LeetCode [310] Minimum Height Trees

Ref
[1] https://leetcode.com/problems/minimum-height-trees/
OJ
[2] https://leetcode.com/discuss/71656/c-solution-o-n-time-o-n-space

LeetCode [309] Best Time to Buy and Sell Stock with Cooldown

Ref
[1] https://leetcode.com/problems/best-time-to-buy-and-sell-stock-with-cooldown/
OJ
[2] https://leetcode.com/discuss/71354/share-my-thinking-process

LeetCode [308] Range Sum Query 2D - Mutable

 308. Range Sum Query 2D - Mutable

Hard

Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3), which contains sum = 8.

Example:

Given matrix = [
  [3, 0, 1, 4, 2],
  [5, 6, 3, 2, 1],
  [1, 2, 0, 1, 5],
  [4, 1, 0, 1, 7],
  [1, 0, 3, 0, 5]
]

sumRegion(2, 1, 4, 3) -> 8
update(3, 2, 2)
sumRegion(2, 1, 4, 3) -> 10

Note:

1. The matrix is only modifiable by the update function.
2. You may assume the number of calls to update and sumRegion function is distributed evenly.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

//C++, Segment Tree
//C++: 784ms
class STNode{
public:
    int sum;
    int ss, se;
    STNode *left, *right;
    STNode(vector<int> &row, int s, int e){
        sum = 0;
        ss = s;
        se = e;
        left = NULL;
        right = NULL;
        if(s==e){
            sum = row[s];
        }else{
            int m = (s+e)/2;
            left = new STNode(row, s, m);
            right = new STNode(row, m+1, e);
            sum = left->sum+right->sum;
        }
    }
};

class NumMatrix {
    int nRows;
    vector<STNode *> roots;
    void updateST(STNode* root, int j, int val){
        if(!root || j<root->ss || j>root->se) return;
        else if(j==root->ss && j==root->se) root->sum = val;
        else{
            updateST(root->left, j, val);
            updateST(root->right, j, val);
            root->sum = (root->left?root->left->sum:0) + (root->right?root->right->sum:0);
        }
    }
    int sumRange(STNode* root, int i, int j){
        if(!root) return 0;
        else if(i>root->se || j<root->ss) return 0;
        else if(i<=root->ss && j>=root->se) return root->sum;
        else return sumRange(root->left, i, j)+sumRange(root->right, i, j);
    }
public:
    NumMatrix(vector<vector<int>> &matrix) {
        nRows = matrix.size();
        roots.resize(nRows);
        for(int i=0; i<nRows; ++i){
            roots[i] = new STNode(matrix[i], 0, (int)matrix[i].size()-1);
        }
    }

    void update(int row, int col, int val) {
        updateST(roots[row], col, val);
    }

    int sumRegion(int row1, int col1, int row2, int col2) {
        int ret = 0;
        for(int i=row1; i<=row2; ++i){
            ret += sumRange(roots[i], col1, col2);
        }
        return ret;
    }
};

//Java, Segment Tree
class SGTree{
    int sum, start, end;
    SGTree left, right;
    SGTree(int[] nums, int l, int r){
        start = l;
        end = r;
        if(start==end){
            sum = nums[l];
        }else{
            int m = (l+r)/2;
            left = new SGTree(nums, l, m);
            right = new SGTree(nums, m+1, r);
            sum = left.sum + right.sum;
        }
    }
};

class NumMatrix {
    int[] nums;
    SGTree root;
    int m, n;
    public NumMatrix(int[][] matrix) {
        m = matrix.length;
        if(m==0) return;
        n = matrix[0].length;
        if(n==0) return;
        nums = new int[m*n];
        for(int i=0; i<m; ++i){
            for(int j=0; j<n; ++j){
                nums[i*n+j] = matrix[i][j];
            }
        }
        root = new SGTree(nums, 0, nums.length-1);
    }

    void updateST(SGTree node, int i, int v){
        if(node==null || i<node.start || i>node.end) return;
        if(node.start==i && node.end==i) node.sum = v;
        else{
            updateST(node.left, i, v);
            updateST(node.right, i, v);
            node.sum = node.left.sum+node.right.sum;
        }
    }

    int sumST(SGTree node, int l, int r){
        if(node==null) return 0;
        if(r<node.start || l>node.end) return 0;
        if(l<=node.start && node.end<=r) return node.sum;
        int s = sumST(node.left, l, r) + sumST(node.right, l, r);
        return s;
    }
    
    public void update(int row, int col, int val) {
        updateST(root, row*n+col,val);
    }
    
    public int sumRegion(int row1, int col1, int row2, int col2) {
        int s = 0;
        for(int i=row1; i<=row2; ++i){
            s += sumST(root, i*n+col1, i*n+col2);
        }
        return s;
    }
};
/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix obj = new NumMatrix(matrix);
 * obj.update(row,col,val);
 * int param_2 = obj.sumRegion(row1,col1,row2,col2);
 */

