Leetcode Maximum Subarray

Find the contiguous subarray within an array (containing at least one number) which have the largest sum.

For example, given the array [−2,1,−3,4,−1,2,1,−5,4] ,
The contiguous Subarray has the [4,−1,2,1] largest sum = 6 .

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More Practice:

If you had figured out the O (n) solution, try coding another solution using the divide and conquer approach, WHI CH is more subtle.

Solution: Dynamic Programming.sum[i] = max (Nums[i], nums[i] + sum[i-1]) The changing condition for Dynamic programming is "We s Hould ignore the sum of the previous n-1 elements if nth element is greater than the sum. "

Imagine if we were to traverse this array from the beginning. For one of the elements in an array, it has only two choices:

1. Either join the previous array plus (group with others)

2. Either set up a single array of your own (one for yourself)

So the choice of this element depends on what group he can contribute to. If you are in a group with someone else, you can always add and get bigger, or a group of others, and if you start a group, your value is larger than the value of the previous sums, then it is better to open a group alone.

So use a sum array to record the maximum value for each round of sum, Sum[i] Indicates whether the current element is the same as the previous array plus a set or a single set of itself, and then maintain a global maximum value of the throne answer.

Java Code:

The first type of notation:

 Public classSolution { Public intMaxsubarray (int[] nums) {        intLen =nums.length; int[] sum =New int[Len]; intmax = Nums[0]; sum[0] = Nums[0];  for(inti = 1; i< Len; i++) {Sum[i]= Math.max (Nums[i], nums[i] + sum[i-1]); Max=Math.max (Max, sum[i]); }        returnMax; }}

The second way: sum does not use an array, only an int

 Public class Solution {    publicint maxsubarray (int[] nums) {        int sum = nums[0];         int max = nums[0];          for (int i = 1; i< nums.length; i++) {            = Math.max (Nums[i], nums[i] + sum);             = Math.max (max, sum);        }         return Max;}    }

Reference:

1. http://www.programcreek.com/2013/02/leetcode-maximum-subarray-java/

2. http://www.programcreek.com/2013/02/leetcode-maximum-subarray-java/

Leetcode Maximum Subarray