` `    ``static` `boolean` `hasDigit(HashMap hashMap, ``int` `digit)` `    ``{`   `        ``// If map contains the digit` `        ``if` `(hashMap.containsKey(digit) && hashMap.get(digit) > ``0``) {`   `            ``// Decrement the frequency of the digit by 1` `            ``hashMap.put(digit, hashMap.get(digit) - ``1``);`   `            ``// True here indicates that the digit was found in the map` `            ``return` `true``;` `        ``}`   `        ``// Digit not found` `        ``return` `false``;` `    ``}`   `    ``// Function to return the maximum possible time in 24-Hours format` `    ``static` `String getMaxTime(``int` `arr[])` `    ``{` `        ``HashMap hashMap = getFrequencyMap(arr);` `        ``int` `i;` `        ``boolean` `flag;` `        ``String time = ``""``;`   `        ``flag = ``false``;`   `        ``// First digit of hours can be from the range [0, 2]` `        ``for` `(i = ``2``; i >= ``0``; i--) {` `            ``if` `(hasDigit(hashMap, i)) {` `                ``flag = ``true``;` `                ``time += i;` `                ``break``;` `            ``}` `        ``}`   `        ``// If no valid digit found` `        ``if` `(!flag) {` `            ``return` `"-1"``;` `        ``}`   `        ``flag = ``false``;`   `        ``// If first digit of hours was chosen as 2 then` `        ``// the second digit of hours can be` `        ``// from the range [0, 3]` `        ``if` `(time.charAt(``0``) == ``'2'``) {` `            ``for` `(i = ``3``; i >= ``0``; i--) {` `                ``if` `(hasDigit(hashMap, i)) {` `                    ``flag = ``true``;` `                    ``time += i;` `                    ``break``;` `                ``}` `            ``}` `        ``}`   `        ``// Else it can be from the range [0, 9]` `        ``else` `{` `            ``for` `(i = ``9``; i >= ``0``; i--) {` `                ``if` `(hasDigit(hashMap, i)) {` `                    ``flag = ``true``;` `                    ``time += i;` `                    ``break``;` `                ``}` `            ``}` `        ``}` `        ``if` `(!flag) {` `            ``return` `"-1"``;` `        ``}`   `        ``// Hours and minutes separator` `        ``time += ``":"``;`   `        ``flag = ``false``;`   `        ``// First digit of minutes can be from the range [0, 5]` `        ``for` `(i = ``5``; i >= ``0``; i--) {` `            ``if` `(hasDigit(hashMap, i)) {` `                ``flag = ``true``;` `                ``time += i;` `                ``break``;` `            ``}` `        ``}` `        ``if` `(!flag) {` `            ``return` `"-1"``;` `        ``}`   `        ``flag = ``false``;`   `        ``// Second digit of minutes can be from the range [0, 9]` `        ``for` `(i = ``9``; i >= ``0``; i--) {` `            ``if` `(hasDigit(hashMap, i)) {` `                ``flag = ``true``;` `                ``time += i;` `                ``break``;` `            ``}` `        ``}` `        ``if` `(!flag) {` `            ``return` `"-1"``;` `        ``}`   `        ``// Return the maximum possible time` `        ``return` `time;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `arr[] = { ``0``, ``0``, ``0``, ``9` `};` `        ``System.out.println(getMaxTime(arr));` `    ``}` `}`

