Problem statement
Given an array of positive integers nums and a positive integer target, return the minimal length of a subarray whose sum is greater than or equal to target. If there is no such subarray, return 0 instead.
Problem statement taken from: https://leetcode.com/problems/minimum-size-subarray-sum
Example 1:
Input: target = 7, nums = [2, 3, 1, 2, 4, 3]
Output: 2
Explanation: The subarray [4, 3] has the minimal length under the problem constraint.
Example 2:
Input: target = 4, nums = [1, 4, 4]
Output: 1
Example 3:
Input: target = 11, nums = [1, 1, 1, 1, 1, 1, 1, 1]
Output: 0
Constraints:
- 1 <= target <= 10^9
- 1 <= nums.length <= 10^5
- 1 <= nums.length <= 10^4
Explanation
Brute force approach
A naive approach is to run two nested loops. The outer loop selects a starting element, and the inner loop iterates over the array. Whenever the sum of elements between the start and end becomes more than target, we update the minimum length if current length is smaller than the smallest length so far.
A C++ snippet of this approach is as below:
int minLength = n + 1;
for (int start = 0; start < n; start++) {
int currentSum = nums[start];
if (currentSum > x) return 1;
for (int end = start + 1; end < n; end++) {
currentSum += nums[end];
if (currentSum > x && (end - start + 1) < minLength)
minLength = (end - start + 1);
}
}
return minLength;
The time-complexity of the above approach is O(n^2), and the
space complexity is O(1).
Efficient solution
An efficient approach is to use a sliding window approach. Let's jump to the algorithm to understand it clearly.
- set l = 0, r = -1
sum = 0
minLength = nums.size() + 1
- loop while l < nums.size()
- if r + 1 < nums.size() && sum < target
- sum += nums[++r]
- else
- sum -= nums[l++]
- if sum >= target
- minLength = min(minLength, r - l + 1)
- loop end
- return minLength == nums.size() + 1 ? 0 : minLength
The time complexity of the above approach is O(n), and the space complexity is O(1).
Let's check our algorithm in C++, Golang, and Javascript.
C++ solution
class Solution {
public:
int minSubArrayLen(int target, vector<int>& nums) {
int l = 0, r = -1;
int sum = 0;
int minLength = nums.size() + 1;
while(l < nums.size()) {
if(r + 1 < nums.size() && sum < target) {
sum += nums[++r];
} else {
sum -= nums[l++];
}
if(sum >= target) {
minLength = min(minLength, r - l + 1);
}
}
return minLength == nums.size() + 1 ? 0 : minLength;
}
};
Golang solution
func minSubArrayLen(target int, nums []int) int {
l, r := 0, -1
sum := 0
minLength := len(nums) + 1
for ;l < len(nums); {
if r + 1 < len(nums) && sum < target {
r += 1
sum += nums[r]
} else {
sum -= nums[l]
l += 1
}
if sum >= target {
minLength = min(minLength, r - l + 1)
}
}
if minLength == len(nums) + 1 {
return 0
}
return minLength
}
func min(a, b int) int {
if a < b {
return a
}
return b
}
Javascript solution
var minSubArrayLen = function(target, nums) {
let l = 0, r = -1;
let sum = 0;
let minLength = nums.length + 1;
while(l < nums.length) {
if(r + 1 < nums.length && sum < target) {
sum += nums[++r];
} else {
sum -= nums[l++];
}
if(sum >= target) {
minLength = Math.min(minLength, r - l + 1);
}
}
return minLength == nums.length + 1 ? 0 : minLength;
};
Let's dry-run our algorithm to see how the solution works.