//Java, Binary Indexed Tree
class NumMatrix {

    int[][] nums;
    int[][] tree;
    int m, n;
    public NumMatrix(int[][] matrix) {
        m = matrix.length;
        if(m==0) return;
        n = matrix[0].length;
        tree = new int[m+1][n+1];
        nums = new int[m][n];
        for(int i=0; i<m; ++i){
            for(int j=0; j<n; ++j){
                update(i, j, matrix[i][j]);
            }
        }
    }
    
    public void update(int row, int col, int val) {
        int d = val-nums[row][col];
        nums[row][col] = val;
        for(int i=row+1; i<=m; i+=i&(-i)){
            for(int j=col+1; j<=n; j+=j&(-j)){
                tree[i][j] += d;
            }
        }
    }
    
    //row and col are corrordinates for tree
    public int sum(int row, int col){
        int s = 0;
        for(int i=row; i>0; i-=i&(-i)){
            for(int j=col; j>0; j-=j&(-j)){
                s += tree[i][j];
            }
        }
        return s;
    }

    public int sumRegion(int row1, int col1, int row2, int col2) {
        return sum(row2+1, col2+1)-sum(row2+1,col1)-sum(row1, col2+1)+sum(row1, col1);
    }
}

/**
 * Your NumMatrix object will be instantiated and called as such:
 * NumMatrix obj = new NumMatrix(matrix);
 * obj.update(row,col,val);
 * int param_2 = obj.sumRegion(row1,col1,row2,col2);
 */

LeetCode [307] Range Sum Query - Mutable

 307. Range Sum Query - Mutable

Medium

Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive.

The update(i, val) function modifies nums by updating the element at index i to val.

Example:

Given nums = [1, 3, 5]

sumRange(0, 2) -> 9
update(1, 2)
sumRange(0, 2) -> 8

 

Constraints:

• The array is only modifiable by the update function.
• You may assume the number of calls to update and sumRange function is distributed evenly.
• 0 <= i <= j <= nums.length - 1

//C++
//C++: 1720ms
class STNode{
public:
    int sum;
    int ss;
    int se;
    STNode *left;
    STNode *right;
    STNode(vector<int> &nums, int s, int e){
        sum = 0;
        ss = s;
        se = e;
        left = NULL;
        right = NULL;
        if(s==e){
            sum = nums[s];
        }else if(s<e){
            int m = (s+e)/2;
            left = new STNode(nums, s, m);
            right = new STNode(nums, m+1, e);
            sum = left->sum + right->sum;
        }
    }
};

class NumArray {
    STNode * root;
    void updateST(STNode* root, int i, int val){
        if(!root || i<root->ss || i>root->se){
            return;
        }if(i==root->ss && i==root->se){
            root->sum = val;
        }else{
            updateST(root->left, i, val);
            updateST(root->right, i, val);
            root->sum = (root->left?root->left->sum:0) + (root->right?root->right->sum:0);
        }
    }
    int sumRange(STNode* root, int i, int j){
        if(!root) return 0;
        else if(i>root->se || j<root->ss) return 0;
        else if(i<=root->ss && j>=root->se) return root->sum;
        else return sumRange(root->left, i, j)+sumRange(root->right, i, j);
    }
public:
    NumArray(vector<int> &nums) {
        int n = nums.size();
        root = new STNode(nums, 0, n-1);
    }

    void update(int i, int val) {
        updateST(root, i, val);
    }

    int sumRange(int i, int j) {
        return sumRange(root, i, j);
    }
};

