LeetCode热门100题算法和思路（day7）
2022-08-21 本文已影响0人
码农朱同学
LeetCode215 数组中的第k个最大元素
题目详情
给定整数数组 nums 和整数 k，请返回数组中第 k 个最大的元素。
请注意，你需要找的是数组排序后的第 k 个最大的元素，而不是第 k 个不同的元素。
你必须设计并实现时间复杂度为 O(n) 的算法解决此问题。
示例 1:
输入: [3,2,1,5,6,4], k = 2
输出: 5
示例 2:
输入: [3,2,3,1,2,4,5,5,6], k = 4
输出: 4
提示：
1 <= k <= nums.length <= 105
-104 <= nums[i] <= 104
代码
class LeetCode215 {
public static void main(String[] args) {
System.out.println(new Solution().findKthLargest(new int[]{3, 2, 1, 5, 6, 4}, 3));
System.out.println(new Solution2().findKthLargest(new int[]{3, 2, 1, 5, 6, 4}, 3));
System.out.println(new Solution3().findKthLargest(new int[]{3, 2, 1, 5, 6, 4}, 3));
}
/*
基于堆排序的选择方法
*/
static class Solution {
public int findKthLargest(int[] nums, int k) {
int heapSize = nums.length;
buildMaxHeap(nums, heapSize);
for (int i = nums.length - 1; i >= nums.length - k + 1; --i) {
swap(nums, 0, i);
--heapSize;
maxHeapify(nums, 0, heapSize);
}
return nums[0];
}
public void buildMaxHeap(int[] a, int heapSize) {
for (int i = heapSize / 2; i >= 0; --i) {
maxHeapify(a, i, heapSize);
}
}
public void maxHeapify(int[] a, int i, int heapSize) {
int l = i * 2 + 1, r = i * 2 + 2, largest = i;
if (l < heapSize && a[l] > a[largest]) {
largest = l;
}
if (r < heapSize && a[r] > a[largest]) {
largest = r;
}
if (largest != i) {
swap(a, i, largest);
maxHeapify(a, largest, heapSize);
}
}
public void swap(int[] a, int i, int j) {
int temp = a[i];
a[i] = a[j];
a[j] = temp;
}
}
static class Solution2 {
public int findKthLargest(int[] nums, int k) {
// 初始化最小元素优先堆
PriorityQueue<Integer> heap = new PriorityQueue<Integer>((n1, n2) -> n1 - n2);
//在堆中保留 k 个最大元素
for (int n : nums) {
heap.add(n);
if (heap.size() > k)
heap.poll();
}
return heap.poll();
}
}
/*
基于快速排序的选择方法
*/
static class Solution3 {
Random random = new Random();
public int findKthLargest(int[] nums, int k) {
return quickSelect(nums, 0, nums.length - 1, nums.length - k);
}
public int quickSelect(int[] a, int l, int r, int index) {
int q = randomPartition(a, l, r);
if (q == index) {
return a[q];
} else {
return q < index ? quickSelect(a, q + 1, r, index) : quickSelect(a, l, q - 1, index);
}
}
public int randomPartition(int[] a, int l, int r) {
int i = random.nextInt(r - l + 1) + l;
swap(a, i, r);
return partition(a, l, r);
}
public int partition(int[] a, int l, int r) {
int x = a[r], i = l - 1;
for (int j = l; j < r; ++j) {
if (a[j] <= x) {
swap(a, ++i, j);
}
}
swap(a, i + 1, r);
return i + 1;
}
public void swap(int[] a, int i, int j) {
int temp = a[i];
a[i] = a[j];
a[j] = temp;
}
}
}
LeetCode221 最大正方形
题目详情
在一个由 '0' 和 '1' 组成的二维矩阵内，找到只包含 '1' 的最大正方形，并返回其面积。
示例 1：
输入：matrix = [["1","0","1","0","0"],["1","0","1","1","1"],["1","1","1","1","1"],["1","0","0","1","0"]]
输出：4
示例 2：
输入：matrix = [["0","1"],["1","0"]]
输出：1
示例 3：
输入：matrix = [["0"]]
输出：0
提示：
m == matrix.length
n == matrix[i].length
1 <= m, n <= 300
matrix[i][j] 为 '0' 或 '1'
代码
public class LeetCode221 {
public static void main(String[] args) {
