# Find minimum length sub-array which has given sub-sequence in it

• Difficulty Level : Hard
• Last Updated : 24 May, 2021

Given an array arr[] of N elements, the task is to find the length of the smallest sub-array which has the sequence {0, 1, 2, 3, 4} as a sub-sequence in it.

Examples:

Input: arr[] = {0, 1, 2, 3, 4, 2, 0, 3, 4}
Output:
The required Subarray is {0, 1, 2, 3, 4} with minimum length.
The entire array also includes the sequence
but it is not minimum in length.

Input: arr[] = {0, 1, 1, 0, 1, 2, 0, 3, 4}
Output: 6

Approach:

• Maintain an array pref[] of size 5 (equal to the size of the sequence) where pref[i] stores the count of i in the given array till now.
• We can increase the count of pref for any number only if pref[Array[i] – 1] > 0. This is because, in order to have the complete sequence as a sub-sequence of the array, all the previous elements of the sequence must occur before the current. Also, store the indices of these elements found so far.
• Whenever we witness 4 i.e., the possible end of the sub-sequence and pref > 0 implies that we have found the sequence in our array. Now mark that index as the end as well as the start point and for all other numbers in sequence from 3 to 0. Apply binary search to find the closest index to the next element of the sequence, which will give us the size of the current valid sub-array.
• The answer is the minimum size of all the valid sub-arrays found in the previous step.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `#define MAX_INT 1000000` `// Function to return the minimum length``// of a sub-array which contains``// {0, 1, 2, 3, 4} as a sub-sequence``int` `solve(``int` `Array[], ``int` `N)``{``    ``// To store the indices where 0, 1, 2,``    ``// 3 and 4 are present``    ``vector<``int``> pos;` `    ``// To store if there exist a valid prefix``    ``// of sequence in array``    ``int` `pref = { 0 };` `    ``// Base Case``    ``if` `(Array == 0) {``        ``pref = 1;``        ``pos.push_back(0);``    ``}` `    ``int` `ans = MAX_INT;` `    ``for` `(``int` `i = 1; i < N; i++) {` `        ``// If current element is 0``        ``if` `(Array[i] == 0) {` `            ``// Update the count of 0s till now``            ``pref++;` `            ``// Push the index of the new 0``            ``pos.push_back(i);``        ``}``        ``else` `{` `            ``// To check if previous element of the``            ``// given sequence is found till now``            ``if` `(pref[Array[i] - 1] > 0) {``                ``pref[Array[i]]++;``                ``pos[Array[i]].push_back(i);` `                ``// If it is the end of sequence``                ``if` `(Array[i] == 4) {``                    ``int` `end = i;``                    ``int` `start = i;` `                    ``// Iterate for other elements of the sequence``                    ``for` `(``int` `j = 3; j >= 0; j--) {``                        ``int` `s = 0;``                        ``int` `e = pos[j].size() - 1;``                        ``int` `temp = -1;` `                        ``// Binary Search to find closest occurrence``                        ``// less than equal to starting point``                        ``while` `(s <= e) {``                            ``int` `m = (s + e) / 2;``                            ``if` `(pos[j][m] <= start) {``                                ``temp = pos[j][m];``                                ``s = m + 1;``                            ``}``                            ``else` `{``                                ``e = m - 1;``                            ``}``                        ``}` `                        ``// Update the starting point``                        ``start = temp;``                    ``}` `                    ``ans = min(ans, end - start + 1);``                ``}``            ``}``        ``}``    ``}` `    ``return` `ans;``}` `// Driver code``int` `main()``{``    ``int` `Array[] = { 0, 1, 2, 3, 4, 2, 0, 3, 4 };``    ``int` `N = ``sizeof``(Array) / ``sizeof``(Array);` `    ``cout << solve(Array, N);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{``static` `int` `MAX_INT = ``1000000``;` `// Function to return the minimum length``// of a sub-array which contains``// {0, 1, 2, 3, 4} as a sub-sequence``static` `int` `solve(``int``[] array, ``int` `N)``{` `    ``// To store the indices where 0, 1, 2,``    ``// 3 and 4 are present``    ``int``[][] pos = ``new` `int``[``5``][``10000``];` `    ``// To store if there exist a valid prefix``    ``// of sequence in array``    ``int``[] pref = ``new` `int``[``5``];` `    ``// Base Case``    ``if` `(array[``0``] == ``0``)``    ``{``        ``pref[``0``] = ``1``;``        ``pos[``0``][pos[``0``].length - ``1``] = ``0``;``    ``}` `    ``int` `ans = MAX_INT;` `    ``for` `(``int` `i = ``1``; i < N; i++)``    ``{` `        ``// If current element is 0``        ``if` `(array[i] == ``0``)``        ``{` `            ``// Update the count of 0s till now``            ``pref[``0``]++;` `            ``// Push the index of the new 0``            ``pos[``0``][pos[``0``].length - ``1``] = i;``        ``}``        ` `        ``else``        ``{` `            ``// To check if previous element of the``            ``// given sequence is found till now``            ``if` `(pref[array[i] - ``1``] > ``0``)``            ``{``                ``pref[array[i]]++;``                ``pos[array[i]][pos[array[i]].length - ``1``] = i;` `                ``// If it is the end of sequence``                ``if` `(array[i] == ``4``)``                ``{``                    ``int` `end = i;``                    ``int` `start = i;` `                    ``// Iterate for other elements of the sequence``                    ``for` `(``int` `j = ``3``; j >= ``0``; j--)``                    ``{``                        ``int` `s = ``0``;``                        ``int` `e = pos[j].length - ``1``;``                        ``int` `temp = -``1``;` `                        ``// Binary Search to find closest occurrence``                        ``// less than equal to starting point``                        ``while` `(s <= e)``                        ``{``                            ``int` `m = (s + e) / ``2``;``                            ``if` `(pos[j][m] <= start)``                            ``{``                                ``temp = pos[j][m];``                                ``s = m + ``1``;``                            ``}``                            ``else``                                ``e = m - ``1``;``                        ``}` `                        ``// Update the starting point``                        ``start = temp;``                    ``}``                    ``ans = Math.min(ans, end - start + ``1``);``                ``}``            ``}``        ``}``    ``}``    ``return` `ans;``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int``[] array = { ``0``, ``1``, ``2``, ``3``, ``4``, ``2``, ``0``, ``3``, ``4` `};``    ``int` `N = array.length;` `    ``System.out.println(solve(array, N));``}``}` `// This code is contributed by``// sanjeev2552`

