[LeetCode] 303. Range Sum Query - Immutable 区域和检索 - 不可变
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.
给一个整数数组，找出两个index之间的数字和。
如果每次遍历i, j之间的数字相加求和，十分的不高效，无法通过OJ。
解法：DP，建一个数组dp，其中dp[i]表示[0, i]区间的数字之和，那么[i,j]就可以表示为dp[j]-dp[i-1]，当i=0时，直接返回dp[j]即可。
Java:
class NumArray {
int[] nums;
public NumArray(int[] nums) {
for(int i = 1; i < nums.length; i++)
nums[i] += nums[i - 1];
this.nums = nums;
}
public int sumRange(int i, int j) {
if(i == 0)
return nums[j];
return nums[j] - nums[i - 1];
}
}
Python:
class NumArray(object):
def __init__(self, nums):
"""
initialize your data structure here.
:type nums: List[int]
"""
self.accu = [0]
for num in nums:
self.accu += self.accu[-1] + num,
def sumRange(self, i, j):
"""
sum of elements nums[i..j], inclusive.
:type i: int
:type j: int
:rtype: int
"""
return self.accu[j + 1] - self.accu[i]
Python:
# Time: ctor: O(n),
# lookup: O(1)
# Space: O(n)
class NumArray(object):
def __init__(self, nums):
"""
initialize your data structure here.
:type nums: List[int]
"""
self.accu = [0]
for num in nums:
self.accu.append(self.accu[-1] + num),
def sumRange(self, i, j):
"""
sum of elements nums[i..j], inclusive.
:type i: int
:type j: int
:rtype: int
"""
return self.accu[j + 1] - self.accu[i]
Python: wo
class NumArray(object):
def __init__(self, nums):
"""
:type nums: List[int]
"""
s, n = 0, len(nums)
self.dp = [0] * (n + 1)
for i in xrange(n):
s += nums[i]
self.dp[i + 1] = s
def sumRange(self, i, j):
"""
:type i: int
:type j: int
:rtype: int
"""
return self.dp[j + 1] - self.dp[i]
C++:
class NumArray {
public:
NumArray(vector<int> &nums) {
accu.push_back(0);
for (int num : nums)
accu.push_back(accu.back() + num);
}
int sumRange(int i, int j) {
return accu[j + 1] - accu[i];
}
private:
vector<int> accu;
};
C++:
class NumArray {
public:
NumArray(vector<int> &nums) {
dp.resize(nums.size() + 1, 0);
for (int i = 1; i <= nums.size(); ++i) {
dp[i] = dp[i - 1] + nums[i - 1];
}
}
int sumRange(int i, int j) {
return dp[j + 1] - dp[i];
}
private:
vector<int> dp;
};
C++:
class NumArray {
public:
NumArray(vector<int> &nums) {
dp = nums;
for (int i = 1; i < nums.size(); ++i) {
dp[i] += dp[i - 1];
}
}
int sumRange(int i, int j) {
return i == 0? dp[j] : dp[j] - dp[i - 1];
}
private:
vector<int> dp;
};
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[LeetCode] 304. Range Sum Query 2D - Immutable 二维区域和检索 - 不可变Range Sum Query - Mutable
Range Sum Query 2D - Mutable