System.out.println(new Solution().maximalSquare(new char[][]{{'1', '0', '1', '0', '0'}, {'1', '0', '1', '1', '1'}, {'1', '1', '1', '1', '1'}, {'1', '0', '0', '1', '0'}}));
System.out.println(new Solution2().maximalSquare(new char[][]{{'1', '0', '1', '0', '0'}, {'1', '0', '1', '1', '1'}, {'1', '1', '1', '1', '1'}, {'1', '0', '0', '1', '0'}}));
}
/*
暴力法
*/
static class Solution {
public int maximalSquare(char[][] matrix) {
int maxSide = 0;
if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
return maxSide;
}
int rows = matrix.length, columns = matrix[0].length;
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
if (matrix[i][j] == '1') {
// 遇到一个 1 作为正方形的左上角
maxSide = Math.max(maxSide, 1);
// 计算可能的最大正方形边长
int currentMaxSide = Math.min(rows - i, columns - j);
for (int k = 1; k < currentMaxSide; k++) {
// 判断新增的一行一列是否均为 1
boolean flag = true;
if (matrix[i + k][j + k] == '0') {
break;
}
for (int m = 0; m < k; m++) {
if (matrix[i + k][j + m] == '0' || matrix[i + m][j + k] == '0') {
flag = false;
break;
}
}
if (flag) {
maxSide = Math.max(maxSide, k + 1);
} else {
break;
}
}
}
}
}
int maxSquare = maxSide * maxSide;
return maxSquare;
}
}
/*
动态规划
*/
static class Solution2 {
public int maximalSquare(char[][] matrix) {
int maxSide = 0;
if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
return maxSide;
}
int rows = matrix.length, columns = matrix[0].length;
int[][] dp = new int[rows][columns];
for (int i = 0; i < rows; i++) {
for (int j = 0; j < columns; j++) {
if (matrix[i][j] == '1') {
if (i == 0 || j == 0) {
dp[i][j] = 1;
} else {
dp[i][j] = Math.min(Math.min(dp[i - 1][j], dp[i][j - 1]), dp[i - 1][j - 1]) + 1;
}
maxSide = Math.max(maxSide, dp[i][j]);
}
}
}
int maxSquare = maxSide * maxSide;
return maxSquare;
}
}
}
LeetCode226 翻转二叉树
题目详情
给你一棵二叉树的根节点 root ，翻转这棵二叉树，并返回其根节点。
示例 1：
输入：root = [4,2,7,1,3,6,9]
输出：[4,7,2,9,6,3,1]
示例 2：
输入：root = [2,1,3]
输出：[2,3,1]
示例 3：
输入：root = []
输出：[]
提示：
树中节点数目范围在 [0, 100] 内
-100 <= Node.val <= 100
代码
public class LeetCode226 {
public static void main(String[] args) {
TreeNode.prettyPrintTree(new Solution().invertTree(TreeNode.buildBinaryTree(new Integer[]{4,2,7,1,3,6,9})));
TreeNode.prettyPrintTree(new Solution2().invertTree(TreeNode.buildBinaryTree(new Integer[]{4,2,7,1,3,6,9})));
TreeNode.prettyPrintTree(new Solution3().invertTree(TreeNode.buildBinaryTree(new Integer[]{4,2,7,1,3,6,9})));
}
/*
递归
*/
static class Solution {
public TreeNode invertTree(TreeNode root) {
if (root == null) {
return null;
}
TreeNode right = invertTree(root.right);
TreeNode left = invertTree(root.left);
root.left = right;
root.right = left;
return root;
}
}
/*
* 层序遍历方式反转
*/
static class Solution2 {
public TreeNode invertTree(TreeNode root) {
if (root == null) {
return null;
}
Queue<TreeNode> queue = new ArrayDeque<>();
queue.offer(root);
while (!queue.isEmpty()) {
TreeNode node = queue.poll();
TreeNode temp = node.left;
node.left = node.right;
node.right = temp;
if (node.left != null) {
queue.offer(node.left);
}
if (node.right != null) {
queue.offer(node.right);
}
}
return root;
