303 Range Sum Query - Immutable
1. Question
Given an integer arraynums, find the sum of the elements between indicesiandj(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.
2. Implementation
(1) DP
class NumArray {
int prefixSum[];
public NumArray(int[] nums) {
int n = nums.length;
prefixSum = new int[n + 1];
for (int i = 1; i <= n; i++) {
prefixSum[i] = prefixSum[i - 1] + nums[i - 1];
}
}
public int sumRange(int i, int j) {
return prefixSum[j + 1] - prefixSum[i];
}
}
/**
* Your NumArray object will be instantiated and called as such:
* NumArray obj = new NumArray(nums);
* int param_1 = obj.sumRange(i,j);
*/
3. Time & Space Complexity
DP: 时间复杂度: NumArray(): O(n), sumRange(): O(1), 空间复杂度O(n)
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