Count number of ways to jump to reach end

Given an array of numbers where each element represents the max number of jumps that can be made forward from that element. For each array element, count number of ways jumps can be made from that element to reach the end of the array. If an element is 0, then move cannot be made through that element. The element that cannot reach to the end should have a count “-1”.

Examples:

Input : {3, 2, 0, 1}
Output : 2 1 -1 0
For 3 number of steps or jumps that 
can be taken are 1, 2 or 3. The different ways are:
3 -> 2 -> 1
3 -> 1

For 2 number of steps or jumps that 
can be taken are 1, or 2. The different ways are:
2 -> 1

For 0 number of steps or jumps that 
can be taken are 0. 
One cannot move forward from this point.

For 1 number of steps or jumps that 
can be taken are 1. But the element is at
the end so no jump is required.

Input : {1, 3, 5, 8, 9, 1, 0, 7, 6, 8, 9}
Output : 52 52 28 16 8 -1 -1 4 2 1 0

This problem is a variation of Minimum number of jumps to reach end(Method 3). Here we need to count all ways to reach end from every cell.

The solution is a modified version of the solution to the problem of Minimum number of jumps to reach end(Method 3).
This problem aims to count the different ways to jump from each element so as to reach to the end. For each element the count is being calculated by adding the counts of all those forward elements that can reach to the end and to which the current element could reach + 1(if the element can directly reach to the end).



Algorithm:

countWays(arr, n)
    Initialize array count_jump[n] = {0}

    count_jump[n-1] = 0
    for i = n-2 to 0
        if arr[i] >= (n-i-1)
         count_jump[i]++
        for j=i+1; j < n-1 && j <= arr[i]+i; i++
          if count_jump[j] != -1
             count_jump[i] += count_jump[j]
        if count_jump[i] == 0
         count_jump[i] = -1

    for i = 0 to n-1
        print count_jump[i]

C++

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// C++ implementation to count number
// of ways to jump to reach end
#include <bits/stdc++.h>
using namespace std;
  
// function to count ways to jump to
// reach end for each array element
void countWaysToJump(int arr[], int n)
{
    // count_jump[i] store number of ways
    // arr[i] can reach to the end
    int count_jump[n];
    memset(count_jump, 0, sizeof(count_jump));
  
    // Last element does not require to jump.
    // Count ways to jump for remaining
    // elements
    for (int i=n-2; i>=0; i--)
    {
        // if the element can directly
        // jump to the end
        if (arr[i] >= n - i - 1)
            count_jump[i]++;
  
        // add the count of all the elements
        // that can reach to end and arr[i] can
        // reach to them
        for (int j=i+1; j < n-1 && j <= arr[i] + i; j++)
  
            // if element can reach to end then add
            // its count to count_jump[i]
            if (count_jump[j] != -1)
                 count_jump[i] += count_jump[j];
  
        // if arr[i] cannot reach to the end
        if (count_jump[i] == 0)
            count_jump[i] = -1;
    }
  
    // print count_jump for each
    // array element
    for (int i=0; i<n; i++)
        cout << count_jump[i] << " ";
}
  
// Driver program to test above
int main()
{
    int arr[] = {1, 3, 5, 8, 9, 1, 0, 7, 6, 8, 9};
    int n = sizeof(arr) / sizeof(arr[0]);
    countWaysToJump(arr, n);
    return 0;
}

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Java














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// Java implementation to count number 


// of ways to jump to reach end 


import java.util.Arrays; 


  


class GFG { 


      


    // function to count ways to jump to 


    // reach end for each array element 


    static void countWaysToJump(int arr[], int n) 


    { 


          


        // count_jump[i] store number of ways 


        // arr[i] can reach to the end 


        int count_jump[] = new int[n]; 


        Arrays.fill(count_jump, 0); 


      


        // Last element does not require to jump. 


        // Count ways to jump for remaining 


        // elements 


        for (int i = n-2; i >= 0; i--) 


        { 


              


            // if the element can directly 


            // jump to the end 


            if (arr[i] >= n - i - 1) 


                count_jump[i]++; 


      


            // add the count of all the elements 


            // that can reach to end and arr[i] can 


            // reach to them 


            for (int j = i+1; j < n-1 && j <= arr[i] + i; j++) 


      


                // if element can reach to end then add 


                // its count to count_jump[i] 


                if (count_jump[j] != -1) 


                    count_jump[i] += count_jump[j]; 


      


            // if arr[i] cannot reach to the end 


            if (count_jump[i] == 0) 


                count_jump[i] = -1; 


        } 


      


        // print count_jump for each 


        // array element 


        for (int i = 0; i < n; i++) 


            System.out.print(count_jump[i] + " "); 


    } 


      


    //driver code 


    public static void main (String[] args) 


    { 


          


        int arr[] = {1, 3, 5, 8, 9, 1, 0, 7, 6, 8, 9}; 


        int n = arr.length; 


          


        countWaysToJump(arr, n); 


    } 


} 


  


// This code is contributed by Anant Agarwal. 



