}
}
/*
* 深度优先遍历的方式反转
*/
static class Solution3 {
public TreeNode invertTree(TreeNode root) {
if (root == null) {
return null;
}
Stack<TreeNode> stack = new Stack<>();
stack.push(root);
while (!stack.isEmpty()) {
int size = stack.size();
for (int i = 0; i < size; i++) {
TreeNode cur = stack.pop();
TreeNode temp = cur.left;
cur.left = cur.right;
cur.right = temp;
if (cur.right != null) {
stack.push(cur.right);
}
if (cur.left != null) {
stack.push(cur.left);
}
}
}
return root;
}
}
}
LeetCode234 回文链表
题目详情
给你一个单链表的头节点 head ，请你判断该链表是否为回文链表。如果是，返回 true ；否则，返回 false 。
示例 1：
输入：head = [1,2,2,1]
输出：true
示例 2：
输入：head = [1,2]
输出：false
提示：
链表中节点数目在范围[1, 105] 内
0 <= Node.val <= 9
进阶：你能否用 O(n) 时间复杂度和 O(1) 空间复杂度解决此题？
代码
public class LeetCode234 {
public static void main(String[] args) {
System.out.println(new Solution().isPalindrome(ListNode.buildNode(new int[]{1, 2, 2, 1})));
System.out.println(new Solution2().isPalindrome(ListNode.buildNode(new int[]{1, 2, 2, 1})));
System.out.println(new Solution3().isPalindrome(ListNode.buildNode(new int[]{1, 2, 2, 1})));
}
/*
将值复制到数组中后用双指针法
*/
static class Solution {
public boolean isPalindrome(ListNode head) {
List<Integer> vals = new ArrayList<Integer>();
// 将链表的值复制到数组中
ListNode currentNode = head;
while (currentNode != null) {
vals.add(currentNode.val);
currentNode = currentNode.next;
}
// 使用双指针判断是否回文
int front = 0;
int back = vals.size() - 1;
while (front < back) {
if (!vals.get(front).equals(vals.get(back))) {
return false;
}
front++;
back--;
}
return true;
}
}
/*
递归
*/
static class Solution2 {
private ListNode frontPointer;
private boolean recursivelyCheck(ListNode currentNode) {
if (currentNode != null) {
if (!recursivelyCheck(currentNode.next)) {
return false;
}
if (currentNode.val != frontPointer.val) {
return false;
}
frontPointer = frontPointer.next;
}
return true;
}
public boolean isPalindrome(ListNode head) {
frontPointer = head;
return recursivelyCheck(head);
}
}
/*
快慢指针
*/
static class Solution3 {
public boolean isPalindrome(ListNode head) {
if (head == null) {
return true;
}
// 找到前半部分链表的尾节点并反转后半部分链表
ListNode firstHalfEnd = endOfFirstHalf(head);
ListNode secondHalfStart = reverseList(firstHalfEnd.next);
// 判断是否回文
ListNode p1 = head;
ListNode p2 = secondHalfStart;
boolean result = true;
while (result && p2 != null) {
if (p1.val != p2.val) {
result = false;
}
p1 = p1.next;
p2 = p2.next;
}
// 还原链表并返回结果
firstHalfEnd.next = reverseList(secondHalfStart);
return result;
}
private ListNode reverseList(ListNode head) {
ListNode prev = null;
ListNode curr = head;
while (curr != null) {
ListNode nextTemp = curr.next;
curr.next = prev;
prev = curr;
curr = nextTemp;
}
return prev;
}
private ListNode endOfFirstHalf(ListNode head) {
ListNode fast = head;
ListNode slow = head;
while (fast.next != null && fast.next.next != null) {
fast = fast.next.next;
slow = slow.next;
}
return slow;
}
}
}
LeetCode236 二叉树的最近公共祖先
题目详情
给定一个二叉树, 找到该树中两个指定节点的最近公共祖先。
百度百科中最近公共祖先的定义为：“对于有根树 T 的两个节点 p、q，最近公共祖先表示为一个节点 x，满足 x 是 p、q 的祖先且 x 的深度尽可能大（一个节点也可以是它自己的祖先）。”
