# Find the minimum number of moves to reach end of the array

Given an array arr[] of size N where every element is from the range [0, 9]. The task is to reach the last index of the array starting from the first index. From ith index we can move to (i – 1)th, (i + 1)th or to any jth index where j ? i and arr[j] = arr[i].

Examples:

Input: arr[] = {1, 2, 3, 4, 1, 5}
Output:
First move from the 0th index to the 4th index
and then from the 4th index to the 5th.

Input: arr[] = {1, 2, 3, 4, 5, 1}
Output:

Approach: Construct the graph from the given array where the number of nodes in the graph will be equal to the size of the array. Every node of the graph i will be connected to the (i 1)th node, (i + 1)th node and a node j such that i ? j and arr[i] = arr[j]. Now, the answer will be the minimum edges in the path from index 0 to index N – 1 in the constructed graph.
The graph for the array arr[] = {1, 2, 3, 4, 1, 5} is shown in the image below:

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;` `#define N 100005`   `vector<``int``> gr[N];`   `// Function to add edge` `void` `add_edge(``int` `u, ``int` `v)` `{` `    ``gr[u].push_back(v);` `    ``gr[v].push_back(u);` `}`   `// Function to return the minimum path` `// from 0th node to the (n - 1)th node` `int` `dijkstra(``int` `n)` `{` `    ``// To check whether an edge is visited or not` `    ``// and to keep distance of vertex from 0th index` `    ``int` `vis[n] = { 0 }, dist[n];`   `    ``for` `(``int` `i = 0; i < n; i++)` `        ``dist[i] = INT_MAX;`   `    ``// Make 0th index visited and distance is zero` `    ``vis[0] = 1;` `    ``dist[0] = 0;`   `    ``// Take a queue and push first element` `    ``queue<``int``> q;` `    ``q.push(0);`   `    ``// Continue this until all vertices are visited` `    ``while` `(!q.empty()) {` `        ``int` `x = q.front();`   `        ``// Remove the first element` `        ``q.pop();`   `        ``for` `(``int` `i = 0; i < gr[x].size(); i++) {`   `            ``// Check if a vertex is already visited or not` `            ``if` `(vis[gr[x][i]] == 1)` `                ``continue``;`   `            ``// Make vertex visited` `            ``vis[gr[x][i]] = 1;`   `            ``// Store the number of moves to reach element` `            ``dist[gr[x][i]] = dist[x] + 1;`   `            ``// Push the current vertex into the queue` `            ``q.push(gr[x][i]);` `        ``}` `    ``}`   `    ``// Return the minimum number of` `    ``// moves to reach (n - 1)th index` `    ``return` `dist[n - 1];` `}`   `// Function to return the minimum number of moves` `// required to reach the end of the array` `int` `Min_Moves(``int` `a[], ``int` `n)` `{`   `    ``// To store the positions of each element` `    ``vector<``int``> fre[10];` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``if` `(i != n - 1)` `            ``add_edge(i, i + 1);`   `        ``fre[a[i]].push_back(i);` `    ``}`   `    ``// Add edge between same elements` `    ``for` `(``int` `i = 0; i < 10; i++) {` `        ``for` `(``int` `j = 0; j < fre[i].size(); j++) {` `            ``for` `(``int` `k = j + 1; k < fre[i].size(); k++) {` `                ``if` `(fre[i][j] + 1 != fre[i][k]` `                    ``and fre[i][j] - 1 != fre[i][k]) {` `                    ``add_edge(fre[i][j], fre[i][k]);` `                ``}` `            ``}` `        ``}` `    ``}`   `    ``// Return the required minimum number of moves` `    ``return` `dijkstra(n);` `}`   `// Driver code` `int` `main()` `{` `    ``int` `a[] = { 1, 2, 3, 4, 1, 5 };` `    ``int` `n = ``sizeof``(a) / ``sizeof``(a[0]);`   `    ``cout << Min_Moves(a, n);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach` `import` `java.io.*;` `import` `java.util.