Prefix Sum Notes

用途：用来解决sub array sum问题。
构造： prefixSum[i] = nums[0] + nums[1] + ....+nums[i - 1] 1 based
用法： sum(i ~ j) = prefixSum[j + 1] - prefixSum[i], 其中upperbound is inclusive and lowerbound 
             is exclusive.
 FAQ 
  1. 为什么要有prefixSum[0]
    2. 因为在求sum(0 ~ j)时，为了保证不越界，index 0对应的是prefixSum[1], 否则根据lowerbound exclusive 特性，会出现prefixSum[-1]的情况。


  • 有时候不一定需要构建preSum数组，直接用动态的sum就可以解决问题。比如：
          Find Pivot Index

  •  和hashtable合用的时候记住初始化(0 , -1)，得到的subarray length就是i - get(sum)。如果是求maximum subarray, 第二次出现sum就不更新，让sum离现在的位置远些。如果是求方案数，就需要更新hashtable value。
           contiguous-array

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