示例 1：
输入：root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
输出：3
解释：节点 5 和节点 1 的最近公共祖先是节点 3 。
示例 2：
输入：root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
输出：5
解释：节点 5 和节点 4 的最近公共祖先是节点 5 。因为根据定义最近公共祖先节点可以为节点本身。
示例 3：
输入：root = [1,2], p = 1, q = 2
输出：1
提示：
树中节点数目在范围 [2, 105] 内。
-109 <= Node.val <= 109
所有 Node.val 互不相同 。
p != q
p 和 q 均存在于给定的二叉树中。
代码
public class LeetCode236 {
public static void main(String[] args) {
TreeNode.prettyPrintTree(new Solution().lowestCommonAncestor(
TreeNode.buildBinaryTree(new Integer[]{3, 5, 1, 6, 2, 0, 8, null, null, 7, 4}),
TreeNode.buildBinaryTree(new Integer[]{5, 1, 6, 2, 0, 8, null, null, 7, 4}),
TreeNode.buildBinaryTree(new Integer[]{1, 6, 2, 0, 8, null, null, 7, 4})));
TreeNode.prettyPrintTree(new Solution2().lowestCommonAncestor(
TreeNode.buildBinaryTree(new Integer[]{3, 5, 1, 6, 2, 0, 8, null, null, 7, 4}),
TreeNode.buildBinaryTree(new Integer[]{5, 1, 6, 2, 0, 8, null, null, 7, 4}),
TreeNode.buildBinaryTree(new Integer[]{1, 6, 2, 0, 8, null, null, 7, 4})));
}
static class Solution {
private TreeNode ans;
public Solution() {
this.ans = null;
}
private boolean dfs(TreeNode root, TreeNode p, TreeNode q) {
if (root == null) return false;
boolean lson = dfs(root.left, p, q);
boolean rson = dfs(root.right, p, q);
if ((lson && rson) || ((root.val == p.val || root.val == q.val) && (lson || rson))) {
ans = root;
}
return lson || rson || (root.val == p.val || root.val == q.val);
}
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
this.dfs(root, p, q);
return this.ans;
}
}
/*
递归-存储父节点
*/
static class Solution2 {
Map<Integer, TreeNode> parent = new HashMap<Integer, TreeNode>();
Set<Integer> visited = new HashSet<Integer>();
public void dfs(TreeNode root) {
if (root.left != null) {
parent.put(root.left.val, root);
dfs(root.left);
}
if (root.right != null) {
parent.put(root.right.val, root);
dfs(root.right);
}
}
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
dfs(root);
while (p != null) {
visited.add(p.val);
p = parent.get(p.val);
}
while (q != null) {
if (visited.contains(q.val)) {
return q;
}
q = parent.get(q.val);
}
return null;
}
}
}
LeetCode238 除自身以外数组的乘积
题目详情
给你一个整数数组 nums，返回 数组 answer ，其中 answer[i] 等于 nums 中除 nums[i] 之外其余各元素的乘积 。
题目数据 保证 数组 nums之中任意元素的全部前缀元素和后缀的乘积都在 32 位 整数范围内。
请不要使用除法，且在 O(n) 时间复杂度内完成此题。
示例 1:
输入: nums = [1,2,3,4]
输出: [24,12,8,6]
示例 2:
输入: nums = [-1,1,0,-3,3]
输出: [0,0,9,0,0]
提示：
2 <= nums.length <= 105
-30 <= nums[i] <= 30
保证 数组 nums之中任意元素的全部前缀元素和后缀的乘积都在 32 位 整数范围内
进阶：你可以在 O(1) 的额外空间复杂度内完成这个题目吗？（ 出于对空间复杂度分析的目的，输出数组不被视为额外空间。）
代码
public class LeetCode238 {
public static void main(String[] args) {
System.out.println(Arrays.toString(new Solution().productExceptSelf(new int[]{1, 2, 3, 4})));
System.out.println(Arrays.toString(new Solution2().productExceptSelf(new int[]{1, 2, 3, 4})));
}
/*
左右乘积列表
*/
static class Solution {
public int[] productExceptSelf(int[] nums) {
int length = nums.length;
// L 和 R 分别表示左右两侧的乘积列表
int[] L = new int[length];
