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# Minimum Initial Energy Required To Cross Street

Given an array containing positive and negative numbers. The array represents checkpoints from one end to other end of street. Positive and negative values represent amount of energy at that checkpoint. Positive numbers increase the energy and negative numbers decrease. Find the minimum initial energy required to cross the street such that Energy level never becomes 0 or less than 0.

Note : The value of minimum initial energy required will be 1 even if we cross street successfully without losing energy to less than and equal to 0 at any checkpoint. The 1 is required for initial check point.

Examples :

```Input : arr[] = {4, -10, 4, 4, 4}
Output: 7
Suppose initially we have energy = 0, now at 1st
checkpoint, we get 4. At 2nd checkpoint, energy gets
reduced by -10 so we have 4 + (-10) = -6 but at any
checkpoint value of energy can not less than equals
to 0. So initial energy must be at least 7 because
having 7 as initial energy value at 1st checkpoint
our energy will be = 7+4 = 11 and then we can cross
2nd checkpoint successfully. Now after 2nd checkpoint,
all checkpoint have positive value so we can cross
street successfully with 7 initial energy.

Input : arr[] = {3, 5, 2, 6, 1}
Output: 1
We need at least 1 initial energy to reach first
checkpoint

Input : arr[] = {-1, -5, -9}
Output: 16```
Recommended Practice

Brute force approach :

• For every possible initial energy level (starting from 1), simulate the crossing of the street using that energy level and check if the energy level remains positive at all times.
• Return the minimum initial energy level that ensures that the energy level never becomes zero or negative.

Below is the code for above approach :

## C++

 `#include``using` `namespace` `std;` `// Function to check if energy level never becomes negative or zero``bool` `check(``int` `arr[], ``int` `n, ``int` `initEnergy) {``    ``int` `energy = initEnergy;``    ``for` `(``int` `i = 0; i < n; i++) {``        ``energy += arr[i];``        ``if` `(energy <= 0) {``            ``return` `false``;``        ``}``    ``}``    ``return` `true``;``}` `// Function to calculate minimum initial energy``// arr[] stores energy at each checkpoints on street``int` `minInitialEnergy(``int` `arr[], ``int` `n) {``    ``int` `minEnergy = 1;``    ``while` `(!check(arr, n, minEnergy)) {``        ``minEnergy++;``    ``}``    ``return` `minEnergy;``}` `// Driver code``int` `main() {``    ``int` `arr[] = {4, -10, 4, 4, 4};``    ``int` `n = ``sizeof``(arr)/``sizeof``(arr[0]);``    ``cout << minInitialEnergy(arr, n);``    ``return` `0;``}`

Output :

`7`

Time Complexity : O(2^n)

Auxiliary Space : O(n)

We take initial minimum energy 0 i.e; initMinEnergy = 0 and energy at any checkpoint as currEnergy = 0. Now traverse each checkpoint linearly and add energy level at each i’th checkpoint i.e; currEnergy = currEnergy + arr[i]. If currEnergy becomes non-positive, then we need at least “abs(currEnergy) + 1” extra initial energy to cross this point. Therefore we update initMinEnergy = (initMinEnergy + abs(currEnergy) + 1). We also update currEnergy = 1 as we now have the required extra minimum initial energy for next point.

Below is the implementation of above idea.

## C++

 `// C++ program to find minimum initial energy to``// reach end``#include``using` `namespace` `std;` `// Function to calculate minimum initial energy``// arr[] stores energy at each checkpoints on street``int` `minInitialEnergy(``int` `arr[], ``int` `n)``{``    ``// initMinEnergy is variable to store minimum initial``    ``// energy required.``    ``int` `initMinEnergy = 0;` `    ``// currEnergy is variable to store current value of``    ``// energy at i'th checkpoint on street``    ``int` `currEnergy = 0;` `    ``// flag to check if we have successfully crossed the``    ``// street without any energy loss <= o at any checkpoint``    ``bool` `flag = 0;` `    ``// Traverse each check point linearly``    ``for` `(``int` `i=0; i

