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  • maxSubArray

    Description:

    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.

    Thoughts:

    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[n]), 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.

    there is my java code:

    package easy.array;
    
    public class MaxSubArray {
        public int maxSubArray(int[] nums){
            int maxsofar = nums[0];
            int maxtotal = nums[0];
            for(int i = 1; i< nums.length;i++){
                maxsofar = Math.max(maxsofar+nums[i], nums[i]);
                maxtotal = Math.max(maxtotal, maxsofar);
            }
            return maxtotal;
        }
        
        public static void main(String[] args){
            int[] nums = new int[]{-2, 1, -3, 4, -1, 2, 1, -5, 4};
            MaxSubArray max = new MaxSubArray();
            int num = max.maxSubArray(nums);
            System.out.println(num);
        }
    }
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  • 原文地址:https://www.cnblogs.com/whatyouknow123/p/7663575.html
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