int[] R = new int[length];
int[] answer = new int[length];
// L[i] 为索引 i 左侧所有元素的乘积
// 对于索引为 '0' 的元素，因为左侧没有元素，所以 L[0] = 1
L[0] = 1;
for (int i = 1; i < length; i++) {
L[i] = nums[i - 1] * L[i - 1];
}
// R[i] 为索引 i 右侧所有元素的乘积
// 对于索引为 'length-1' 的元素，因为右侧没有元素，所以 R[length-1] = 1
R[length - 1] = 1;
for (int i = length - 2; i >= 0; i--) {
R[i] = nums[i + 1] * R[i + 1];
}
// 对于索引 i，除 nums[i] 之外其余各元素的乘积就是左侧所有元素的乘积乘以右侧所有元素的乘积
for (int i = 0; i < length; i++) {
answer[i] = L[i] * R[i];
}
return answer;
}
}
/*
空间复杂度 O(1) 的方法
*/
static class Solution2 {
public int[] productExceptSelf(int[] nums) {
int length = nums.length;
int[] answer = new int[length];
// answer[i] 表示索引 i 左侧所有元素的乘积
// 因为索引为 '0' 的元素左侧没有元素， 所以 answer[0] = 1
answer[0] = 1;
for (int i = 1; i < length; i++) {
answer[i] = nums[i - 1] * answer[i - 1];
}
// R 为右侧所有元素的乘积
// 刚开始右边没有元素，所以 R = 1
int R = 1;
for (int i = length - 1; i >= 0; i--) {
// 对于索引 i，左边的乘积为 answer[i]，右边的乘积为 R
answer[i] = answer[i] * R;
// R 需要包含右边所有的乘积，所以计算下一个结果时需要将当前值乘到 R 上
R *= nums[i];
}
return answer;
}
}
}
LeetCode239 滑动窗口最大值
题目详情
给你一个整数数组 nums，有一个大小为 k 的滑动窗口从数组的最左侧移动到数组的最右侧。你只可以看到在滑动窗口内的 k 个数字。滑动窗口每次只向右移动一位。
返回 滑动窗口中的最大值 。
示例 1：
输入：nums = [1,3,-1,-3,5,3,6,7], k = 3
输出：[3,3,5,5,6,7]
解释：
滑动窗口的位置 最大值
[1 3 -1] -3 5 3 6 7 3
1 [3 -1 -3] 5 3 6 7 3
1 3 [-1 -3 5] 3 6 7 5
1 3 -1 [-3 5 3] 6 7 5
1 3 -1 -3 [5 3 6] 7 6
1 3 -1 -3 5 [3 6 7] 7
示例 2：
输入：nums = [1], k = 1
输出：[1]
提示：
1 <= nums.length <= 105
-104 <= nums[i] <= 104
1 <= k <= nums.length
代码
public class LeetCode239 {
public static void main(String[] args) {
System.out.println(Arrays.toString(new Solution().maxSlidingWindow(new int[]{1, 3, -1, -3, 5, 3, 6, 7}, 3)));
System.out.println(Arrays.toString(new Solution2().maxSlidingWindow(new int[]{1, 3, -1, -3, 5, 3, 6, 7}, 3)));
System.out.println(Arrays.toString(new Solution3().maxSlidingWindow(new int[]{1, 3, -1, -3, 5, 3, 6, 7}, 3)));
System.out.println(Arrays.toString(new Solution4().maxSlidingWindow(new int[]{1, 3, -1, -3, 5, 3, 6, 7}, 3)));
}
/*
单调队列
*/
static class Solution {
public int[] maxSlidingWindow(int[] nums, int k) {
int n = nums.length;
Deque<Integer> deque = new LinkedList<Integer>();
for (int i = 0; i < k; ++i) {
while (!deque.isEmpty() && nums[i] >= nums[deque.peekLast()]) {
deque.pollLast();
}
deque.offerLast(i);
}
int[] ans = new int[n - k + 1];
ans[0] = nums[deque.peekFirst()];
for (int i = k; i < n; ++i) {
while (!deque.isEmpty() && nums[i] >= nums[deque.peekLast()]) {
deque.pollLast();
}
deque.offerLast(i);
while (deque.peekFirst() <= i - k) {
deque.pollFirst();
}
ans[i - k + 1] = nums[deque.peekFirst()];
}
return ans;
}
}
static class Solution2 {
public int[] maxSlidingWindow(int[] nums, int k) {
// 窗口个数
int[] res = new int[nums.length - k + 1];
LinkedList<Integer> queue = new LinkedList<>();
// 遍历数组中元素，right表示滑动窗口右边界
for (int right = 0; right < nums.length; right++) {
// 如果队列不为空且当前考察元素大于等于队尾元素，则将队尾元素移除。
// 直到，队列为空或当前考察元素小于新的队尾元素
while (!queue.isEmpty() && nums[right] >= nums[queue.peekLast()]) {
