# 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 the number of ways jumps can be made from that element to reach the end of the array. If an element is **0**, then a move cannot be made through that element. The element that cannot reach the end should have a count “**-1**“.

**Examples:**

Input:{3, 2, 0, 1}Output:2 1 -1 0Explanation:

- For
3number of steps or jumps that can be taken are 1, 2 or 3. The different ways are:3 -> 2 -> 13 -> 1- For
2number of steps or jumps that can be taken are 1, or 2. The different ways are:2 -> 1- For
0number of steps or jumps that can be taken are 0. One cannot move forward from this point.- For
1number 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 the Minimum number of jumps to reach end(Method 3). Here we need to count all the ways to reach the end from every cell.

The solution is a modified version of the solution to the problem of the Minimum number of jumps to reach end(Method 3).

This problem aims to count the different ways to jump from each element to reach the end. For each element, the count is being calculated by adding the counts of all those forward elements that can reach the end and to which the current element could reach + 1(if the element can directly reach the end).

**Algorithm:**

countWays(arr, n)Initialize arraycount_jump[n]= {0} count_jump[n-1] = 0 fori= n-2 to 0 if arr[i] >= (n-i-1) count_jump[i]++ forj=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]

Below is the implementation of the above approach:

## C++

`// 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;` `}` |

## Java

`// 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.` |

## Python3

`# 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.` |

## C#

`// 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` |

## PHP

`<?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` `?>` |

## Javascript

`<script>` `// Javascript 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` ` ` `let count_jump = ` `new` `Array(n);` ` ` `for` `(let i=0;i<n;i++)` ` ` `{` ` ` `count_jump[i]=0;` ` ` `}` ` ` ` ` `// Last element does not require to jump.` ` ` `// Count ways to jump for remaining` ` ` `// elements` ` ` `for` `(let 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` `(let 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` `(let i = 0; i < n; i++)` ` ` `document.write(count_jump[i] + ` `" "` `);` ` ` `}` ` ` ` ` `//driver code` ` ` `let arr=[1, 3, 5, 8, 9, 1, 0, 7, 6, 8, 9];` ` ` `let n = arr.length;` ` ` `countWaysToJump(arr, n);` ` ` ` ` ` ` ` ` `// This code is contributed by avanitrachhadiya2155` `</script>` |

**Output**

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

**Time Complexity:** O(n^{2}), Where n is the size of the given array.**Auxiliary Space: **O(n), As we are creating **count_jump** array of size n.