## Python3

 `# Python3 implementation of the approach ` `from` `collections ``import` `defaultdict`   `# Function to return the updated frequency ` `# map for the array passed as argument ` `def` `getFrequencyMap(arr, n): ` `    `  `    ``hashMap ``=` `defaultdict(``lambda``:``0``) ` `    ``for` `i ``in` `range``(n): ` `        ``hashMap[arr[i]] ``+``=` `1` `        `  `    ``return` `hashMap ` `    `  `# Function that returns true if the passed ` `# digit is present in the map after ` `# decrementing it's frequency by 1 ` `def` `hasDigit(hashMap, digit): ` `    `  `    ``# If map contains the digit ` `    ``if` `hashMap[digit] > ``0``: ` `    `  `        ``# Decrement the frequency of` `        ``# the digit by 1 ` `        ``hashMap[digit] ``-``=` `1` `    `  `        ``# True here indicates that the ` `        ``# digit was found in the map ` `        ``return` `True` `    `  `    ``# Digit not found ` `    ``return` `False` `    `  `# Function to return the maximum possible ` `# time_value in 24-Hours format ` `def` `getMaxtime_value(arr, n): ` `    `  `    ``hashMap ``=` `getFrequencyMap(arr, n) ` `    ``flag ``=` `False` `    ``time_value ``=` `"" ` `    `  `    ``# First digit of hours can be` `    ``# from the range [0, 2] ` `    ``for` `i ``in` `range``(``2``, ``-``1``, ``-``1``): ` `        ``if` `hasDigit(hashMap, i) ``=``=` `True``: ` `            ``flag ``=` `True` `            ``time_value ``+``=` `str``(i)` `            ``break` `    `  `    ``# If no valid digit found ` `    ``if` `not` `flag:` `        ``return` `"-1"` `    `  `    ``flag ``=` `False` `    `  `    ``# If first digit of hours was chosen as 2 then ` `    ``# the second digit of hours can be ` `    ``# from the range [0, 3]` `    ``if``(time_value[``0``] ``=``=` `'2'``):` `        ``for` `i ``in` `range``(``3``, ``-``1``, ``-``1``):` `            ``if` `hasDigit(hashMap, i) ``=``=` `True``: ` `                ``flag ``=` `True` `                ``time_value ``+``=` `str``(i) ` `                ``break` `    `  `    ``# Else it can be from the range [0, 9]` `    ``else``:` `        ``for` `i ``in` `range``(``9``, ``-``1``, ``-``1``):` `            ``if` `hasDigit(hashMap, i) ``=``=` `True``: ` `                ``flag ``=` `True` `                ``time_value ``+``=` `str``(i) ` `                ``break` `            `  `    ``if` `not` `flag: ` `        ``return` `"-1"` `    `  `    ``# Hours and minutes separator ` `    ``time_value ``+``=` `":"` `    `  `    ``flag ``=` `False` `    `  `    ``# First digit of minutes can be` `    ``# from the range [0, 5] ` `    ``for` `i ``in` `range``(``5``, ``-``1``, ``-``1``): ` `        ``if` `hasDigit(hashMap, i) ``=``=` `True``: ` `            ``flag ``=` `True` `            ``time_value ``+``=` `str``(i) ` `            ``break` `        `  `    ``if` `not` `flag:` `        ``return` `"-1"` `    `  `    ``flag ``=` `False` `    `  `    ``# Second digit of minutes can be ` `    ``# from the range [0, 9] ` `    ``for` `i ``in` `range``(``9``, ``-``1``, ``-``1``): ` `        ``if` `hasDigit(hashMap, i) ``=``=` `True``: ` `            ``flag ``=` `True` `            ``time_value ``+``=` `str``(i) ` `            ``break` `        `  `    ``if` `not` `flag:` `        ``return` `"-1"` `    `  `    ``# Return the maximum possible ` `    ``# time_value ` `    ``return` `time_value ` `    `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"``: ` `    `  `    ``arr ``=` `[``0``, ``0``, ``0``, ``9``] ` `    ``n ``=` `len``(arr)` `    ``print``(getMaxtime_value(arr, n)) ` `    `  `# This code is contributed by ` `# Rituraj Jain`