queue.removeLast();
}
// 存储元素下标
queue.addLast(right);
// 计算窗口左侧边界
int left = right - k + 1;
// 当队首元素的下标小于滑动窗口左侧边界left时
// 表示队首元素已经不再滑动窗口内，因此将其从队首移除
if (queue.peekFirst() < left) {
queue.removeFirst();
}
// 由于数组下标从0开始，因此当窗口右边界right+1大于等于窗口大小k时
// 意味着窗口形成。此时，队首元素就是该窗口内的最大值
if (right + 1 >= k) {
res[left] = nums[queue.peekFirst()];
}
}
return res;
}
}
/*
优先队列
*/
static class Solution3 {
public int[] maxSlidingWindow(int[] nums, int k) {
int n = nums.length;
PriorityQueue<int[]> pq = new PriorityQueue<int[]>(new Comparator<int[]>() {
public int compare(int[] pair1, int[] pair2) {
return pair1[0] != pair2[0] ? pair2[0] - pair1[0] : pair2[1] - pair1[1];
}
});
for (int i = 0; i < k; ++i) {
pq.offer(new int[]{nums[i], i});
}
int[] ans = new int[n - k + 1];
ans[0] = pq.peek()[0];
for (int i = k; i < n; ++i) {
pq.offer(new int[]{nums[i], i});
while (pq.peek()[1] <= i - k) {
pq.poll();
}
ans[i - k + 1] = pq.peek()[0];
}
return ans;
}
}
/*
分块 + 预处理
*/
static class Solution4 {
public int[] maxSlidingWindow(int[] nums, int k) {
int n = nums.length;
int[] prefixMax = new int[n];
int[] suffixMax = new int[n];
for (int i = 0; i < n; ++i) {
if (i % k == 0) {
prefixMax[i] = nums[i];
} else {
prefixMax[i] = Math.max(prefixMax[i - 1], nums[i]);
}
}
for (int i = n - 1; i >= 0; --i) {
if (i == n - 1 || (i + 1) % k == 0) {
suffixMax[i] = nums[i];
} else {
suffixMax[i] = Math.max(suffixMax[i + 1], nums[i]);
}
}
int[] ans = new int[n - k + 1];
for (int i = 0; i <= n - k; ++i) {
ans[i] = Math.max(suffixMax[i], prefixMax[i + k - 1]);
}
return ans;
}
}
}
LeetCode240 搜索二维矩阵-二
题目详情
编写一个高效的算法来搜索 m x n 矩阵 matrix 中的一个目标值 target 。该矩阵具有以下特性：
每行的元素从左到右升序排列。
每列的元素从上到下升序排列。
示例 1：
输入：matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 5
输出：true
示例 2：
输入：matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 20
输出：false
提示：
m == matrix.length
n == matrix[i].length
1 <= n, m <= 300
-109 <= matrix[i][j] <= 109
每行的所有元素从左到右升序排列
每列的所有元素从上到下升序排列
-109 <= target <= 109
代码
public class LeetCode240 {
public static void main(String[] args) {
System.out.println(new Solution().searchMatrix(new int[][]{{1, 4, 7, 11, 15}, {2, 5, 8, 12, 19}, {3, 6, 9, 16, 22}, {10, 13, 14, 17, 24}, {18, 21, 23, 26, 30}}, 5));
System.out.println(new Solution2().searchMatrix(new int[][]{{1, 4, 7, 11, 15}, {2, 5, 8, 12, 19}, {3, 6, 9, 16, 22}, {10, 13, 14, 17, 24}, {18, 21, 23, 26, 30}}, 5));
System.out.println(new Solution3().searchMatrix(new int[][]{{1, 4, 7, 11, 15}, {2, 5, 8, 12, 19}, {3, 6, 9, 16, 22}, {10, 13, 14, 17, 24}, {18, 21, 23, 26, 30}}, 5));
System.out.println(new Solution4().searchMatrix(new int[][]{{1, 4, 7, 11, 15}, {2, 5, 8, 12, 19}, {3, 6, 9, 16, 22}, {10, 13, 14, 17, 24}, {18, 21, 23, 26, 30}}, 5));
}
/*
暴力搜索
*/
static class Solution {
public boolean searchMatrix(int[][] matrix, int target) {
for (int i = 0; i < matrix.length; i++) {
for (int j = 0; j < matrix[0].length; j++) {
if (matrix[i][j] == target) {
return true;
}
}
}
return false;
}
}
/*
二分查找
*/
static class Solution2 {
