leetcode-DP-   303. Range Sum Query – Immutable

Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive.

Example

Given nums = [-2, 0, 3, -5, 2, -1]
                
                sumRange(0, 2) -> 1
                sumRange(2, 5) -> -1
                sumRange(0, 5) -> -3

Note

1. You may assume that the array does not change.
2. There are many calls to sumRange function.

DP解法：先计算从下标 0 到第 i 项的前缀和，最终 sumRange(i, j) 的结果即为 0-j 的前缀和减去 0-(i-1) 的前缀和。

class NumArray {
                public:
                	vector<int> sums;
                	int s;
                	NumArray(  vector<int> nums)
                	{
                		s = nums.size();
                		if (s <= 0)return ;
                		sums.reserve(100);
                
                		sums.push_back(nums[0]);
                
                		for (int i = 1; i < nums.size(); i++)
                		{
                
                
                			int a = sums[i - 1] + nums[i];
                
                			sums.push_back(a);
                
                
                		}
                
                	}
                
                
                	int sumRange(int i, int j) {
                		if (s <= 0)return 0;
                
                		if (i == 0)return sums[j];
                		return sums[j]-sums[i-1];
                	}
                
                
                
                };