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Python3














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# Python3 implementation to count  


# number of ways to jump to reach end 


  


# Function to count ways to jump to 


# reach end for each array element 


def countWaysToJump(arr, n): 


  


    # count_jump[i] store number of ways 


    # arr[i] can reach to the end 


    count_jump = [0 for i in range(n)] 


  


    # Last element does not require  


    # to jump. Count ways to jump for  


    # remaining elements 


    for i in range(n - 2, -1, -1): 


      


        # if the element can directly 


        # jump to the end 


        if (arr[i] >= n - i - 1): 


            count_jump[i] += 1


  


        # Add the count of all the elements 


        # that can reach to end and arr[i]  


        # can reach to them 


        j = i + 1


        while(j < n-1 and j <= arr[i] + i): 


  


            # if element can reach to end then  


            # add its count to count_jump[i] 


            if (count_jump[j] != -1): 


                count_jump[i] += count_jump[j] 


            j += 1


              


        # if arr[i] cannot reach to the end 


        if (count_jump[i] == 0): 


            count_jump[i] = -1


      


  


    # print count_jump for each 


    # array element 


    for i in range(n): 


        print(count_jump[i], end = " ") 


  


# Driver code 


arr = [1, 3, 5, 8, 9, 1, 0, 7, 6, 8, 9] 


n = len(arr) 


countWaysToJump(arr, n) 


  


# This code is contributed by Anant Agarwal. 



















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C#














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// C# implementation to count number  


// of ways to jump to reach end  


using System; 


  


class GFG {  


      


    // function to count ways to jump to  


    // reach end for each array element  


    static void countWaysToJump(int[] arr, int n)  


    {  


          


        // count_jump[i] store number of ways  


        // arr[i] can reach to the end  


        int[] count_jump = new int[n]; 


          


        for(int i = 0; i < n; i++) 


            count_jump[i] = 0; 


          


      


        // Last element does not require to jump.  


        // Count ways to jump for remaining  


        // elements  


        for (int i = n-2; i >= 0; i--)  


        {  


              


            // if the element can directly  


            // jump to the end  


            if (arr[i] >= n - i - 1)  


                count_jump[i]++;  


      


            // add the count of all the elements  


            // that can reach to end and arr[i] can  


            // reach to them  


            for (int j = i+1; j < n-1 && j <= arr[i] + i; j++)  


      


                // if element can reach to end then add  


                // its count to count_jump[i]  


                if (count_jump[j] != -1)  


                    count_jump[i] += count_jump[j];  


      


            // if arr[i] cannot reach to the end  


            if (count_jump[i] == 0)  


                count_jump[i] = -1;  


        }  


      


        // print count_jump for each  


        // array element  


        for (int i = 0; i < n; i++)  


            Console.Write(count_jump[i] + " ");  


    }  


      


    // Driver code  


    public static void Main ()  


    {  


        int[] arr = {1, 3, 5, 8, 9, 


                 1, 0, 7, 6, 8, 9};  


        int n = arr.Length;  


        countWaysToJump(arr, n);  


    }  


}  


  


// This code is contributed by ChitraNayal 



















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PHP














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<?php 


// PHP implementation to count number 


// of ways to jump to reach end 


  


// function to count ways to jump to 


// reach end for each array element 


function countWaysToJump($arr, $n) 


{ 


    // count_jump[i] store number of ways 


    // arr[i] can reach to the end 


    $count_jump; 


    for($i = 0; $i < $n; $i++) 


        $count_jump[$i] = 0; 


  


    // Last element does not require to jump. 


    // Count ways to jump for remaining 


    // elements 


    for ($i = $n - 2; $i >= 0; $i--) 


    { 


        // if the element can directly 


        // jump to the end 


        if ($arr[$i] >= $n - $i - 1) 


            $count_jump[$i]++; 


  


        // add the count of all the elements 


        // that can reach to end and arr[i]  


        // can reach to them 


        for ($j = $i + 1; $j < $n - 1 && 


             $j <= $arr[$i] + $i; $j++) 


  


            // if element can reach to end then  


            // add its count to count_jump[i] 


            if ($count_jump[$j] != -1) 


                $count_jump[$i] += $count_jump[$j]; 


  


        // if arr[i] cannot reach to the end 


        if ($count_jump[$i] == 0) 


            $count_jump[$i] = -1; 


    } 


  


    // print count_jump for each 


    // array element 


    for ($i = 0; $i < $n; $i++) 


        echo $count_jump[$i] . " "; 


} 


  


// Driver Code 


$arr = array(1, 3, 5, 8, 9, 1, 


                0, 7, 6, 8, 9); 


$n = count($arr); 


countWaysToJump($arr, $n); 


  


// This code is contributed by Rajput-Ji 


?> 



















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Output:


52 52 28 16 8 -1 -1 4 2 1 0



Time Complexity: O(n2) in worst case.


This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.


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