*;`   `class` `GFG{` `    `  `static` `ArrayList<` `       ``ArrayList> gr = ``new` `ArrayList<` `                                    ``ArrayList>();` `static` `int` `N = ``100005``;`   `// Function to add edge ` `static` `void` `add_edge(``int` `u, ``int` `v) ` `{` `    ``for``(``int` `i = ``0``; i < N; i++)` `    ``{` `        ``gr.add(``new` `ArrayList());` `    ``}` `    ``gr.get(u).add(v);` `    ``gr.get(v).add(u);` `}`   `// Function to return the minimum path ` `// from 0th node to the (n - 1)th node ` `static` `int` `dijkstra(``int` `n)` `{` `    `  `    ``// To check whether an edge is visited` `    ``// or not and to keep distance of ` `    ``// vertex from 0th index ` `    ``int``[] vis = ``new` `int``[n];` `    ``Arrays.fill(vis, ``0``);` `    `  `    ``int``[] dist = ``new` `int``[n];` `    ``for``(``int` `i = ``0``; i < n; i++)` `    ``{` `        ``dist[i] = Integer.MAX_VALUE;` `    ``}` `    `  `    ``// Make 0th index visited and ` `    ``// distance is zero ` `    ``vis[``0``] = ``1``; ` `    ``dist[``0``] = ``0``;` `    `  `    ``// Take a queue and push first element ` `    ``Queue q = ``new` `LinkedList<>();` `    ``q.add(``0``);` `    `  `    ``// Continue this until all vertices ` `    ``// are visited ` `    ``while` `(q.size() > ``0``)` `    ``{` `        `  `        ``// Remove the first element ` `        ``int` `x = q.poll();` `        ``for``(``int` `i = ``0``; i < gr.get(x).size(); i++)` `        ``{` `            `  `            ``// Check if a vertex is already ` `            ``// visited or not ` `            ``if` `(vis[gr.get(x).get(i)] == ``1``)` `            ``{` `                ``continue``;` `            ``}` `            `  `            ``// Make vertex visited` `            ``vis[gr.get(x).get(i)] = ``1``;` `            `  `            ``// Store the number of moves to ` `            ``// reach element` `            ``dist[gr.get(x).get(i)] = dist[x] + ``1``;` `            `  `            ``// Push the current vertex into ` `            ``// the queue` `            ``q.add(gr.get(x).get(i));` `        ``}` `    ``}` `    `  `    ``// Return the minimum number of ` `    ``// moves to reach (n - 1)th index` `    ``return` `dist[n - ``1``];` `}`   `// Function to return the minimum number of moves ` `// required to reach the end of the array ` `static` `int` `Min_Moves(``int``[] a, ``int` `n) ` `{` `    `  `    ``// To store the positions of each element` `    ``ArrayList<` `    ``ArrayList> fre = ``new` `ArrayList<` `                                  ``ArrayList>();` `    ``for``(``int` `i = ``0``; i < ``10``; i++)` `    ``{` `        ``fre.add(``new` `ArrayList());` `    ``}` `    ``for``(``int` `i = ``0``; i < n; i++)` `    ``{` `        ``if` `(i != n - ``1``)` `        ``{` `            ``add_edge(i, i + ``1``);` `        ``}` `        ``fre.get(a[i]).add(i);` `    ``}` `    `  `    ``// Add edge between same elements ` `    ``for``(``int` `i = ``0``; i < ``10``; i++)` `    ``{` `        ``for``(``int` `j = ``0``; ` `                ``j < fre.get(i).size(); ` `                ``j++) ` `        ``{` `            ``for``(``int` `k = j + ``1``; ` `                    ``k < fre.get(i).size(); ` `                    ``k++)` `            ``{` `                ``if` `(fre.get(i).get(j) + ``1` `!= ` `                    ``fre.get(i).get(k) && ` `                    ``fre.get(i).get(j) - ``1` `!= ` `                    ``fre.get(i).get(k))` `                ``{` `                    ``add_edge(fre.get(i).get(j),` `                             ``fre.get(i).get(k));` `                ``}` `            ``}` `        ``}` `    ``}` `    `  `    ``// Return the required minimum ` `    ``// number of moves ` `    ``return` `dijkstra(n);` `}`   `// Driver code ` `public` `static` `void` `main(String[] args) ` `{` `    ``int``[] a = { ``1``, ``2``, ``3``, ``4``, ``1``, ``5` `};` `    ``int` `n = a.length;` `    `  `    ``System.out.println(Min_Moves(a, n));` `}` `}`   `// This code is contributed by avanitrachhadiya2155`

