Gegeven een array die getallen uit één cijfer bevat, ervan uitgaande dat we op de eerste index staan, moeten we het einde van de array bereiken met een minimaal aantal stappen, waarbij we in één stap naar aangrenzende indices kunnen springen of naar een positie met dezelfde waarde kunnen springen.
Met andere woorden, als we ons op index i bevinden, kun je in één stap arr[i-1] of arr[i+1] of arr[K] bereiken, zodat arr[K] = arr[i] (waarde van arr[K] is hetzelfde als arr[i])
Voorbeelden:
Input : arr[] = {5 4 2 5 0} Output : 2 Explanation : Total 2 step required. We start from 5(0) in first step jump to next 5 and in second step we move to value 0 (End of arr[]). Input : arr[] = [0 1 2 3 4 5 6 7 5 4 3 6 0 1 2 3 4 5 7] Output : 5 Explanation : Total 5 step required. 0(0) -> 0(12) -> 6(11) -> 6(6) -> 7(7) -> (18) (inside parenthesis indices are shown) Dit probleem kan worden opgelost met behulp van BFS . We kunnen de gegeven array beschouwen als een ongewogen grafiek waarbij elk hoekpunt twee randen heeft naar volgende en vorige array-elementen en meer randen naar array-elementen met dezelfde waarden. Voor een snelle verwerking van het derde type randen houden we er nu 10 aan vectoren waarin alle indices worden opgeslagen waarin de cijfers 0 tot en met 9 aanwezig zijn. In het bovenstaande voorbeeld slaat de vector die overeenkomt met 0 [0 12] 2 indices op waarin 0 is opgetreden in een gegeven array.
Er wordt een andere Booleaanse array gebruikt, zodat we dezelfde index niet vaker dan één keer bezoeken. Omdat we BFS gebruiken en BFS niveau voor niveau verloopt, zijn optimale minimale stappen gegarandeerd.
Uitvoering:
C++// C++ program to find minimum jumps to reach end // of array #include
// Java program to find minimum jumps // to reach end of array import java.util.*; class GFG { // Method returns minimum step // to reach end of array static int getMinStepToReachEnd(int arr[] int N) { // visit boolean array checks whether // current index is previously visited boolean []visit = new boolean[N]; // distance array stores distance of // current index from starting index int []distance = new int[N]; // digit vector stores indices where a // particular number resides Vector<Integer> []digit = new Vector[10]; for(int i = 0; i < 10; i++) digit[i] = new Vector<>(); // In starting all index are unvisited for(int i = 0; i < N; i++) visit[i] = false; // storing indices of each number // in digit vector for (int i = 1; i < N; i++) digit[arr[i]].add(i); // for starting index distance will be zero distance[0] = 0; visit[0] = true; // Creating a queue and inserting index 0. Queue<Integer> q = new LinkedList<>(); q.add(0); // loop until queue in not empty while(!q.isEmpty()) { // Get an item from queue q. int idx = q.peek(); q.remove(); // If we reached to last // index break from loop if (idx == N - 1) break; // Find value of dequeued index int d = arr[idx]; // looping for all indices with value as d. for (int i = 0; i < digit[d].size(); i++) { int nextidx = digit[d].get(i); if (!visit[nextidx]) { visit[nextidx] = true; q.add(nextidx); // update the distance of this nextidx distance[nextidx] = distance[idx] + 1; } } // clear all indices for digit d // because all of them are processed digit[d].clear(); // checking condition for previous index if (idx - 1 >= 0 && !visit[idx - 1]) { visit[idx - 1] = true; q.add(idx - 1); distance[idx - 1] = distance[idx] + 1; } // checking condition for next index if (idx + 1 < N && !visit[idx + 1]) { visit[idx + 1] = true; q.add(idx + 1); distance[idx + 1] = distance[idx] + 1; } } // N-1th position has the final result return distance[N - 1]; } // Driver Code public static void main(String []args) { int arr[] = {0 1 2 3 4 5 6 7 5 4 3 6 0 1 2 3 4 5 7}; int N = arr.length; System.out.println(getMinStepToReachEnd(arr N)); } } // This code is contributed by 29AjayKumar
# Python 3 program to find minimum jumps to reach end# of array # Method returns minimum step to reach end of array def getMinStepToReachEnd(arrN): # visit boolean array checks whether current index # is previously visited visit = [False for i in range(N)] # distance array stores distance of current # index from starting index distance = [0 for i in range(N)] # digit vector stores indices where a # particular number resides digit = [[0 for i in range(N)] for j in range(10)] # storing indices of each number in digit vector for i in range(1N): digit[arr[i]].append(i) # for starting index distance will be zero distance[0] = 0 visit[0] = True # Creating a queue and inserting index 0. q = [] q.append(0) # loop until queue in not empty while(len(q)> 0): # Get an item from queue q. idx = q[0] q.remove(q[0]) # If we reached to last index break from loop if (idx == N-1): break # Find value of dequeued index d = arr[idx] # looping for all indices with value as d. for i in range(len(digit[d])): nextidx = digit[d][i] if (visit[nextidx] == False): visit[nextidx] = True q.append(nextidx) # update the distance of this nextidx distance[nextidx] = distance[idx] + 1 # clear all indices for digit d