## Python3

 `# Python3 implementation of the approach` `MAX_INT``=``1000000` `# Function to return the minimum length``# of a sub-array which contains``# 0, 1, 2, 3, 4 as a sub-sequence``def` `solve(Array, N):` `    ``# To store the indices where 0, 1, 2,``    ``# 3 and 4 are present``    ``pos``=``[[] ``for` `i ``in` `range``(``5``)]` `    ``# To store if there exist a valid prefix``    ``# of sequence in array``    ``pref``=``[``0` `for` `i ``in` `range``(``5``)]` `    ``# Base Case``    ``if` `(Array[``0``] ``=``=` `0``):``        ``pref[``0``] ``=` `1``        ``pos[``0``].append(``0``)``    `  `    ``ans ``=` `MAX_INT` `    ``for` `i ``in` `range``(N):` `        ``# If current element is 0``        ``if` `(Array[i] ``=``=` `0``):` `            ``# Update the count of 0s till now``            ``pref[``0``]``+``=``1` `            ``# Push the index of the new 0``            ``pos[``0``].append(i)``        ` `        ``else` `:` `            ``# To check if previous element of the``            ``# given sequence is found till now``            ``if` `(pref[Array[i] ``-` `1``] > ``0``):``                ``pref[Array[i]]``+``=``1``                ``pos[Array[i]].append(i)` `                ``# If it is the end of sequence``                ``if` `(Array[i] ``=``=` `4``) :``                    ``end ``=` `i``                    ``start ``=` `i` `                    ``# Iterate for other elements of the sequence``                    ``for` `j ``in` `range``(``3``,``-``1``,``-``1``):``                        ``s ``=` `0``                        ``e ``=` `len``(pos[j]) ``-` `1``                        ``temp ``=` `-``1` `                        ``# Binary Search to find closest occurrence``                        ``# less than equal to starting point``                        ``while` `(s <``=` `e):``                            ``m ``=` `(s ``+` `e) ``/``/` `2``                            ``if` `(pos[j][m] <``=` `start) :``                                ``temp ``=` `pos[j][m]``                                ``s ``=` `m ``+` `1``                            ` `                            ``else` `:``                                ``e ``=` `m ``-` `1``                            ` `                        `  `                        ``# Update the starting point``                        ``start ``=` `temp``                    `  `                    ``ans ``=` `min``(ans, end ``-` `start ``+` `1``)``                ` `            ` `        ` `    `  `    ``return` `ans` `# Driver code` `Array ``=` `[ ``0``, ``1``, ``2``, ``3``, ``4``, ``2``, ``0``, ``3``, ``4``]``N ``=` `len``(Array)` `print``(solve(Array, N))` `# This code is contributed by mohit kumar 29`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{``static` `int` `MAX_INT = 1000000;`` ` `// Function to return the minimum length``// of a sub-array which contains``// {0, 1, 2, 3, 4} as a sub-sequence``static` `int` `solve(``int``[] array, ``int` `N)``{`` ` `    ``// To store the indices where 0, 1, 2,``    ``// 3 and 4 are present``    ``int``[,] pos = ``new` `int``[5,10000];`` ` `    ``// To store if there exist a valid prefix``    ``// of sequence in array``    ``int``[] pref = ``new` `int``;`` ` `    ``// Base Case``    ``if` `(array == 0)``    ``{``        ``pref = 1;``        ``pos[0,pos.GetLength(0)- 1] = 0;``    ``}`` ` `    ``int` `ans = MAX_INT;`` ` `    ``for` `(``int` `i = 1; i < N; i++)``    ``{`` ` `        ``// If current element is 0``        ``if` `(array[i] == 0)``        ``{`` ` `            ``// Update the count of 0s till now``            ``pref++;`` ` `            ``// Push the index of the new 0``            ``pos[0,pos.GetLength(0) - 1] = i;``        ``}``         ` `        ``else``        ``{`` ` `            ``// To check if previous element of the``            ``// given sequence is found till now``            ``if` `(pref[array[i] - 1] > 0)``            ``{``                ``pref[array[i]]++;``                ``pos[array[i],pos.GetLength(1) - 1] = i;`` ` `                ``// If it is the end of sequence``                ``if` `(array[i] == 4)``                ``{``                    ``int` `end = i;``                    ``int` `start = i;`` ` `                    ``// Iterate for other elements of the sequence``                    ``for` `(``int` `j = 3; j >= 0; j--)``                    ``{``                        ``int` `s = 0;``                        ``int` `e = pos.GetLength(1) - 1;``                        ``int` `temp = -1;`` ` `                        ``// Binary Search to find closest occurrence``                        ``// less than equal to starting point``                        ``while` `(s <= e)``                        ``{``                            ``int` `m = (s + e) / 2;``                            ``if` `(pos[j,m] <= start)``                            ``{``                                ``temp = pos[j,m];``                                ``s = m + 1;``                            ``}``                            ``else``                                ``e = m - 1;``                        ``}`` ` `                        ``// Update the starting point``                        ``start = temp;``                    ``}``                    ``ans = Math.Min(ans, end - start + 1);``                ``}``            ``}``        ``}``    ``}``    ``return` `ans;``}`` ` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int``[] array = { 0, 1, 2, 3, 4, 2, 0, 3, 4 };``    ``int` `N = array.Length;`` ` `    ``Console.WriteLine(solve(array, N));``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output:

`5`

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