Week 3 @ 2025 算法周记【前缀和 + 双指针数组】

1 前缀和
- 1.1 LC 303. Range Sum Query - Immutable 区域和检索 - 数组不可变
- 1.2 LC 304. Range Sum Query 2D - Immutable 二维区域和检索 - 矩阵不可变
2 双指针数组

前缀和

LC 303. Range Sum Query - Immutable 区域和检索 - 数组不可变

https://leetcode.com/problems/range-sum-query-immutable/

type NumArray struct {
    sums []int
}


func Constructor(nums []int) NumArray {
    sums := make([]int, len(nums))
    sums[0] = nums[0]
    for i := 1; i < len(nums); i++ {
        sums[i] = sums[i-1] + nums[i]
    }
    return NumArray{sums}
}


func (this *NumArray) SumRange(left int, right int) int {
    if left == 0 {
        return this.sums[right] 
    }
    
    return this.sums[right] - this.sums[left-1]
}


/**
 * Your NumArray object will be instantiated and called as such:
 * obj := Constructor(nums);
 * param_1 := obj.SumRange(left,right);
 */

LC 304. Range Sum Query 2D - Immutable 二维区域和检索 - 矩阵不可变

https://leetcode.com/problems/range-sum-query-2d-immutable/

type NumMatrix struct {
    sums [][]int
}


func Constructor(matrix [][]int) NumMatrix {
    sums := make([][]int, len(matrix)+1)
    sums[0] = make([]int, len(matrix[0])+1)
    for i := range matrix {
        sums[i+1] = make([]int, len(matrix[0])+1)

        for j := range matrix[i] {
            sums[i+1][j+1] = sums[i+1][j] + matrix[i][j]
        }
    }
    // fmt.Println(sums)
    for i := range matrix {
        for j := range matrix[i] {
            sums[i+1][j+1] += sums[i][j+1]
        }
    }

    // for i := range sums {
    //     for j := range sums[i] {
    //         fmt.Printf("%2d ", sums[i][j])
    //     }
    //     fmt.Println()
    // }

    return NumMatrix { sums }
}


func (this *NumMatrix) SumRegion(row1 int, col1 int, row2 int, col2 int) int {
    return this.sums[row2+1][col2+1] - this.sums[row1][col2+1] - this.sums[row2+1][col1]  +  this.sums[row1][col1]
}


/**
 * Your NumMatrix object will be instantiated and called as such:
 * obj := Constructor(matrix);
 * param_1 := obj.SumRegion(row1,col1,row2,col2);
 */

双指针数组

LC 88. Merge Sorted Array 合并两个有序数组

https://leetcode.com/problems/merge-sorted-array/

func merge(nums1 []int, m int, nums2 []int, n int)  {
    i, j := m-1, n-1
    p := m+n-1
    for i >= 0 && j >= 0 {
        if nums1[i] >= nums2[j] {
            nums1[p] = nums1[i]
            p--
            i--
        } else {
            nums1[p] = nums2[j]
            p--
            j--
        }
    }
    for i >= 0 {
        nums1[p] = nums1[i]
        p--
        i--
    }
    for j >= 0 {
        nums1[p] = nums2[j]
        p--
        j--
    }
}

LC 977. Squares of a Sorted Array 有序数组的平方

https://leetcode.com/problems/squares-of-a-sorted-array/description/

待复习

LC 360. 有序转化数组 [Premium]

https://leetcode.com/problems/sort-transformed-array/description/

未完成

LC 1329. 将矩阵按对角线排序

https://leetcode.com/problems/sort-the-matrix-diagonally/description/

待复习

LC 1260. Shift 2D Grid 二维网格迁移

https://leetcode.com/problems/shift-2d-grid/

不引入额外空间做法

待复习

知识库

Week 3 @ 2025 算法周记【前缀和 + 双指针数组】

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前缀和

LC 303. Range Sum Query - Immutable 区域和检索 - 数组不可变

LC 304. Range Sum Query 2D - Immutable 二维区域和检索 - 矩阵不可变

双指针数组

LC 88. Merge Sorted Array 合并两个有序数组

LC 977. Squares of a Sorted Array 有序数组的平方

LC 360. 有序转化数组 [Premium]

LC 1329. 将矩阵按对角线排序

LC 1260. Shift 2D Grid 二维网格迁移

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