leetcode-53

Maximum Subarray

题目

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

For example, given the array

[-2,1,-3,4,-1,2,1,-5,4]

,

the contiguous subarray

[4,-1,2,1]

has the largest sum =

6

.

解题思路

this problem was discussed by Jon Bentley (Sep. 1984 Vol. 27 No. 9 Communications of the ACM P885)

the paragraph below was copied from his paper (with a little modifications)

algorithm that operates on arrays: it starts at the left end (element A[1]) and scans through to the right end (element A
), keeping track of the maximum sum subvector seen so far. The maximum is initially A[0]. Suppose we've solved the problem for A[1
.. i - 1]; how can we extend that to A[1 .. i]? The maximum

sum in the first I elements is either the maximum sum in the first i - 1 elements (which we'll call MaxSoFar), or it is that of a subvector that ends in position i (which we'll call MaxEndingHere).

MaxEndingHere is either A[i] plus the previous MaxEndingHere, or just A[i], whichever is larger.

java代码：

public class Solution {
public int maxSubArray(int[] nums) {
int maxSoFar = nums[0], maxEndingHere = nums[0];
for (int i = 1;i<nums.length;++i){
maxEndingHere= Math.max( maxEndingHere + nums[i], nums[i] );
maxSoFar=Math.max(maxSoFar, maxEndingHere);
}
return maxSoFar;
}
}

原题地址