## Java

 `// Java program to find minimum``// initial energy to reach end` `class` `GFG {``    ` `// Function to calculate minimum``// initial energy arr[] stores energy``// at each checkpoints on street``static` `int` `minInitialEnergy(``int` `arr[], ``int` `n)``{``    ``// initMinEnergy is variable to store``    ``// minimum initial energy required.``    ``int` `initMinEnergy = ``0``;` `    ``// currEnergy is variable to store``    ``// current value of energy at``    ``// i'th checkpoint on street``    ``int` `currEnergy = ``0``;` `    ``// flag to check if we have successfully``    ``// crossed the street without any energy``    ``// loss <= o at any checkpoint``    ``boolean` `flag = ``false``;` `    ``// Traverse each check point linearly``    ``for` `(``int` `i = ``0``; i < n; i++) {``    ``currEnergy += arr[i];` `    ``// If current energy, becomes negative or 0,``    ``// increment initial minimum energy by the negative``    ``// value plus 1. to keep current energy``    ``// positive (at least 1). Also``    ``// update current energy and flag.``    ``if` `(currEnergy <= ``0``) {``        ``initMinEnergy += Math.abs(currEnergy) + ``1``;``        ``currEnergy = ``1``;``        ``flag = ``true``;``    ``}``    ``}` `    ``// If energy never became negative or 0, then``    ``// return 1. Else return computed initMinEnergy``    ``return` `(flag == ``false``) ? ``1` `: initMinEnergy;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = {``4``, -``10``, ``4``, ``4``, ``4``};``    ``int` `n = arr.length;``    ``System.out.print(minInitialEnergy(arr, n));``}``}` `// This code is contributed by Anant Agarwal.`

## Python3

 `# Python program to find minimum initial energy to``# reach end` `# Function to calculate minimum initial energy``# arr[] stores energy at each checkpoints on street``def` `minInitialEnergy(arr):``    ``n ``=` `len``(arr)``    ` `    ``# initMinEnergy is variable to store minimum initial``    ``# energy required``    ``initMinEnergy ``=` `0``;``    ` `    ``# currEnergy is variable to store current value of``    ``# energy at i'th checkpoint on street``    ``currEnergy ``=` `0` `    ``# flag to check if we have successfully crossed the``    ``# street without any energy loss <= 0 at any checkpoint``    ``flag ``=` `0``    ` `    ``# Traverse each check point linearly``    ``for` `i ``in` `range``(n):``        ``currEnergy ``+``=` `arr[i]``        ` `        ``# If current energy, becomes negative or 0, increment``        ``# initial minimum energy by the negative value plus 1.``        ``# to keep current energy positive (at least 1). Also``        ``# update current energy and flag.``        ``if` `currEnergy <``=` `0` `:``            ``initMinEnergy ``+``=` `(``abs``(currEnergy) ``+``1``)``            ``currEnergy ``=` `1``            ``flag ``=` `1` `    ``# If energy never became negative or 0, then``    ``# return 1. Else return computed initMinEnergy``    ``return` `1` `if` `flag ``=``=` `0` `else` `initMinEnergy`  `# Driver program to test above function``arr ``=` `[``4``, ``-``10` `, ``4``, ``4``, ``4``]``print` `(minInitialEnergy(arr))` `# This code is contributed by Nikhil Kumar Singh(nickzuck_007)`

## C#

 `// C# program to find minimum``// C# program to find minimum``// initial energy to reach end``using` `System;` `class` `GFG {``    ` `// Function to calculate minimum``// initial energy arr[] stores energy``// at each checkpoints on street``static` `int` `minInitialEnergy(``int` `[]arr, ``int` `n)``{``    ` `    ``// initMinEnergy is variable to store``    ``// minimum initial energy required.``    ``int` `initMinEnergy = 0;` `    ``// currEnergy is variable to store``    ``// current value of energy at``    ``// i'th checkpoint on street``    ``int` `currEnergy = 0;` `    ``// flag to check if we have successfully``    ``// crossed the street without any energy``    ``// loss <= o at any checkpoint``    ``bool` `flag = ``false``;` `    ``// Traverse each check point linearly``    ``for` `(``int` `i = 0; i < n; i++) {``    ``currEnergy += arr[i];` `    ``// If current energy, becomes negative or 0,``    ``// negativeincrement initial minimum energy``    ``// by the value plus 1. to keep current``    ``// energy positive (at least 1). Also``    ``// update current energy and flag.``    ``if` `(currEnergy <= 0)``    ``{``        ``initMinEnergy += Math.Abs(currEnergy) + 1;``        ``currEnergy = 1;``        ``flag = ``true``;``    ``}``    ``}` `    ``// If energy never became negative``    ``// or 0, then return 1. Else return``    ``// computed initMinEnergy``    ``return` `(flag == ``false``) ? 1 : initMinEnergy;``}` `// Driver code``public` `static` `void` `Main()``{``    ``int` `[]arr = {4, -10, 4, 4, 4};``    ``int` `n = arr.Length;``    ``Console.Write(minInitialEnergy(arr, n));``}``}` `// This code is contributed by Nitin Mittal.`

## PHP

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## Javascript

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Output

`7`

Time Complexity : O(n)
Auxiliary Space : O(1)

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