862. Shortest Subarray with Sum at Least K

Posted 2021-01-18 ruruozhenhao

Return the length of the shortest, non-empty, contiguous subarray of A with sum at least K.

If there is no non-empty subarray with sum at least K, return -1.

 

Example 1:

Input: A = [1], K = 1
Output: 1

Example 2:

Input: A = [1,2], K = 4
Output: -1

Example 3:

Input: A = [2,-1,2], K = 3
Output: 3

 

Note:

1. 1 <= A.length <= 50000
2. -10 ^ 5 <= A[i] <= 10 ^ 5
3. 1 <= K <= 10 ^ 9

 

Approach #1: prefix sum. [Time Limit Exceeded]

class Solution {
public:
    int shortestSubarray(vector<int>& A, int K) {
        int len = A.size();
        if (len == 1 && A[0] >= K) return 1;
        int step = INT_MAX;
        vector<int> prefixSum(len, 0);
        prefixSum[0] = A[0];
        for (int i = 1; i < len; ++i)
            prefixSum[i] = prefixSum[i-1] + A[i];
        for (int i = 0; i < len; ++i) {
            if (prefixSum[i] >= K) 
                step = min(step, i+1);
            for (int j = i+1; j < len; ++j) {
                if (prefixSum[j]-prefixSum[i] >= K) {
                    step = min(step, j-i);
                }
            }
        }
        if (step == INT_MAX) return -1;
        else return step;
    }
};

　　

Approach #2:  deque.

class Solution {
public:
    int shortestSubarray(vector<int>& A, int K) {
        int len = A.size();
        int res = len + 1;
        vector<int> sum(len+1, 0);
        for (int i = 0; i < len; ++i)
            sum[i+1] = sum[i] + A[i];
        deque<int> d;
        for (int i = 0; i < len+1; ++i) {
            while (!d.empty() && sum[i]-sum[d.front()] >= K) 
                res = min(res, i-d.front()), d.pop_front();
            while (!d.empty() && sum[i] <= sum[d.back()])
                d.pop_back();
            d.push_back(i);
        }
        return res <= len ? res : -1;
    }
};

Runtime: 144 ms, faster than 33.12% of C++ online submissions for Shortest Subarray with Sum at Least K.

 

Analysis:

deque Member functions

(constructor)

Construct deque container (public member function )

(destructor)

Deque destructor (public member function )

operator=

Assign content (public member function )

Iterators:

begin

Return iterator to beginning (public member function )

end

Return iterator to end (public member function )

rbegin

Return reverse iterator to reverse beginning (public member function )

rend

Return reverse iterator to reverse end (public member function )

cbegin 

Return const_iterator to beginning (public member function )

cend 

Return const_iterator to end (public member function )

crbegin 

Return const_reverse_iterator to reverse beginning (public member function )

crend 

Return const_reverse_iterator to reverse end (public member function )

Capacity:

size

Return size (public member function )

max_size

Return maximum size (public member function )

resize

Change size (public member function )

empty

Test whether container is empty (public member function )

shrink_to_fit 

Shrink to fit (public member function )

Element access:

operator[]

Access element (public member function )

at

Access element (public member function )

front

Access first element (public member function )

back

Access last element (public member function )

Modifiers:

assign

Assign container content (public member function )

push_back

Add element at the end (public member function )

push_front

Insert element at beginning (public member function )

pop_back

Delete last element (public member function )

pop_front

Delete first element (public member function )

insert

Insert elements (public member function )

erase

Erase elements (public member function )

swap

Swap content (public member function )

clear

Clear content (public member function )

emplace 

Construct and insert element (public member function )

emplace_front 

Construct and insert element at beginning (public member function )

emplace_back 

Construct and insert element at the end (public member function )

Allocator:

get_allocator

Get allocator (public member function )

Non-member functions overloads

relational operators

Relational operators for deque (function )

swap

Exchanges the contents of two deque containers (function template )