//Java
class SGTree{
    int sum;
    int start;
    int end;
    SGTree left;
    SGTree right;
    SGTree(int[] nums, int l, int r){
        start = l;
        end = r;
        if(start==end){
            sum = nums[l];
        }else{
            int m = (l+r)/2;
            left = new SGTree(nums, l, m);
            right = new SGTree(nums, m+1, r);
            sum = left.sum + right.sum;
        }
    }
};

public class NumArray { 
    SGTree sgTree;
    public NumArray(int[] nums) {
        if(nums.length>0)
            sgTree = new SGTree(nums, 0, nums.length-1);
    }

    void updateST(SGTree node, int i, int v){
        if(node==null || i<node.start || i>node.end) return;
        if(i==node.start && i==node.end) node.sum = v;
        else{
            updateST(node.left, i, v);
            updateST(node.right, i, v);
            node.sum = node.left.sum + node.right.sum;
        }
    }

    int sumST(SGTree node, int i, int j){
        if(node==null || j<node.start || i>node.end) return 0;
        if(i<=node.start && node.end<=j) return node.sum;
        return sumST(node.left, i, j)+sumST(node.right, i, j);
    }
    
    public void update(int i, int val) {
        updateST(sgTree, i, val);
    }
    
    public int sumRange(int i, int j) {
        return sumST(sgTree, i, j);
    }
}

/**
 * Your NumArray object will be instantiated and called as such:
 * NumArray obj = new NumArray(nums);
 * obj.update(i,val);
 * int param_2 = obj.sumRange(i,j);
 */

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

class NumArray { int n; int[] bit; int[] arr; int getNext(int i){ return i+(i&(-i)); } int getParent(int i){ return i-(i&(-i)); } public NumArray(int[] nums) { n = nums.length; bit = new int[n+1]; arr = new int[n]; for(int i=0; i<n; ++i){ update(i, nums[i]); } } public void update(int index, int val) { int diff = val-arr[index]; arr[index] = val; int p = index+1; while(p<=n){ bit[p] += diff; p = getNext(p); } } int getPreSum(int index){ int sum = 0; int p = index+1; while(p>0){ sum += bit[p]; p = getParent(p); } return sum; } public int sumRange(int left, int right) { return getPreSum(right)-getPreSum(left-1); } } /** * Your NumArray object will be instantiated and called as such: * NumArray obj = new NumArray(nums); * obj.update(index,val); * int param_2 = obj.sumRange(left,right); */

LeetCode [306] Additive Number

Ref
[1] https://leetcode.com/problems/additive-number/
OJ

LeetCode [305] Number of Islands II

======================= =====================

Note:
    1. differentiate the islands by "id"
    2. "islands" records the total number of islands
    3, "state" records the ids of the islands
Example:  
 0  0  0  0
 0  0  0  0
 0  0  0  0
 0  0  0  0

step 1: [0, 1]
 0  1  0  0
 0  0  0  0
 0  0  0  0
 0  0  0  0
islands = 1

step 2: [1, 0]
 0  1  0  0
 2  0  0  0
 0  0  0  0
 0  0  0  0
islands = 2

step 3: [2, 1]
 0  1  0  0
 2  0  0  0
 0  3  0  0
 0  0  0  0
islands = 3

step 4: [1, 1]
at this step, id_t = 1, id_l = 2, id_b = 3 and id_r = 0
thus, id is set to the minimal minimum one, which is 1
since the new island (1,1) connects the other 3 existing islands
merge them into one island and update their ids accordingly
after step 4, "state" becomes:
 0  1  0  0
 1  1  0  0
 0  1  0  0
 0  0  0  0
islands = 1

the set "merged" is used to avoid cases like
 0  2  0  0  0
 2  2  0  1  0
 0  2  2  0  0
 0  0  0  0  0
 0  0  0  0  0
currently, there are two islands 1 and 2.
if a new land [1, 2] is created, both id_l and id_b is 2
but "islands" should be decreased once
so after [1,2] is created
the state becomes:
 0  1  0  0  0
 1  1  1  1  0
 0  1  1  0  0
 0  0  0  0  0
 0  0  0  0  0


 Ref
[1] https://leetcode.com/problems/number-of-islands-ii/
OJ
[2] https://leetcode.com/discuss/69572/easiest-java-solution-with-explanations

LeetCode [304] Range Sum Query 2D - Immutable

 304. Range Sum Query 2D - Immutable

Medium

Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2).

The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, col2) = (4, 3), which contains sum = 8.

