线性表 - 数组和矩阵
数组是一种连续存储线性结构，元素类型相同，大小相等，数组是多维的，通过使用整型索引值来访问他们的元素，数组尺寸不能改变。@pdai
知识点
数组的优点:
- 存取速度快
数组的缺点:
- 事先必须知道数组的长度
- 插入删除元素很慢
- 空间通常是有限制的
- 需要大块连续的内存块
- 插入删除元素的效率很低
JDK中关于ArrayList的实现，请参考:
数组与矩阵相关题目
把数组中的 0 移到末尾
For example, given nums = [0, 1, 0, 3, 12], after calling your function, nums should be [1, 3, 12, 0, 0].
public void moveZeroes(int[] nums) {
int idx = 0;
for (int num : nums) {
if (num != 0) {
nums[idx++] = num;
}
}
while (idx < nums.length) {
nums[idx++] = 0;
}
}
改变矩阵维度
566. Reshape the Matrix (Easy)
Input:
nums =
[[1,2],
[3,4]]
r = 1, c = 4
Output:
[[1,2,3,4]]
Explanation:
The row-traversing of nums is [1,2,3,4]. The new reshaped matrix is a 1 * 4 matrix, fill it row by row by using the previous list.
public int[][] matrixReshape(int[][] nums, int r, int c) {
int m = nums.length, n = nums[0].length;
if (m * n != r * c) {
return nums;
}
int[][] reshapedNums = new int[r][c];
int index = 0;
for (int i = 0; i < r; i++) {
for (int j = 0; j < c; j++) {
reshapedNums[i][j] = nums[index / n][index % n];
index++;
}
}
return reshapedNums;
}
找出数组中最长的连续 1
485. Max Consecutive Ones (Easy)
public int findMaxConsecutiveOnes(int[] nums) {
int max = 0, cur = 0;
for (int x : nums) {
cur = x == 0 ? 0 : cur + 1;
max = Math.max(max, cur);
}
return max;
}
有序矩阵查找
240. Search a 2D Matrix II (Medium)
[
[ 1, 5, 9],
[10, 11, 13],
[12, 13, 15]
]
public boolean searchMatrix(int[][] matrix, int target) {
if (matrix == null || matrix.length == 0 || matrix[0].length == 0) return false;
int m = matrix.length, n = matrix[0].length;
int row = 0, col = n - 1;
while (row < m && col >= 0) {
if (target == matrix[row][col]) return true;
else if (target < matrix[row][col]) col--;
else row++;
}
return false;
}
有序矩阵的 Kth Element
378. Kth Smallest Element in a Sorted Matrix ((Medium))
matrix = [
[ 1, 5, 9],
[10, 11, 13],
[12, 13, 15]
],
k = 8,
return 13.
解题参考: Share my thoughts and Clean Java Code
二分查找解法:
public int kthSmallest(int[][] matrix, int k) {
int m = matrix.length, n = matrix[0].length;
int lo = matrix[0][0], hi = matrix[m - 1][n - 1];
while (lo <= hi) {
int mid = lo + (hi - lo) / 2;
int cnt = 0;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n && matrix[i][j] <= mid; j++) {
cnt++;
}
}
if (cnt < k) lo = mid + 1;
else hi = mid - 1;
}
return lo;
}
堆解法:
public int kthSmallest(int[][] matrix, int k) {
int m = matrix.length, n = matrix[0].length;
PriorityQueue<Tuple> pq = new PriorityQueue<Tuple>();
for(int j = 0; j < n; j++) pq.offer(new Tuple(0, j, matrix[0][j]));
for(int i = 0; i < k - 1; i++) { // 小根堆，去掉 k - 1 个堆顶元素，此时堆顶元素就是第 k 的数
Tuple t = pq.poll();
if(t.x == m - 1) continue;
pq.offer(new Tuple(t.x + 1, t.y, matrix[t.x + 1][t.y]));
}
return pq.poll().val;
}
class Tuple implements Comparable<Tuple> {
int x, y, val;
public Tuple(int x, int y, int val) {
this.x = x; this.y = y; this.val = val;
}
@Override
public int compareTo(Tuple that) {
return this.val - that.val;
}
}
一个数组元素在 [1, n] 之间，其中一个数被替换为另一个数，找出重复的数和丢失的数
Input: nums = [1,2,2,4]
Output: [2,3]
Input: nums = [1,2,2,4]
Output: [2,3]
最直接的方法是先对数组进行排序，这种方法时间复杂度为 O(NlogN)。本题可以以 O(N) 的时间复杂度、O(1) 空间复杂度来求解。
主要思想是通过交换数组元素，使得数组上的元素在正确的位置上。
public int[] findErrorNums(int[] nums) {
for (int i = 0; i < nums.length; i++) {
while (nums[i] != i + 1 && nums[nums[i] - 1] != nums[i]) {
swap(nums, i, nums[i] - 1);
}
}
for (int i = 0; i < nums.length; i++) {
if (nums[i] != i + 1) {
return new int[]{nums[i], i + 1};
}
}
return null;
}
private void swap(int[] nums, int i, int j) {
int tmp = nums[i];
nums[i] = nums[j];
nums[j] = tmp;
}
类似题目:
- 448. Find All Numbers Disappeared in an Array (Easy)，寻找所有丢失的元素
- 442. Find All Duplicates in an Array (Medium)，寻找所有重复的元素。
找出数组中重复的数，数组值在 [1, n] 之间
287. Find the Duplicate Number (Medium)
要求不能修改数组，也不能使用额外的空间。
二分查找解法:
public int findDuplicate(int[] nums) {
int l = 1, h = nums.length - 1;
while (l <= h) {
int mid = l + (h - l) / 2;
int cnt = 0;
for (int i = 0; i < nums.length; i++) {
if (nums[i] <= mid) cnt++;
}
if (cnt > mid) h = mid - 1;
else l = mid + 1;
}
return l;
}
双指针解法，类似于有环链表中找出环的入口:
public int findDuplicate(int[] nums) {
int slow = nums[0], fast = nums[nums[0]];
while (slow != fast) {
slow = nums[slow];
fast = nums[nums[fast]];
}
fast = 0;
while (slow != fast) {
slow = nums[slow];
fast = nums[fast];
}
return slow;
}
数组相邻差值的个数
667. Beautiful Arrangement II (Medium)
Input: n = 3, k = 2
Output: [1, 3, 2]
Explanation: The [1, 3, 2] has three different positive integers ranging from 1 to 3, and the [2, 1] has exactly 2 distinct integers: 1 and 2.