## Python3

 `# Python3 implementation of the approach` `from` `collections ``import` `deque` `N ``=` `100005`   `gr ``=` `[[] ``for` `i ``in` `range``(N)]`   `# Function to add edge` `def` `add_edge(u, v):` `    ``gr[u].append(v)` `    ``gr[v].append(u)`   `# Function to return the minimum path` `# from 0th node to the (n - 1)th node` `def` `dijkstra(n):` `    `  `    ``# To check whether an edge is visited` `    ``# or not and to keep distance of vertex` `    ``# from 0th index` `    ``vis ``=` `[``0` `for` `i ``in` `range``(n)]` `    ``dist ``=` `[``10``*``*``9` `for` `i ``in` `range``(n)]`   `    ``# Make 0th index visited and ` `    ``# distance is zero` `    ``vis[``0``] ``=` `1` `    ``dist[``0``] ``=` `0`   `    ``# Take a queue and ` `    ``# append first element` `    ``q ``=` `deque()` `    ``q.append(``0``)`   `    ``# Continue this until  ` `    ``# all vertices are visited` `    ``while` `(``len``(q) > ``0``):` `        ``x ``=` `q.popleft()`   `        ``# Remove the first element` `        ``for` `i ``in` `gr[x]:`   `            ``# Check if a vertex is ` `            ``# already visited or not` `            ``if` `(vis[i] ``=``=` `1``):` `                ``continue`   `            ``# Make vertex visited` `            ``vis[i] ``=` `1`   `            ``# Store the number of moves ` `            ``# to reach element` `            ``dist[i] ``=` `dist[x] ``+` `1`   `            ``# Push the current vertex` `            ``# into the queue` `            ``q.append(i)`   `    ``# Return the minimum number of` `    ``# moves to reach (n - 1)th index` `    ``return` `dist[n ``-` `1``]`   `# Function to return the minimum number of moves` `# required to reach the end of the array` `def` `Min_Moves(a, n):`   `    ``# To store the positions of each element` `    ``fre ``=` `[[] ``for` `i ``in` `range``(``10``)]` `    ``for` `i ``in` `range``(n):` `        ``if` `(i !``=` `n ``-` `1``):` `            ``add_edge(i, i ``+` `1``)`   `        ``fre[a[i]].append(i)`   `    ``# Add edge between same elements` `    ``for` `i ``in` `range``(``10``):` `        ``for` `j ``in` `range``(``len``(fre[i])):` `            ``for` `k ``in` `range``(j ``+` `1``,``len``(fre[i])):` `                ``if` `(fre[i][j] ``+` `1` `!``=` `fre[i][k] ``and` `                    ``fre[i][j] ``-` `1` `!``=` `fre[i][k]):` `                    ``add_edge(fre[i][j], fre[i][k])`   `    ``# Return the required ` `    ``# minimum number of moves` `    ``return` `dijkstra(n)`   `# Driver code` `a ``=` `[``1``, ``2``, ``3``, ``4``, ``1``, ``5``]` `n ``=` `len``(a)`   `print``(Min_Moves(a, n))`   `# This code is contributed by Mohit Kumar`

