410. Split Array Largest Sum 把数组划分为m组,怎样使最大和最小

[抄题]:

Given an array 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.

Note:
If n is the length of array, assume the following constraints are satisfied:

  • 1 ≤ n ≤ 1000
  • 1 ≤ m ≤ min(50, n)

 

Examples:

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.

 [暴力解法]:

时间分析:

空间分析:

 [优化后]:

时间分析:

空间分析:

[奇葩输出条件]:

[奇葩corner case]:

[思维问题]:

不知道干嘛用二分法:二分法可以通过mid的移动 找一个位置

[英文数据结构或算法,为什么不用别的数据结构或算法]:

[一句话思路]:

想不到:最大的数肯定要分隔开,就看能往左划几个数和它一组

[7,2,5,10,8,105550]
3
返回105550

分组不超过m就往扩展 否则往右

[输入量]:空: 正常情况:特大:特小:程序里处理到的特殊情况:异常情况(不合法不合理的输入):

[画图]:

[一刷]:

l r都必须定义成long型,在返回的时候切换回来

[二刷]:

[三刷]:

[四刷]:

[五刷]:

  [五分钟肉眼debug的结果]:

[总结]:

多试试几个case 自然就明白了

数组中找一个位置,就可以用二分查找

[复杂度]:Time complexity: O(lgn) Space complexity: O(1)

[算法思想:迭代/递归/分治/贪心]:迭代

[关键模板化代码]:

while (l <= r) {
            long mid = (l + r) / 2;
            if (noLongerThanM(mid, nums, m)) r = mid - 1;
            else l = mid + 1;
        }
        
        return (int)l; 
    }

[其他解法]:

dp麻烦

[Follow Up]:

[LC给出的题目变变变]:

 [代码风格] :

 [是否头一次写此类driver funcion的代码] :

class Solution {
    public int splitArray(int[] nums, int m) {
        //ini: sum, l, r
        int max = nums[0]; long sum = 0;
        for (int num : nums) {
            sum += num;
            max = Math.max(max, num);
        }

        //cc
        if (nums.length == 1) return (int)sum;
        long l = max, r = sum;
        
        // b - s
        while (l <= r) {
            long mid = (l + r) / 2;
            if (noLongerThanM(mid, nums, m)) r = mid - 1;
            else l = mid + 1;
        }
        
        return (int)l; 
    }
    
    public boolean noLongerThanM(long value, int[] nums, int m) {
        int count = 1, sum = 0;
        
        for (int num : nums) {
            sum += num;
            if (sum > value) {
                sum = num;
                count++;
                if (count > m) return false;
            }
        }
        
        return true;
    }
}
View Code

 

转载于:https://www.cnblogs.com/immiao0319/p/9097881.html

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