题目描述: 数组元素为 1~n 的整数，要求构建数组，使得相邻元素的差值不相同的个数为 k。
让前 k+1 个元素构建出 k 个不相同的差值，序列为: 1 k+1 2 k 3 k-1 ... k/2 k/2+1.
public int[] constructArray(int n, int k) {
int[] ret = new int[n];
ret[0] = 1;
for (int i = 1, interval = k; i <= k; i++, interval--) {
ret[i] = i % 2 == 1 ? ret[i - 1] + interval : ret[i - 1] - interval;
}
for (int i = k + 1; i < n; i++) {
ret[i] = i + 1;
}
return ret;
}
数组的度
697. Degree of an Array (Easy)
Input: [1,2,2,3,1,4,2]
Output: 6
题目描述: 数组的度定义为元素出现的最高频率，例如上面的数组度为 3。要求找到一个最小的子数组，这个子数组的度和原数组一样。
public int findShortestSubArray(int[] nums) {
Map<Integer, Integer> numsCnt = new HashMap<>();
Map<Integer, Integer> numsLastIndex = new HashMap<>();
Map<Integer, Integer> numsFirstIndex = new HashMap<>();
for (int i = 0; i < nums.length; i++) {
int num = nums[i];
numsCnt.put(num, numsCnt.getOrDefault(num, 0) + 1);
numsLastIndex.put(num, i);
if (!numsFirstIndex.containsKey(num)) {
numsFirstIndex.put(num, i);
}
}
int maxCnt = 0;
for (int num : nums) {
maxCnt = Math.max(maxCnt, numsCnt.get(num));
}
int ret = nums.length;
for (int i = 0; i < nums.length; i++) {
int num = nums[i];
int cnt = numsCnt.get(num);
if (cnt != maxCnt) continue;
ret = Math.min(ret, numsLastIndex.get(num) - numsFirstIndex.get(num) + 1);
}
return ret;
}
对角元素相等的矩阵
1234
5123
9512
In the above grid, the diagonals are "[9]", "[5, 5]", "[1, 1, 1]", "[2, 2, 2]", "[3, 3]", "[4]", and in each diagonal all elements are the same, so the answer is True.
public boolean isToeplitzMatrix(int[][] matrix) {
for (int i = 0; i < matrix[0].length; i++) {
if (!check(matrix, matrix[0][i], 0, i)) {
return false;
}
}
for (int i = 0; i < matrix.length; i++) {
if (!check(matrix, matrix[i][0], i, 0)) {
return false;
}
}
return true;
}
private boolean check(int[][] matrix, int expectValue, int row, int col) {
if (row >= matrix.length || col >= matrix[0].length) {
return true;
}
if (matrix[row][col] != expectValue) {
return false;
}
return check(matrix, expectValue, row + 1, col + 1);
}
嵌套数组
Input: A = [5,4,0,3,1,6,2]
Output: 4
Explanation:
A[0] = 5, A[1] = 4, A[2] = 0, A[3] = 3, A[4] = 1, A[5] = 6, A[6] = 2.
One of the longest S[K]:
S[0] = {A[0], A[5], A[6], A[2]} = {5, 6, 2, 0}
题目描述: S[i] 表示一个集合，集合的第一个元素是 A[i]，第二个元素是 A[A[i]]，如此嵌套下去。求最大的 S[i]。
public int arrayNesting(int[] nums) {
int max = 0;
for (int i = 0; i < nums.length; i++) {
int cnt = 0;
for (int j = i; nums[j] != -1; ) {
cnt++;
int t = nums[j];
nums[j] = -1; // 标记该位置已经被访问
j = t;
}
max = Math.max(max, cnt);
}
return max;
}
分隔数组
769. Max Chunks To Make Sorted (Medium)
Input: arr = [1,0,2,3,4]
Output: 4
Explanation:
We can split into two chunks, such as [1, 0], [2, 3, 4].
However, splitting into [1, 0], [2], [3], [4] is the highest number of chunks possible.
题目描述: 分隔数组，使得对每部分排序后数组就为有序。
public int maxChunksToSorted(int[] arr) {
if (arr == null) return 0;
int ret = 0;
int right = arr[0];
for (int i = 0; i < arr.length; i++) {
right = Math.max(right, arr[i]);
if (right == i) ret++;
}
return ret;
}