## C#

 `// C# implementation of the approach` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG ` `{`   `    ``// Function to return the updated frequency map` `    ``// for the array passed as argument` `    ``static` `Dictionary<``int``, ``int``> getFrequencyMap(``int` `[]arr)` `    ``{` `        ``Dictionary<``int``, ``int``> hashMap = ``new` `Dictionary<``int``, ``int``>();` `        ``for` `(``int` `i = 0; i < arr.Length; i++)` `        ``{` `            ``if` `(hashMap.ContainsKey(arr[i]))` `            ``{` `                ``hashMap[arr[i]] = hashMap[arr[i]] + 1;` `            ``}` `            ``else` `            ``{` `                ``hashMap.Add(arr[i], 1);` `            ``}` `        ``}` `        ``return` `hashMap;` `    ``}`   `    ``// Function that returns true if the passed digit is present` `    ``// in the map after decrementing it's frequency by 1` `    ``static` `bool` `hasDigit(Dictionary<``int``, ``int``> hashMap, ``int` `digit)` `    ``{`   `        ``// If map contains the digit` `        ``if` `(hashMap.ContainsKey(digit) && hashMap[digit] > 0)` `        ``{`   `            ``// Decrement the frequency of the digit by 1` `            ``hashMap[digit] = hashMap[digit] - 1;`   `            ``// True here indicates that the ` `            ``// digit was found in the map` `            ``return` `true``;` `        ``}`   `        ``// Digit not found` `        ``return` `false``;` `    ``}`   `    ``// Function to return the maximum ` `    ``// possible time in 24-Hours format` `    ``static` `String getMaxTime(``int` `[]arr)` `    ``{` `        ``Dictionary<``int``, ``int``> hashMap = getFrequencyMap(arr);` `        ``int` `i;` `        ``bool` `flag;` `        ``String time = ``""``;`   `        ``flag = ``false``;`   `        ``// First digit of hours can be from the range [0, 2]` `        ``for` `(i = 2; i >= 0; i--) ` `        ``{` `            ``if` `(hasDigit(hashMap, i)) ` `            ``{` `                ``flag = ``true``;` `                ``time += i;` `                ``break``;` `            ``}` `        ``}`   `        ``// If no valid digit found` `        ``if` `(!flag)` `        ``{` `            ``return` `"-1"``;` `        ``}`   `        ``flag = ``false``;`   `        ``// If first digit of hours was chosen as 2 then` `        ``// the second digit of hours can be` `        ``// from the range [0, 3]` `        ``if` `(time[0] == ``'2'``) ` `        ``{` `            ``for` `(i = 3; i >= 0; i--) ` `            ``{` `                ``if` `(hasDigit(hashMap, i)) ` `                ``{` `                    ``flag = ``true``;` `                    ``time += i;` `                    ``break``;` `                ``}` `            ``}` `        ``}`   `        ``// Else it can be from the range [0, 9]` `        ``else` `        ``{` `            ``for` `(i = 9; i >= 0; i--)` `            ``{` `                ``if` `(hasDigit(hashMap, i)) ` `                ``{` `                    ``flag = ``true``;` `                    ``time += i;` `                    ``break``;` `                ``}` `            ``}` `        ``}` `        ``if` `(!flag)` `        ``{` `            ``return` `"-1"``;` `        ``}`   `        ``// Hours and minutes separator` `        ``time += ``":"``;`   `        ``flag = ``false``;`   `        ``// First digit of minutes can be from the range [0, 5]` `        ``for` `(i = 5; i >= 0; i--) ` `        ``{` `            ``if` `(hasDigit(hashMap, i))` `            ``{` `                ``flag = ``true``;` `                ``time += i;` `                ``break``;` `            ``}` `        ``}` `        ``if` `(!flag)` `        ``{` `            ``return` `"-1"``;` `        ``}`   `        ``flag = ``false``;`   `        ``// Second digit of minutes can be from the range [0, 9]` `        ``for` `(i = 9; i >= 0; i--) ` `        ``{` `            ``if` `(hasDigit(hashMap, i))` `            ``{` `                ``flag = ``true``;` `                ``time += i;` `                ``break``;` `            ``}` `        ``}` `        ``if` `(!flag)` `        ``{` `            ``return` `"-1"``;` `        ``}`   `        ``// Return the maximum possible time` `        ``return` `time;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``int` `[]arr = { 0, 0, 0, 9 };` `        ``Console.WriteLine(getMaxTime(arr));` `    ``}` `}`   `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output

`09:00`

Complexity Analysis:

• Time Complexity: O(n), since the loop runs from 0 to (n – 1).
• Auxiliary Space: O(n), since n extra space has been taken.

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