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)struct Solution;
impl Solution {
fn split_array(nums: Vec<i32>, m: i32) -> i32 {
let mut lo = *nums.iter().max().unwrap();
let mut hi = nums.iter().sum();
let n = nums.len();
while lo <= hi {
let mid = (lo + hi) / 2;
if Self::split(&nums, mid, n) <= m {
hi = mid - 1;
} else {
lo = mid + 1;
}
}
lo
}
fn split(nums: &[i32], max: i32, n: usize) -> i32 {
let mut sum = 0;
let mut res = 1;
for i in 0..n {
if nums[i] + sum > max {
sum = nums[i];
res += 1;
} else {
sum += nums[i];
}
}
res
}
}
#[test]
fn test() {
let nums = vec![7, 2, 5, 10, 8];
let m = 2;
let res = 18;
assert_eq!(Solution::split_array(nums, m), res);
let nums = vec![1, 2, 3, 4, 5];
let m = 2;
let res = 9;
assert_eq!(Solution::split_array(nums, m), res);
let nums = vec![1, 4, 4];
let m = 3;
let res = 4;
assert_eq!(Solution::split_array(nums, m), res);
let nums = vec![2, 3, 1, 2, 4, 3];
let m = 5;
let res = 4;
assert_eq!(Solution::split_array(nums, m), res);
}