算法两道题 - 技术栈

算法一

Write a function:

int solution(vector<int>&A);

that, given an array A of length N, returns as an integer the minimum number of moves needed to transform a zero-filled array into A.

Examples:

Given A = $2, 1, 3$ , the function should return 4. For example, the following sequence of moves leads to the solution: $0, 0, 0$ → $1, 1, 1$ → $2, 1, 1$ → $2, 1, 2$ → $2, 1, 3$ .
Given A = $2, 2, 0, 0, 1$ , the function should return 3. The following sequence of moves leads to the solution: $0, 0, 0, 0, 0$ → $1, 1, 0, 0, 0$ → $2, 2, 0, 0, 0$ → $2, 2, 0, 0, 1$ .
Given A = $5, 4, 2, 4, 1$ , the function should return 7. One possible optimal sequence of moves is: $0, 0, 0, 0, 0$ → $1, 1, 1, 1, 1$ → $2, 2, 2, 2, 1$ → $3, 3, 2, 2, 1$ → $4, 4, 2, 2, 1$ → $5, 4, 2, 2, 1$ → $5, 4, 2, 3, 1$ → $5, 4, 2, 4, 1$ .

Write an efficient algorithm for the following assumptions:

N is an integer within the range $1..100,000$ ; each element of array A is an integer within therange $0..1,000,000,000$ :

we guarantee that the answer will not exceed1,000,000,000.

上面这道题大概就是将一个全0数组变成到目标数组需要多少步骤。每次只能对连续的数字进行增加1的操作。

python 复制代码

# vector<int>& A
def solution(A) {
    int n = len(A);
    
    if (n == 0) return 0;
    
    # Variable to store the total number of moves required
    int moves = A[0];  # We need at least A[0] moves to reach the first element's value
    
    for (int i = 1; i < n; ++i) {
        # If current element is greater than the previous one, 
        # we need extra moves to reach it
        if (A[i] > A[i - 1]) {
            moves += (A[i] - A[i - 1]);
        }
    }
    
    return moves;
}

算法二

There is an array, named `digits`, consisting of N digits. Choose at most three digits (not necessarily adjacent) and merge them into a new integer without changing the order of the digits. What is the biggest number that can be obtained this way?

Write a function:

def solution(digits)

that, given an array of N digits, returns the biggest number that can be built.

Examples:

Given digits = $7, 2, 3, 3, 4, 9$ , the function

should return 749.

Given digits = $0, 0, 5, 7$ , the function should

return 57.

Assume that:

N is an integer within the range $3..50$ ;

each element of array, named `digits`, is an

integer within the range $0..9$ .

In your solution, focus on correctness. The

performance of your solution will not be the focus of

the assessment.

算法是要从一个数组里面选出三个数用来组成一个新的三位数，这三个数字的相对位置不能改变，求能够组成的最大的数字。

算法思路就是先从0~n-2之前挑出最大的数字，然后从上一个数字的索引往后直到n-1之前挑出第二个最大的数字，再从上一个数字的索引到n挑出第三大的数字即可。