穿过街道所需的最低初始能量

给定一个包含正数和负数的数组。该数组表示从街道一端到另一端的检查点。正值和负值表示该检查点的能量量。正数增加能量，负数减少。找到穿过街道所需的最小初始能量，使得能量水平永远不会变为 0 或小于 0。

注意：即使我们成功过马路，并且在任何检查点没有将能量损失到小于等于 0，所需的最小初始能量的值也将为 1。初始检查点需要 1。

例子 ：

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

我们取初始最小能量 0 即； initMinEnergy = 0 和任何检查点的能量为 currEnergy = 0。现在线性遍历每个检查点并在每个 i'th 检查点添加能量水平，即； currEnergy = currEnergy + arr[i]。如果 currEnergy 变为非正数，那么我们至少需要“abs(currEnergy) + 1”额外的初始能量才能越过这一点。因此我们更新 initMinEnergy = (initMinEnergy + abs(currEnergy) + 1)。我们还更新了 currEnergy = 1，因为我们现在拥有下一个点所需的额外最小初始能量。

下面是上述想法的实现。

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.

Javascript

// Javascript program to find minimum
// initial energy to reach end
 
// Function to calculate minimum
// initial energy arr[] stores
// energy at each checkpoints on street
function minInitialEnergy(arr, n) {
    // initMinEnergy is variable
    // to store minimum initial
    // energy required.
    let initMinEnergy = 0;
 
    // currEnergy is variable to
    // store current value of energy
    // at i'th checkpoint on street
    let currEnergy = 0;
 
    // flag to check if we have
    // successfully crossed the
    // street without any energy
    // loss <= o at any checkpoint
    let flag = 0;
 
    // Traverse each check
    // point linearly
    for (let 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 = 1;
        }
    }
 
    // If energy never became
    // negative or 0, then
    // return 1. Else return
    // computed initMinEnergy
    return (flag == 0) ? 1 : initMinEnergy;
}
 
// Driver Code
let arr = new Array(4, -10, 4, 4, 4);
let n = arr.length;
document.write(minInitialEnergy(arr, n));
 
// This code is contributed
// by Saurabh Jaiswal

输出 ：

7

时间复杂度： O(n)
辅助空间： O(1)