# Minimum number of jumps to reach end | Set 2 (O(n) solution)

Given an array of integers where each element represents the max number of steps that can be made forward from that element. Write a function to return the minimum number of jumps to reach the end of the array (starting from the first element). If an element is 0, then we cannot move through that element.

Examples:

```Input :  arr[] = {1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9}
Output :  3 (1-> 3 -> 8 -> 9)
```

In this post, its O(n) solution will be discussed.

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

In Set -1, O(n2) solution is discussed.

Implementation:
Variables to be used:

1. maxReach The variable maxReach stores at all time the maximal reachable index in the array.
2. step The variable step stores the number of steps we can still take(and is initialized with value at index 0,i.e. initial number of steps)
3. jump jump stores the amount of jumps necessary to reach that maximal reachable position.

Given array arr = 1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9

• maxReach = arr; // arr = 1, so the maximum index we can reach at the moment is 1.
step = arr; // arr = 1, the amount of steps we can still take is also 1.
jump = 1; // we will always need to take at least one jump.
• Now, starting iteration from index 1, the above values are updated as follows:
1. First we test whether we have reached the end of the array, in that case we just need to return the jump variable.

```if (i == arr.length - 1)
return jump;
```
2. Next we update the maxReach. This is equal to the maximum of maxReach and i+arr[i](the number of steps we can take from the current position).
```maxReach = Math.max(maxReach,i+arr[i]);
```
3. We used up a step to get to the current index, so steps has to be decreased.
```step--;
```
4. If no more steps are remaining (i.e. steps=0, then we must have used a jump. Therefore increase jump. Since we know that it is possible somehow to reach maxReach, we again initialize the steps to the number of steps to reach maxReach from position i. But before re-initializing step, we also check whether a step is becoming zero or negative. In this case, It is not possible to reach further.
```if (step == 0) {
jump++;
if(i>=maxReach)
return -1;
step = maxReach - i;
}
```

## C++

 `// C++ program to count Minimum number ` `// of jumps to reach end ` `#include ` `using` `namespace` `std; ` ` `  `int` `max(``int` `x, ``int` `y) ` ` ``{  ` `  ``return` `(x > y)? x: y;  ` ` ``} ` ` `  `// Returns minimum number of jumps to reach arr[n-1] from arr ` `int` `minJumps(``int` `arr[], ``int` `n) ` `{ ` `     `  `    ``// The number of jumps needed to reach the starting index is 0 ` `    ``if` `(n <= 1) ` `        ``return` `0; ` ` `  `    ``// Return -1 if not possible to jump ` `    ``if` `(arr == 0) ` `        ``return` `-1; ` ` `  `    ``// initialization ` `    ``int` `maxReach = arr;  ``// stores all time the maximal reachable index in the array. ` `    ``int` `step = arr;      ``// stores the number of steps we can still take ` `    ``int` `jump =1;``//stores the number of jumps necessary to reach that maximal reachable position. ` ` `  `    ``// Start traversing array ` `    ``int` `i=1; ` `    ``for` `(i = 1; i < n; i++) ` `    ``{ ` `        ``// Check if we have reached the end of the array ` `        ``if` `(i == n-1) ` `            ``return` `jump; ` ` `  `        ``// updating maxReach ` `        ``maxReach = max(maxReach, i+arr[i]); ` ` `  `        ``// we use a step to get to the current index ` `        ``step--; ` ` `  `        ``// If no further steps left ` `        ``if` `(step == 0) ` `        ``{ ` `            ``// we must have used a jump ` `            ``jump++; ` ` `  `            ``// Check if the current index/position or lesser index ` `            ``// is the maximum reach point from the previous indexes ` `            ``if``(i >= maxReach) ` `                ``return` `-1; ` ` `  `            ``// re-initialize the steps to the amount ` `            ``// of steps to reach maxReach from position i. ` `            ``step = maxReach - i; ` `        ``} ` `    ``} ` ` `  `    ``return` `-1; ` `} ` ` `  `// Driver program to test above function ` `int` `main() ` `{ ` `    ``int` `arr[]={1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9}; ` `    ``int` `size = ``sizeof``(arr)/``sizeof``(``int``); ` ` `  `    ``// Calling the minJumps function ` `    ``cout<<(``"Minimum number of jumps to reach end is %d "``, minJumps(arr,size)); ` `    ``return` `0; ` `} ` `// This code is contributed by ` `// Shashank_Sharma `

