[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:

1. You may assume that the array does not change.
2. 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;
};

　　

类似题目：

[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

　　

 

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