public boolean searchMatrix(int[][] matrix, int target) {
for (int[] row : matrix) {
int index = search(row, target);
if (index >= 0) {
return true;
}
}
return false;
}
public int search(int[] nums, int target) {
int low = 0, high = nums.length - 1;
while (low <= high) {
int mid = (high - low) / 2 + low;
int num = nums[mid];
if (num == target) {
return mid;
} else if (num > target) {
high = mid - 1;
} else {
low = mid + 1;
}
}
return -1;
}
}
static class Solution3 {
private boolean binarySearch(int[][] matrix, int target, int start, boolean vertical) {
int lo = start;
int hi = vertical ? matrix[0].length - 1 : matrix.length - 1;
while (hi >= lo) {
int mid = (lo + hi) / 2;
if (vertical) { //搜索列
if (matrix[start][mid] < target) {
lo = mid + 1;
} else if (matrix[start][mid] > target) {
hi = mid - 1;
} else {
return true;
}
} else { //搜索行
if (matrix[mid][start] < target) {
lo = mid + 1;
} else if (matrix[mid][start] > target) {
hi = mid - 1;
} else {
return true;
}
}
}
return false;
}
public boolean searchMatrix(int[][] matrix, int target) {
// 一个空矩阵显然不包含“目标”
if (matrix == null || matrix.length == 0) {
return false;
}
// 遍历矩阵对角线
int shorterDim = Math.min(matrix.length, matrix[0].length);
for (int i = 0; i < shorterDim; i++) {
boolean verticalFound = binarySearch(matrix, target, i, true);
boolean horizontalFound = binarySearch(matrix, target, i, false);
if (verticalFound || horizontalFound) {
return true;
}
}
return false;
}
}
/*
Z 字形查找
*/
static class Solution4 {
public boolean searchMatrix(int[][] matrix, int target) {
int m = matrix.length, n = matrix[0].length;
int x = 0, y = n - 1;
while (x < m && y >= 0) {
if (matrix[x][y] == target) {
return true;
}
if (matrix[x][y] > target) {
--y;
} else {
++x;
}
}
return false;
}
}
}
LeetCode253 会议室-二
题目详情
给定一个会议时间安排的数组，每个会议时间都会包括开始和结束的时间 [[s1,e1],[s2,e2],...] (si < ei)，为避免会议冲突，同时要考虑充分利用会议室资源，请你计算至少需要多少间会议室，才能满足这些会议安排。
示例 1:
输入: [[0, 30],[5, 10],[15, 20]]
输出: 2
示例 2:
输入: [[7,10],[2,4]]
输出: 1
代码
public class LeetCode253 {
public static void main(String[] args) {
System.out.println(new Solution().minMeetingRooms(new int[][]{{0, 30}, {5, 10}, {15, 20}}));
System.out.println(new Solution2().minMeetingRooms(new int[][]{{0, 30}, {5, 10}, {15, 20}}));
}
/*
优先队列
*/
static class Solution {
public int minMeetingRooms(int[][] intervals) {
// Check for the base case. If there are no intervals, return 0
if (intervals.length == 0) {
return 0;
}
// Min heap
PriorityQueue<Integer> allocator =
new PriorityQueue<Integer>(
intervals.length,
new Comparator<Integer>() {
public int compare(Integer a, Integer b) {
return a - b;
}
});
// Sort the intervals by start time
Arrays.sort(
intervals,
new Comparator<int[]>() {
public int compare(final int[] a, final int[] b) {
return a[0] - b[0];
}
});
// Add the first meeting
allocator.add(intervals[0][1]);
// Iterate over remaining intervals
for (int i = 1; i < intervals.length; i++) {
// If the room due to free up the earliest is free, assign that room to this meeting.