## C

 `// C program to count Minimum number ` `// of jumps to reach end ` `#include ` ` `  `int` `max(``int` `x, ``int` `y) { ``return` `(x > y)? x: y; } ` ` `  `// Returns minimum number of jumps to reach arr[n-1] from arr ` `int` `minJumps(``int` `arr[], ``int` `n) ` `{ ` `     `  `    ``// The number of jumps needed to reach the starting index is 0 ` `    ``if` `(n <= 1) ` `        ``return` `0; ` ` `  `    ``// Return -1 if not possible to jump ` `    ``if` `(arr == 0) ` `        ``return` `-1; ` ` `  `    ``// initialization ` `    ``int` `maxReach = arr;  ``// stores all time the maximal reachable index in the array. ` `    ``int` `step = arr;      ``// stores the number of steps we can still take ` `    ``int` `jump =1;``//stores the number of jumps necessary to reach that maximal reachable position. ` ` `  `    ``// Start traversing array ` `    ``int` `i=1; ` `    ``for` `(i = 1; i < n; i++) ` `    ``{ ` `        ``// Check if we have reached the end of the array ` `        ``if` `(i == n-1) ` `            ``return` `jump; ` ` `  `        ``// updating maxReach ` `        ``maxReach = max(maxReach, i+arr[i]); ` ` `  `        ``// we use a step to get to the current index ` `        ``step--; ` ` `  `        ``// If no further steps left ` `        ``if` `(step == 0) ` `        ``{ ` `            ``// we must have used a jump ` `            ``jump++; ` ` `  `            ``// Check if the current index/position or lesser index ` `            ``// is the maximum reach point from the previous indexes ` `            ``if``(i >= maxReach) ` `                ``return` `-1; ` ` `  `            ``// re-initialize the steps to the amount ` `            ``// of steps to reach maxReach from position i. ` `            ``step = maxReach - i; ` `        ``} ` `    ``} ` ` `  `    ``return` `-1; ` `} ` ` `  `// Driver program to test above function ` `int` `main() ` `{ ` `    ``int` `arr[]={1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9}; ` `    ``int` `size = ``sizeof``(arr)/``sizeof``(``int``); ` ` `  `    ``// Calling the minJumps function ` `    ``printf``(``"Minimum number of jumps to reach end is %d "``, minJumps(arr,size)); ` `    ``return` `0; ` `} ` `// This code is contributed by Abhishek Kumar Singh `

## Java

 `// Java program to count Minimum number ` `// of jumps to reach end ` ` `  `class` `Test ` `{ ` `    ``static` `int` `minJumps(``int` `arr[]) ` `    ``{ ` `        ``if` `(arr.length <= ``1``) ` `            ``return` `0``; ` ` `  `        ``// Return -1 if not possible to jump ` `        ``if` `(arr[``0``] == ``0``) ` `            ``return` `-``1``; ` ` `  `        ``// initialization ` `        ``int` `maxReach = arr[``0``]; ` `        ``int` `step = arr[``0``]; ` `        ``int` `jump = ``1``; ` ` `  ` `  `        ``// Start traversing array ` `        ``for` `(``int` `i = ``1``; i < arr.length; i++) ` `        ``{ ` `            ``// Check if we have reached the end of the array ` `            ``if` `(i == arr.length - ``1``) ` `                ``return` `jump; ` ` `  `            ``// updating maxReach ` `            ``maxReach = Math.max(maxReach, i+arr[i]); ` ` `  `            ``// we use a step to get to the current index ` `            ``step--; ` ` `  `            ``// If no further steps left ` `            ``if` `(step == ``0``) ` `            ``{ ` `                ``//  we must have used a jump ` `                ``jump++; ` `                  `  `                ``//Check if the current index/position  or lesser index ` `                ``// is the maximum reach point from the previous indexes ` `                ``if``(i>=maxReach) ` `                   ``return` `-``1``; ` ` `  `                ``// re-initialize the steps to the amount ` `                ``// of steps to reach maxReach from position i. ` `                ``step = maxReach - i; ` `            ``} ` `        ``} ` ` `  `        ``return` `-``1``; ` `    ``} ` ` `  `    ``// Driver method to test the above function ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `arr[] = ``new` `int``[] {``1``, ``3``, ``5``, ``8``, ``9``, ``2``, ``6``, ``7``, ``6``, ``8``, ``9``}; ` ` `  `        ``// calling minJumps method ` `        ``System.out.println(minJumps(arr)); ` `    ``} ` `} `

