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:
- You may assume that the array does not change.
- There are many calls to sumRange function.
Solution: Note that there are many calls to sumRange function, so the tranverse method is inefficient(O(n^3)). We use the idea of cumulative histogram to build an array A of cumulative sums. A[i] is sum[0,i], sum(i,j)=A[j]-A[i-1](i!=0)
1 class NumArray { 2 private: 3 vector<int> accumNums; 4 public: 5 NumArray(vector<int> nums) { 6 accumNums=nums; 7 for (int i=1;i<nums.size();i++){ 8 accumNums[i]+=accumNums[i-1]; //calculate the cumulative sums 9 } 10 } 11 12 int sumRange(int i, int j) { 13 return (i==0)? accumNums[j]:accumNums[j]-accumNums[i-1]; 14 } 15 }; 16 17 /** 18 * Your NumArray object will be instantiated and called as such: 19 * NumArray obj = new NumArray(nums); 20 * int param_1 = obj.sumRange(i,j); 21 */