Description
https://leetcode.com/problems/split-array-largest-sum/
Given an array nums which consists of non-negative integers and an integer m, you can split the array into m non-empty continuous subarrays.
Write an algorithm to minimize the largest sum among these m subarrays.
Example 1:
Input: nums = [7,2,5,10,8], m = 2 Output: 18 Explanation: There are four ways to split nums into two subarrays. The best way is to split it into [7,2,5] and [10,8], where the largest sum among the two subarrays is only 18.
Example 2:
Input: nums = [1,2,3,4,5], m = 2 Output: 9
Example 3:
Input: nums = [1,4,4], m = 3 Output: 4
Constraints:
1 <= nums.length <= 10000 <= nums[i] <= 1061 <= m <= min(50, nums.length)
Explanation
Python Solution
class Solution:
def splitArray(self, nums: List[int], m: int) -> int:
if not nums:
return 0
n = len(nums)
start = max(nums)
end = sum(nums)
while start + 1 < end:
largest_sum = (start + end) // 2
if self.largest_sum_satisfy_m(nums, m, largest_sum):
end = largest_sum
else:
start = largest_sum
if self.largest_sum_satisfy_m(nums, m, start):
return start
return end
def largest_sum_satisfy_m(self, nums, m, largest_sum):
num_of_sub = 0
current_sum = 0
for num in nums:
if current_sum + num <= largest_sum:
current_sum += num
else:
num_of_sub += 1
current_sum = num
num_of_sub += 1
return num_of_sub <= m
- Time Complexity: ~NlogX where X = sum(nums) – max(nums)
- Space Complexity: ~1.
class Solution {
public int firstMissingPositive(int[] A) {
int m = 1;
HashSet set = new HashSet();
for(int num: nums){
if(num>m){
set.add(num);
}else if(num==m){
m++;
while(set.contains(m)){
set.remove(m);
m++;
}
}
}
return m;
}
}