## Python

 `# python program to count Minimum number ` `# of jumps to reach end ` `  `  `# Returns minimum number of jumps to reach arr[n-1] from arr ` `def` `minJumps(arr, n): ` `  ``# The number of jumps needed to reach the starting index is 0 ` `  ``if` `(n <``=` `1``): ` `    ``return` `0` `  `  `  ``# Return -1 if not possible to jump ` `  ``if` `(arr[``0``] ``=``=` `0``): ` `    ``return` `-``1` `  `  `  ``# initialization ` `  ``# stores all time the maximal reachable index in the array ` `  ``maxReach ``=` `arr[``0``]   ` `  ``# stores the amount of steps we can still take ` `  ``step ``=` `arr[``0``] ` `  ``# stores the amount of jumps necessary to reach that maximal reachable position ` `  ``jump ``=``1`  `  `  `  ``# Start traversing array ` `  `  `  ``for` `i ``in` `range``(``1``,n): ` `    ``# Check if we have reached the end of the array ` `    ``if` `(i ``=``=` `n``-``1``): ` `      ``return` `jump ` `  `  `    ``# updating maxReach ` `    ``maxReach ``=` `max``(maxReach, i``+``arr[i]) ` `  `  `    ``# we use a step to get to the current index ` `    ``step ``-``=` `1``; ` `  `  `    ``# If no further steps left ` `    ``if` `(step ``=``=` `0``): ` `      ``# we must have used a jump ` `      ``jump ``+``=` `1` `       `  `      ``# Check if the current index/position or lesser index ` `      ``# is the maximum reach point from the previous indexes ` `      ``if``(i >``=` `maxReach): ` `        ``return` `-``1` `  `  `      ``# re-initialize the steps to the amount ` `      ``# of steps to reach maxReach from position i. ` `      ``step ``=` `maxReach ``-` `i; ` `  ``return` `-``1` `  `  ` `  `# Driver program to test above function ` `arr ``=` `[``1``, ``3``, ``5``, ``8``, ``9``, ``2``, ``6``, ``7``, ``6``, ``8``, ``9``] ` `size ``=` `len``(arr) ` `  `  `# Calling the minJumps function ` `print``(``"Minimum number of jumps to reach end is %d "` `%``minJumps(arr,size)) ` ` `  ` `  `# This code is contributed by Aditi Sharma `

## C#

 `// C# program to count Minimum  ` `// number of jumps to reach end ` `using` `System;  ` ` `  `class` `GFG ` `{ ` `    ``static` `int` `minJumps(``int` `[]arr) ` `    ``{ ` `        ``if` `(arr.Length <= 1) ` `            ``return` `0; ` ` `  `        ``// Return -1 if not  ` `        ``// possible to jump ` `        ``if` `(arr == 0) ` `            ``return` `-1; ` ` `  `        ``// initialization ` `        ``int` `maxReach = arr; ` `        ``int` `step = arr; ` `        ``int` `jump = 1; ` ` `  ` `  `        ``// Start traversing array ` `        ``for` `(``int` `i = 1; i < arr.Length; i++) ` `        ``{ ` `            ``// Check if we have reached  ` `            ``// the end of the array ` `            ``if` `(i == arr.Length - 1) ` `                ``return` `jump; ` ` `  `            ``// updating maxReach ` `            ``maxReach = Math.Max(maxReach, i + arr[i]); ` ` `  `            ``// we use a step to get ` `            ``// to the current index ` `            ``step--; ` ` `  `            ``// If no further steps left ` `            ``if` `(step == 0) ` `            ``{ ` `                ``// we must have used a jump ` `                ``jump++; ` `                 `  `                ``// Check if the current index/position  ` `                ``// or lesser index is the maximum reach ` `                ``// point from the previous indexes ` `                ``if``(i >= maxReach) ` `                ``return` `-1; ` ` `  `                ``// re-initialize the steps to ` `                ``// the amount of steps to reach  ` `                ``// maxReach from position i. ` `                ``step = maxReach - i; ` `            ``} ` `        ``} ` ` `  `        ``return` `-1; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[]arr = ``new` `int``[] {1, 3, 5, 8, 9, 2, ` `                               ``6, 7, 6, 8, 9}; ` ` `  `        ``// calling minJumps method ` `        ``Console.Write(minJumps(arr)); ` `    ``} ` `} ` ` `  `// This code is contributed  ` `// by nitin mittal `

## PHP

 `= ``\$maxReach``) ` `                ``return` `-1; ` `  `  `            ``// re-initialize the steps to the amount ` `            ``// of steps to reach maxReach from position i. ` `            ``\$step` `= ``\$maxReach` `- ``\$i``; ` `        ``} ` `    ``} ` `  `  `    ``return` `-1; ` `} ` `  `  `// Driver program to test above function ` ` `  `\$arr``=``array``(1, 3, 5, 8, 9, 2, 6, 7, 6, 8, 9); ` `\$size` `= sizeof(``\$arr``)/sizeof(``\$arr``); ` `  `  `// Calling the minJumps function ` `echo` `"Minimum number of jumps to reach end is "` `     ``. minJumps(``\$arr``,``\$size``); ` `return` `0; ` `// This code is contribute by Ita_c. ` `?> `

Output:

```3
```

References :- Stackoverflow

Thanks to Chiranjeev Jain for suggesting this solution.

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