Example:

Given matrix = [
  [3, 0, 1, 4, 2],
  [5, 6, 3, 2, 1],
  [1, 2, 0, 1, 5],
  [4, 1, 0, 1, 7],
  [1, 0, 3, 0, 5]
]

sumRegion(2, 1, 4, 3) -> 8
sumRegion(1, 1, 2, 2) -> 11
sumRegion(1, 2, 2, 4) -> 12

Note:

1. You may assume that the matrix does not change.
2. There are many calls to sumRegion function.
3. You may assume that row1 ≤ row2 and col1 ≤ col2.

//C++: 
class NumMatrix {
    vector<vector<int>> mt;
public:
    NumMatrix(vector<vector<int>> &matrix) {
        int m = matrix.size();
        if(m==0) return;
        int n = matrix[0].size();
        if(n==0) return;
        mt.resize(m+1, vector<int>(n+1, 0));
        for(int i=1; i<=m; ++i){
            for(int j=1; j<=n; ++j){
                mt[i][j] += matrix[i-1][j-1] + mt[i-1][j] + mt[i][j-1] - mt[i-1][j-1];
            }
        }
    }

    int sumRegion(int row1, int col1, int row2, int col2) {
        return mt[row2+1][col2+1] - mt[row2+1][col1] - mt[row1][col2+1] + mt[row1][col1];
    }
};

//Java
class NumMatrix {
    int[][] extMatrix;
    public NumMatrix(int[][] matrix) {
        int m = matrix.length;
        if(m==0) return;
        int n = matrix[0].length;
        if(n==0) return;
        extMatrix = new int[m+1][n+1];
        for(int i=1; i<=m; ++i){
            for(int j=1; j<=n; ++j){
                extMatrix[i][j] = extMatrix[i-1][j]+extMatrix[i][j-1]+matrix[i-1][j-1]-extMatrix[i-1][j-1];
            }
        }
    }
    
    public int sumRegion(int row1, int col1, int row2, int col2) {
        int r = extMatrix[row2+1][col2+1]-extMatrix[row2+1][col1]-extMatrix[row1][col2+1]+extMatrix[row1][col1];
        return r;
    }
}

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

//Java, BIT
class NumArray {
    int[] arr;
    int[] tree;
    int m;
    public NumArray(int[] nums) {
        m = nums.length;
        arr = new int[m];
        tree = new int[m+1];
        for(int i=0; i<m; ++i){
            update(i, nums[i]);
        }
    }
    
    //index for arr
    public void update(int k, int val) {
        int d = val-arr[k];
        arr[k] = val;
        for(int i=k+1; i<=m; i+=i&(-i)){
            tree[i]+=d;
        }
    }
    
    //index for tree
    public int sum(int k){
        int s = 0;
        for(int i=k; i>0; i-=i&(-i)){
            s += tree[i];
        }
        return s;
    }
    public int sumRange(int i, int j) {
        return sum(j+1)-sum(i);
    }
}

/**
 * Your NumArray object will be instantiated and called as such:
 * NumArray obj = new NumArray(nums);
 * obj.update(i,val);
 * int param_2 = obj.sumRange(i,j);
 */

LeetCode [303] Range Sum Query - Immutable

 303. Range Sum Query - Immutable

Easy

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

 

Constraints:

• You may assume that the array does not change.
• There are many calls to sumRange function.
• 0 <= nums.length <= 10^4
• -10^5 <= nums[i] <= 10^5
• 0 <= i <= j < nums.length

//C++
class NumArray {
    vector<int> sum;
public:
    NumArray(vector<int> &nums) {
        for(auto n:nums){
            sum.push_back(n+(sum.empty()?0:sum.back()));
        }
    }

    int sumRange(int i, int j) {
        return sum[j]-(i==0?0:sum[i-1]);
    }
};
// Your NumArray object will be instantiated and called as such:
// NumArray numArray(nums);
// numArray.sumRange(0, 1);
// numArray.sumRange(1, 2);

//Java
class NumArray {
    int[] nums;
    public NumArray(int[] nums) {
        int s = 0;
        this.nums = Arrays.copyOf(nums, nums.length);
        for(int i=0; i<nums.length; ++i){
            s += nums[i];
            this.nums[i] = s;
        }
    }
    
    public int sumRange(int i, int j) {
        return this.nums[j] - (i-1>=0?this.nums[i-1]:0);
    }
}

/**
 * Your NumArray object will be instantiated and called as such:
 * NumArray obj = new NumArray(nums);
 * int param_1 = obj.sumRange(i,j);
 */