if (intervals[i][0] >= allocator.peek()) {
allocator.poll();
}
// If a new room is to be assigned, then also we add to the heap,
// If an old room is allocated, then also we have to add to the heap with updated end time.
allocator.add(intervals[i][1]);
}
// The size of the heap tells us the minimum rooms required for all the meetings.
return allocator.size();
}
}
/*
有序化
*/
static class Solution2 {
public int minMeetingRooms(int[][] intervals) {
// Check for the base case. If there are no intervals, return 0
if (intervals.length == 0) {
return 0;
}
Integer[] start = new Integer[intervals.length];
Integer[] end = new Integer[intervals.length];
for (int i = 0; i < intervals.length; i++) {
start[i] = intervals[i][0];
end[i] = intervals[i][1];
}
// Sort the intervals by end time
Arrays.sort(
end,
new Comparator<Integer>() {
public int compare(Integer a, Integer b) {
return a - b;
}
});
// Sort the intervals by start time
Arrays.sort(
start,
new Comparator<Integer>() {
public int compare(Integer a, Integer b) {
return a - b;
}
});
// The two pointers in the algorithm: e_ptr and s_ptr.
int startPointer = 0, endPointer = 0;
// Variables to keep track of maximum number of rooms used.
int usedRooms = 0;
// Iterate over intervals.
while (startPointer < intervals.length) {
// If there is a meeting that has ended by the time the meeting at `start_pointer` starts
if (start[startPointer] >= end[endPointer]) {
usedRooms -= 1;
endPointer += 1;
}
// We do this irrespective of whether a room frees up or not.
// If a room got free, then this used_rooms += 1 wouldn't have any effect. used_rooms would
// remain the same in that case. If no room was free, then this would increase used_rooms
usedRooms += 1;
startPointer += 1;
}
return usedRooms;
}
}
}
LeetCode279 完全平方数
题目详情
给你一个整数 n ，返回 和为 n 的完全平方数的最少数量 。
完全平方数 是一个整数，其值等于另一个整数的平方；换句话说，其值等于一个整数自乘的积。例如，1、4、9 和 16 都是完全平方数，而 3 和 11 不是。
示例 1：
输入：n = 12
输出：3
解释：12 = 4 + 4 + 4
示例 2：
输入：n = 13
输出：2
解释：13 = 4 + 9
提示：
1 <= n <= 104
代码
public class LeetCode279 {
public static void main(String[] args) {
System.out.println(new Solution().numSquares(12));
System.out.println(new Solution2().numSquares(12));
}
/*
动态规划
*/
static class Solution {
public int numSquares(int n) {
int[] f = new int[n + 1];
for (int i = 1; i <= n; i++) {
int minn = Integer.MAX_VALUE;
for (int j = 1; j * j <= i; j++) {
minn = Math.min(minn, f[i - j * j]);
}
f[i] = minn + 1;
}
return f[n];
}
}
/*
数学
*/
static class Solution2 {
public int numSquares(int n) {
if (isPerfectSquare(n)) {
return 1;
}
if (checkAnswer4(n)) {
return 4;
}
for (int i = 1; i * i <= n; i++) {
int j = n - i * i;
if (isPerfectSquare(j)) {
return 2;
}
}
return 3;
}
// 判断是否为完全平方数
public boolean isPerfectSquare(int x) {
int y = (int) Math.sqrt(x);
return y * y == x;
}
// 判断是否能表示为 4^k*(8m+7)
public boolean checkAnswer4(int x) {
while (x % 4 == 0) {
x /= 4;
}
return x % 8 == 7;
}
}
}