because all # of them are processed # checking condition for previous index if (idx-1 >= 0 and visit[idx - 1] == False): visit[idx - 1] = True q.append(idx - 1) distance[idx - 1] = distance[idx] + 1 # checking condition for next index if (idx + 1 < N and visit[idx + 1] == False): visit[idx + 1] = True q.append(idx + 1) distance[idx + 1] = distance[idx] + 1 # N-1th position has the final result return distance[N - 1] # driver code to test above methods if __name__ == '__main__': arr = [0 1 2 3 4 5 6 7 5 4 3 6 0 1 2 3 4 5 7] N = len(arr) print(getMinStepToReachEnd(arr N)) # This code is contributed by # Surendra_Gangwar
// C# program to find minimum jumps // to reach end of array using System; using System.Collections.Generic; class GFG { // Method returns minimum step // to reach end of array static int getMinStepToReachEnd(int []arr int N) { // visit boolean array checks whether // current index is previously visited bool []visit = new bool[N]; // distance array stores distance of // current index from starting index int []distance = new int[N]; // digit vector stores indices where a // particular number resides List<int> []digit = new List<int>[10]; for(int i = 0; i < 10; i++) digit[i] = new List<int>(); // In starting all index are unvisited for(int i = 0; i < N; i++) visit[i] = false; // storing indices of each number // in digit vector for (int i = 1; i < N; i++) digit[arr[i]].Add(i); // for starting index distance will be zero distance[0] = 0; visit[0] = true; // Creating a queue and inserting index 0. Queue<int> q = new Queue<int>(); q.Enqueue(0); // loop until queue in not empty while(q.Count != 0) { // Get an item from queue q. int idx = q.Peek(); q.Dequeue(); // If we reached to last // index break from loop if (idx == N - 1) break; // Find value of dequeued index int d = arr[idx]; // looping for all indices with value as d. for (int i = 0; i < digit[d].Count; i++) { int nextidx = digit[d][i]; if (!visit[nextidx]) { visit[nextidx] = true; q.Enqueue(nextidx); // update the distance of this nextidx distance[nextidx] = distance[idx] + 1; } } // clear all indices for digit d // because all of them are processed digit[d].Clear(); // checking condition for previous index if (idx - 1 >= 0 && !visit[idx - 1]) { visit[idx - 1] = true; q.Enqueue(idx - 1); distance[idx - 1] = distance[idx] + 1; } // checking condition for next index if (idx + 1 < N && !visit[idx + 1]) { visit[idx + 1] = true; q.Enqueue(idx + 1); distance[idx + 1] = distance[idx] + 1; } } // N-1th position has the final result return distance[N - 1]; } // Driver Code public static void Main(String []args) { int []arr = {0 1 2 3 4 5 6 7 5 4 3 6 0 1 2 3 4 5 7}; int N = arr.Length; Console.WriteLine(getMinStepToReachEnd(arr N)); } } // This code is contributed by PrinciRaj1992
<script> // Javascript program to find minimum jumps // to reach end of array // Method returns minimum step // to reach end of array function getMinStepToReachEnd(arrN) { // visit boolean array checks whether // current index is previously visited let visit = new Array(N); // distance array stores distance of // current index from starting index let distance = new Array(N); // digit vector stores indices where a // particular number resides let digit = new Array(10); for(let i = 0; i < 10; i++) digit[i] = []; // In starting all index are unvisited for(let i = 0; i < N; i++) visit[i] = false; // storing indices of each number // in digit vector for (let i = 1; i < N; i++) digit[arr[i]].push(i); // for starting index distance will be zero distance[0] = 0; visit[0] = true; // Creating a queue and inserting index 0. let q = []; q.push(0); // loop until queue in not empty while(q.length!=0) { // Get an item from queue q. let idx = q.shift(); // If we reached to last // index break from loop if (idx == N - 1) break; // Find value of dequeued index let d = arr[idx]; // looping for all indices with value as d. for (let i = 0; i < digit[d].length; i++) { let nextidx = digit[d][i]; if (!visit[nextidx]) { visit[nextidx] = true; q.push(nextidx); // update the distance of this nextidx distance[nextidx] = distance[idx] + 1; } } // clear all indices for digit d // because all of them are processed digit[d]=[]; // checking condition for previous index if (idx - 1 >= 0 && !visit[idx - 1]) { visit[idx - 1] = true; q.push(idx - 1); distance[idx - 1] = distance[idx] + 1; } // checking condition for next index if (idx + 1 < N && !visit[idx + 1]) { visit[idx + 1] = true; q.push(idx + 1); distance[idx + 1] = distance[idx] + 1; } } // N-1th position has the final result return distance[N - 1]; } // Driver Code let arr=[0 1 2 3 4 5 6 7 5 4 3 6 0 1 2 3 4 5 7]; let N = arr.length; document.write(getMinStepToReachEnd(arr N)); // This code is contributed by rag2127 </script>
Uitvoer
5
Tijdcomplexiteit: O(N) waarbij N het aantal elementen in de array is.
Ruimtecomplexiteit: O(N) waarbij N het aantal elementen in de array is. We gebruiken een afstands- en bezoekarray van grootte N en een wachtrij van grootte N om de indices van de array op te slaan.