力扣打卡day03
数组–前缀和
1.303. 区域和检索 - 数组不可变
class NumArray {
int preSum[];
public NumArray(int[] nums) {
preSum=new int[nums.length+1];
preSum[0]=0;
for(int i=1;i<preSum.length;i++){
preSum[i]=preSum[i-1]+nums[i-1];
}
}
public int sumRange(int left, int right) {
int result=0;
result=preSum[right+1]-preSum[left];
return result;
}
}
2.304. 二维区域和检索 - 矩阵不可变
class NumMatrix {
int preSum[][];
public NumMatrix(int[][] matrix) {
int m=matrix.length;
int n=matrix[0].length;
preSum=new int[m+1][n+1];
for(int i=1;i<m+1;i++){
for(int j=1;j<n+1;j++){
preSum[i][j]=preSum[i-1][j]+preSum[i][j-1]-preSum[i-1][j-1]+matrix[i-1][j-1];
//matrix为啥是i-1和j-1不是i和j呢
}
}
}
public int sumRegion(int row1, int col1, int row2, int col2) {
return preSum[row2+1][col2+1]-preSum[row2+1][col1]-preSum[row1][col2+1]+preSum[row1][col1];
//这个为啥都要加一
}
}
数组–差分数组
3. 1109. 航班预订统计
class Solution {
public int[] corpFlightBookings(int[][] bookings, int n){
int[] nums=new int[n];
Difference diff=new Difference(nums);
for(int[] booking:bookings){
int i=booking[0]-1;
int j=booking[1]-1;
int val=booking[2];
diff.increment(i,j,val);
}
return diff.result();
}
}
class Difference{
private int[] diff;
public Difference(int[] nums){
diff=new int[nums.length];
diff[0]=nums[0];
for(int i=1;i<nums.length;i++){
diff[i]=nums[i]-nums[i-1];
}
}
public void increment(int i,int j,int val){
diff[i]+=val;
if(j+1<diff.length){
diff[j+1]-=val;
}
}
public int[] result(){
int[] res=new int[diff.length];
res[0]=diff[0];
for(int i=1;i<diff.length;i++){
res[i]=diff[i]+res[i-1];
}
return res;
}
}
4.1094. 拼车
class Solution {
public boolean carPooling(int[][] trips, int capacity) {
int[] nums=new int[1001];
Difference diff=new Difference(nums);
for(int[] trip:trips){
int val=trip[0];
int i=trip[1];
//trip[1] 站有trip[0]个乘客上车,trip[2] 站有trip[0]个乘客下车
//即乘客在车上的区间是 [trip[1], trip[2] - 1]
int j=trip[2]-1;
diff.increment(i,j,val);
}
int[] res=diff.result();
for(int i=0;i<res.length;i++){
if(res[i]>capacity){
return false;
}
}
return true;
}
}
class Difference{
private int[] diff;
public Difference(int[] nums){
diff=new int[nums.length];
diff[0]=nums[0];
for(int i=1;i<nums.length;i++){
diff[i]=nums[i]-nums[i-1];
}
}
public void increment(int i,int j,int val){
diff[i]+=val;
if(j+1<diff.length){
diff[j+1]-=val;
}
}
public int[] result(){
int[] res=new int[diff.length];
res[0]=diff[0];
for(int i=1;i<diff.length;i++){
res[i]=diff[i]+res[i-1];
}
return res;
}
}
5.370区间加法
int[] getModifiedArray(int length, int[][] updates) {
// nums 初始化为全 0
int[] nums = new int[length];
// 构造差分解法
Difference df = new Difference(nums);
for (int[] update : updates) {
int i = update[0];
int j = update[1];
int val = update[2];
df.increment(i, j, val);
}
return df.result();
}
class Difference{
private int[] diff;
public Difference(int[] nums){
diff=new int[nums.length];
diff[0]=nums[0];
for(int i=1;i<nums.length;i++){
diff[i]=nums[i]-nums[i-1];
}
}
public void increment(int i,int j,int val){
diff[i]+=val;
if(j+1<diff.length){
diff[j+1]-=val;
}
}
public int[] result(){
int[] res=new int[diff.length];
res[0]=diff[0];
for(int i=1;i<diff.length;i++){
res[i]=res[i-1]+diff[i];
}
return res;
}
}
6.59. 螺旋矩阵 II
class Solution {
public int[][] generateMatrix(int n) {
int count=1;//填充的数字
int start=0;//每次循环的开始点
int offset=1;//左闭右开不包含终止值，终止值每圈都变
int loop=n/2;
int[][] nums=new int[n][n];
int i,j;
while(loop-->0){
for(j=start;j<n-offset;j++){
nums[start][j]=count++;
}
for(i=start;i<n-offset;i++){
nums[i][j]=count++;
}
for(;j>start;j--){
nums[i][j]=count++;
}
for(;i>start;i--){
nums[i][j]=count++;
}
start++;
offset++;
}
if(n%2==1){
nums[start][start]=count;
}
return nums;
}
}
7.54 螺旋矩阵
List<Integer> spiralOrder(int[][] matrix) {
int m = matrix.length, n = matrix[0].length;
int upper_bound = 0, lower_bound = m - 1;
int left_bound = 0, right_bound = n - 1;
List<Integer> res = new LinkedList<>();
// res.size() == m * n 则遍历完整个数组
while (res.size() < m * n) {
if (upper_bound <= lower_bound) {
// 在顶部从左向右遍历
for (int j = left_bound; j <= right_bound; j++) {
res.add(matrix[upper_bound][j]);
}
// 上边界下移
upper_bound++;
}
if (left_bound <= right_bound) {
// 在右侧从上向下遍历
for (int i = upper_bound; i <= lower_bound; i++) {
res.add(matrix[i][right_bound]);
}
// 右边界左移
right_bound--;
}
if (upper_bound <= lower_bound) {
// 在底部从右向左遍历
for (int j = right_bound; j >= left_bound; j--) {
res.add(matrix[lower_bound][j]);
}
// 下边界上移
lower_bound--;
}
if (left_bound <= right_bound) {
// 在左侧从下向上遍历
for (int i = lower_bound; i >= upper_bound; i--) {
res.add(matrix[i][left_bound]);
}
// 左边界右移
left_bound++;
}
}
return res;
}
8.旋转图像
//将二维矩阵原地顺时针旋转 90 度
public void rotate(int[][] matrix) {
int n = matrix.length;
// 先沿对角线镜像对称二维矩阵
for (int i = 0; i < n; i++) {
for (int j = i; j < n; j++) {
// swap(matrix[i][j], matrix[j][i]);
int temp = matrix[i][j];
matrix[i][j] = matrix[j][i];
matrix[j][i] = temp;
}
}
// 然后反转二维矩阵的每一行
for (int[] row : matrix) {
reverse(row);
}
}
// 反转一维数组
void reverse(int[] arr) {
int i = 0, j = arr.length - 1;
while (j > i) {
// swap(arr[i], arr[j]);
int temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
i++;
j--;
}
}