最小化对给定 Array 的相邻元素执行的算术运算以减少它

给定一个数组arr[] ，任务是按顺序对arr[]执行算术运算（+、-、*、/） 。对相邻元素执行这些操作，直到数组大小减小到1 。最后，返回减少的值和所需的操作数。请参阅示例以获得更清晰的信息。

例子：

Input: arr = {12, 10, 2, 9, 1, 2}
Output: Reduced Value: 10
Operations Performed:
+ : 2
– : 1
* : 1
/ : 1

Explanation:
Step 1: perform addition of consecutive element [22, 12, 11, 10, 3]
Step 2: perform subtraction of consecutive element [10, 1, 1, 7]
Step 3: perform multiplication of consecutive element[10, 1, 7]
Step 4: perform division of consecutive element [10, 0]
Step 5: Again perform addition of consecutive element[10]

Input: arr = {5, -2, -1, 2, 4, 5}
Output: Reduced Value: -3
Operations Performed:
+ : 2
– : 2
* : 1
/ : 1

编程需要懂一点英语

方法：由于在这个问题中，我们必须根据顺序执行运算，例如先加法然后减法，然后乘法然后除法，因此我们可以使用 Switch case 来解决这个问题。

初始化一个字典，其中运算符（+、-、*、/）作为键，0 作为值。使用函数add、sub、mul和div，将对数组执行操作。它具有 as函数Operation，它根据c%4的值将数组映射到函数并返回缩减后的数组。其中c跟踪执行的操作数。字典跟踪执行的每个操作，直到数组大小减少到1 。
请按照以下步骤解决给定的问题。

第 1 步：将c赋值为1并声明字典d 。

步骤 2：如果c%4==1则使用 Operation 函数对连续元素执行加法运算。
第 3 步：如果c%4==2则使用运算函数对连续元素执行减法运算。
第 4 步：如果c%4==3则使用 Operation 函数对连续元素执行乘法运算。
步骤 5：如果c%4==0则使用 Operation 函数对连续元素执行除法运算。
第 6 步：将重复第2步，直到数组的大小等于1 。
步骤 7： d用于跟踪执行的每个操作。

下面是上述方法的实现：

Python3

# Function for adding consecutive element
def add(a):
    return [a[i]+a[i + 1] for i in range(len(a)-1)]
 
# Function for subtracting consecutive element
def sub(a):
    return [a[i] - a[i + 1] for i in range(len(a)- 1)]
 
# Function for multiplication of consecutive element
def mul(a):
    return [a[i] * a[i + 1] for i in range(len(a) - 1)]
 
# Function for division of consecutive element
def div(a):
    return [0 if a[i] == 0 or a[i + 1] == 0 \
            else a[i]//a[i + 1] \
                 for i in range(len(a) - 1)]
 
# Operation function which maps array
# to corresponding function
# based on value of i.
def Operation(i, A):
    switcher = {
        1: add,
        2: sub,
        3: mul,
        0: div
    }
    func = switcher.get(i, lambda: 'Invalid')
    return func(A)
  
# Driver Code
c = 1
 
# dictionary value which keep track
# of no of operation of each operator.
d = {'+':0, '-':0, '*':0, '/':0 }
 
arr =[5, -2, -1, 2, 1, 4, 5]
 
# loop till size of array become equal to 1.
while len(arr)!= 1:
    x = c % 4
    # After each operation value
    # in dictionary value is incremented
    # also reduced array
    # is assigned to original array.
    if x == 1:
        d['+'] += 1
        arr = Operation(x, arr)
    elif x == 2:
        d['-'] += 1
        arr = Operation(x, arr)
    elif x == 3:
        d['*'] += 1
        arr = Operation(x, arr)
    elif x == 0:
        d['/'] += 1
        arr = Operation(x, arr)
    c += 1
 
# Printing reduced value
print("Reduced value:", *arr)
 
 
# Printing value of each operation
# performed to reduce size of array to 1.
print("Operations Performed:")
for i in d.keys():
    print(str(i) + " : " +str(d[i]))

输出

Reduced value: -3
Operations Performed:
+ : 2
- : 2
* : 1
/ : 1

时间复杂度： O(N)
辅助空间： O(N)