In computer science, the maximum subarray problem is the task of finding the contiguous subarray within a one-dimensional array of numbers which has the largest sum. For example, for the sequence of values −2, 1, −3, 4, −1, 2, 1, −5, 4; the contiguou…

问题简介   本文将介绍计算机算法中的经典问题--最大子数组问题(maximum subarray problem).所谓的最大子数组问题,指的是:给定一个数组A,寻找A的和最大的非空连续子数组.比如,数组 A = [-2, -3, 4, -1, -2, 1, 5, -3], 最大子数组应为[4, -1, -2, 1, 5],其和为7.   首先,如果A中的元素全部为正(或非负数),则最大子数组就是它本身:如果A中的元素全部为负,则最大子数组就是第一个元素组成的数组.以上两种情形是平凡的,那么,…

转自:http://kartikkukreja.wordpress.com/2013/06/17/kadanes-algorithm/ 本来打算自己写的,后来看到上述链接的博客已经说得很清楚了,就不重复劳动啦. Here, I describe variants of Kadane’s algorithm to solve the maximum subarray and the minimum subarray problems. The maximum subarray problem is…

最大子数组:Maximum Subarray 参考来源:Maximum subarray problem Kadane算法扫描一次整个数列的所有数值,在每一个扫描点计算以该点数值为结束点的子数列的最大和(正数和).该子数列由两部分组成:以前一个位置为结束点的最大子数列.该位置的数值.因为该算法用到了“最佳子结构”(以每个位置为终点的最大子数列都是基于其前一位置的最大子数列计算得出)时间复杂度O(n) public class Solution { public int maxSubArray(i…

这两个系列的题目其实是同一套题,可以互相转换. 首先我们定义一个数组: prefixSum (前序和数组) Given nums: [1, 2, -2, 3] prefixSum: [0, 1, 3, 1, 4 ] 现在我们发现对prefixSum做Best Time To Buy And Sell Stock和对nums做Maximum Subarray,结果相同. 接下来我们就利用prefixSum解这两个系列的题目. Maximum Subarray Question Given an a…

D. Yet Another Subarray Problem You are given an array \(a_1, a_2, \dots , a_n\) and two integers \(m\) and \(k\). You can choose some subarray \(a_l, a_{l+1}, \dots, a_{r-1}, a_r\). The cost of subarray \(a_l, a_{l+1}, \dots, a_{r-1}, a_r\) is equal…

Given an array of integers, find a contiguous subarray which has the largest sum. Notice The subarray should contain at least one number. Have you met this question in a real interview? Yes Example Given the array [−2,2,−3,4,−1,2,1,−5,3], the contigu…

1.   Maximum Subarray (#53) 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 s…

<算法导论>一书中演示分治算法的第二个例子,第一个例子是递归排序,较为简单.寻找maximum subarray稍微复杂点. 题目是这样的:给定序列x = [1, -4, 4, 4, 5, -3, -4, 9, 6 - 4, 6, 4, 3, -5]:寻找一个连续的子序列,使得其和是最大. 这个题目有意义的地方在于,序列X的元素有正有负. 思路很简单,把序列分为相同的两部分A和B,在其内寻找maximum subarray,那么maximum subarray有可能在A中,也有可能在B中,也有…

Maximum Subarray 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. More practice:…