## C#

 `// C# implementation of the approach` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG` `{` `    ``static` `List> gr = ``new` `List>();` `    ``static` `int` `N = 100005;` `  `  `    ``// Function to add edge ` `    ``static` `void` `add_edge(``int` `u, ``int` `v)` `    ``{` `        ``for``(``int` `i = 0; i < N; i++)` `        ``{` `            ``gr.Add(``new` `List<``int``>());` `        ``}` `        ``gr[u].Add(v);` `        ``gr[v].Add(u);` `    ``}` `  `  `    ``// Function to return the minimum path ` `    ``// from 0th node to the (n - 1)th node ` `    ``static` `int` `dijkstra(``int` `n)` `    ``{` `      `  `        ``// To check whether an edge is visited` `        ``// or not and to keep distance of ` `        ``// vertex from 0th index` `        ``int``[] vis = ``new` `int``[n];` `        ``Array.Fill(vis, 0);` `        ``int``[] dist = ``new` `int``[n];` `        ``for``(``int` `i = 0; i < n; i++)` `        ``{` `            ``dist[i] = Int32.MaxValue;` `        ``}` `      `  `        ``// Make 0th index visited and ` `        ``// distance is zero ` `        ``vis[0] = 1; ` `        ``dist[0] = 0;` `        `  `        ``// Take a queue and push first element ` `        ``Queue<``int``> q = ``new` `Queue<``int``>();` `        ``q.Enqueue(0);` `        `  `        ``// Continue this until all vertices ` `        ``// are visited ` `        ``while``(q.Count > 0)` `        ``{` `          `  `            ``// Remove the first element ` `            ``int` `x = q.Dequeue();` `            ``for``(``int` `i = 0; i < gr[x].Count; i++ )` `            ``{` `              `  `                ``// Check if a vertex is already ` `                ``// visited or not ` `                ``if``(vis[gr[x][i]] == 1)` `                ``{` `                    ``continue``;` `                ``}` `              `  `                ``// Make vertex visited` `                ``vis[gr[x][i]] = 1;` `              `  `                ``// Store the number of moves to ` `                ``// reach element` `                ``dist[gr[x][i]] = dist[x] + 1;` `                `  `                ``// Push the current vertex into ` `                ``// the queue` `                ``q.Enqueue(gr[x][i]);` `            ``}` `        ``}` `      `  `        ``// Return the minimum number of ` `        ``// moves to reach (n - 1)th index` `        ``return` `dist[n - 1];` `    ``}` `  `  `    ``// Function to return the minimum number of moves ` `    ``// required to reach the end of the array ` `    ``static` `int` `Min_Moves(``int``[] a, ``int` `n) ` `    ``{` `      `  `        ``// To store the positions of each element` `        ``List> fre = ``new` `List>();` `        ``for``(``int` `i = 0; i < 10; i++)` `        ``{` `            ``fre.Add(``new` `List<``int``>());          ` `        ``}` `        ``for``(``int` `i = 0; i < n; i++)` `        ``{` `            ``if` `(i != n - 1)` `            ``{` `                ``add_edge(i, i + 1);` `            ``}` `            ``fre[a[i]].Add(i);` `        ``}` `      `  `        ``// Add edge between same elements ` `        ``for``(``int` `i = 0; i < 10; i++)` `        ``{` `            ``for``(``int` `j = 0; j < fre[i].Count; j++)` `            ``{` `                ``for``(``int` `k = j + 1; k < fre[i].Count; k++)` `                ``{` `                    ``if``(fre[i][j] + 1 != fre[i][k] && ` `                       ``fre[i][j] - 1 != fre[i][k])` `                    ``{` `                        ``add_edge(fre[i][j], fre[i][k]);` `                    ``}` `                ``}` `            ``}` `        ``}` `      `  `        ``// Return the required minimum ` `        ``// number of moves ` `        ``return` `dijkstra(n);` `    ``}` `  `  `    ``// Driver code ` `    ``static` `public` `void` `Main ()` `    ``{` `        ``int``[] a = { 1, 2, 3, 4, 1, 5 };` `        ``int` `n = a.Length;` `        ``Console.WriteLine(Min_Moves(a, n));` `    ``}` `}`   `// This code is contributed by rag2127`

## Javascript

 ``

Output:

`2`

Time complexity: O(n2)

Auxiliary Space: O(n)

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