Input: target = 7, nums = [2, 3, 1, 2, 4, 3]
Step 1: l = 0, r = -1
sum = 0
minLength = nums.size() + 1
= 6 + 1
= 7
Step 2: loop while l < nums.size()
0 < 6
true
if r + 1 < nums.size() && sum < target
-1 + 1 < 6 && 0 < 7
0 < 6 && 0 < 7
true
sum = sum + nums[++r]
= 0 + nums[0]
= 0 + 2
= 2
r = 0
if sum >= target
2 >= 7
false
Step 3: loop while l < nums.size()
0 < 6
true
if r + 1 < nums.size() && sum < target
0 + 1 < 6 && 2 < 7
1 < 6 && 2 < 7
true
sum = sum + nums[++r]
= 2 + nums[1]
= 2 + 3
= 5
r = 1
if sum >= target
5 >= 7
false
Step 4: loop while l < nums.size()
0 < 6
true
if r + 1 < nums.size() && sum < target
1 + 1 < 6 && 5 < 7
2 < 6 && 5 < 7
true
sum = sum + nums[++r]
= 5 + nums[2]
= 5 + 1
= 6
r = 2
if sum >= target
6 >= 7
false
Step 5: loop while l < nums.size()
0 < 6
true
if r + 1 < nums.size() && sum < target
2 + 1 < 6 && 6 < 7
3 < 6 && 6 < 7
true
sum = sum + nums[++r]
= 6 + nums[3]
= 6 + 2
= 8
r = 3
if sum >= target
8 >= 7
true
minLength = min(minLength, r - l + 1)
= min(7, 3 - 0 + 1)
= min(7, 4)
= 4
Step 6: loop while l < nums.size()
0 < 6
true
if r + 1 < nums.size() && sum < target
3 + 1 < 6 && 8 < 7
4 < 6 && 8 < 7
false
else
sum = sum - nums[l++]
= 8 - nums[0]
= 8 - 2
= 6
l = 1
Step 7: loop while l < nums.size()
1 < 6
true
if r + 1 < nums.size() && sum < target
3 + 1 < 6 && 6 < 7
4 < 6 && 6 < 7
true
sum = sum + nums[++r]
= 6 + nums[4]
= 6 + 4
= 10
r = 4
if sum >= target
10 >= 7
true
minLength = min(minLength, r - l + 1)
= min(4, 4 - 1 + 1)
= min(4, 4)
= 4
Step 8: loop while l < nums.size()
1 < 6
true
if r + 1 < nums.size() && sum < target
4 + 1 < 6 && 10 < 7
5 < 6 && 10 < 7
false
else
sum = sum - nums[l++]
= 10 - nums[1]
= 10 - 3
= 7
l = 2
if sum >= target
7 >= 7
true
minLength = min(minLength, r - l + 1)
= min(4, 4 - 2 + 1)
= min(4, 3)
= 3
Step 9: loop while l < nums.size()
2 < 6
true
if r + 1 < nums.size() && sum < target
4 + 1 < 6 && 7 < 7
5 < 6 && 7 < 7
false
else
sum = sum - nums[l++]
= 7 - nums[2]
= 7 - 1
= 6
l = 3
if sum >= target
6 >= 7
false
Step 10: loop while l < nums.size()
3 < 6
true
if r + 1 < nums.size() && sum < target
4 + 1 < 6 && 6 < 7
5 < 6 && 6 < 7
true
sum = sum + nums[++r]
= 6 + nums[5]
= 6 + 3
= 9
r = 5
if sum >= target
9 >= 7
true
minLength = min(minLength, r - l + 1)
= min(3, 5 - 3 + 1)
= min(3, 3)
= 3
Step 11: loop while l < nums.size()
3 < 6
true
if r + 1 < nums.size() && sum < target
5 + 1 < 6 && 9 < 7
6 < 6 && 9 < 7
false
else
sum = sum - nums[l++]
= 9 - nums[3]
= 9 - 2
= 7
l = 4
if sum >= target
7 >= 7
true
minLength = min(minLength, r - l + 1)
= min(3, 5 - 4 + 1)
= min(3, 2)
= 2
Step 12: loop while l < nums.size()
4 < 6
true
if r + 1 < nums.size() && sum < target
5 + 1 < 6 && 7 < 7
6 < 6 && 7 < 7
false
else
sum = sum - nums[l++]
= 7 - nums[4]
= 7 - 4
= 3
l = 5
if sum >= target
3 >= 7
false
Step 13: loop while l < nums.size()
5 < 6
true
if r + 1 < nums.size() && sum < target
5 + 1 < 6 && 3 < 7
6 < 6 && 3 < 7
false
else
sum = sum - nums[l++]
= 3 - nums[5]
= 3 - 3
= 0
l = 6
if sum >= target
0 >= 7
false
Step 14: loop while l < nums.size()
6 < 6
false
Step 15: minLength == nums.size() + 1 ? 0 : minLength
2 == 6 + 1 ? 0 : 2
2 == 7 ? 0 : 2
false
We return the result as 2.
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