数组的旋转是指将数组假设为圆形数组，每次旋转时将数组的元素向左或向右旋转一个索引，一端的元素可以采用另一端的值。递增数组意味着每个元素将大于或等于其前一个元素，递减数组意味着每个元素将小于或等于前一个元素。
在这个问题中，我们给定一个数组，我们可以向左或向右旋转数组，我们必须找出在一定的旋转（可能为零）之后是否可以使数组增加或减少。 p>
天真的方法
在这种方法中，我们将旋转数组，并且对于每次旋转，我们将检查当前数组是增加还是减少。
示例
在下面的示例中，我们检查是否可以通过旋转给定数组来增加或减少它。以下是输入和预期输出。
输入：arr = [3, 4, 5, 6, 1, 2]
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预期输出：是
输入：arr = [ 5, 1, 6, 2, 5, 3 ]
预期输出：否
示例
// function to rotate the given array
function rotate(arr){
var l = 0;
var r = arr.length-1;
while(l < r){
arr[l] += arr[r];
arr[r] = arr[l]-arr[r];
arr[l] = arr[l]-arr[r];
l++;
}
return arr;
}
// function to check if the given array is increasing or not
function increasing(arr){
// getting the size of array
var len = arr.length
// traversing over the array
for(var i = 1; i < len; i++){
if(arr[i] < arr[i-1]){
return false;
}
}
return true;
}
// function to check if the given array is decreasing or not
function decreasing(arr){
// getting the size of array
var len = arr.length
// traversing over the array
for(var i = 1; i < len; i++){
if(arr[i] > arr[i-1]){
return false;
}
}
return true;
}
// function to check whether the given array can become
// increasing or decreasing after certain rotations
function check(arr){
var k = arr.length
while(k--){
if(increasing(arr) || decreasing(arr)){
return true;
}
arr = rotate(arr);
}
return false;
}
// defining the arr's
var arr1 = [3, 4, 5, 6, 1, 2]
var arr2 = [5, 1, 6, 2, 5, 3]
console.log("The given array is: ");
console.log(arr1)
if(check(arr1) == true){
console.log("Yes, after some rotations given array can be transformed into an increasing or decreasing array");
}
else{
console.log("No, after some rotations given array cannot be transformed into an increasing or decreasing array");
}
console.log("The given array is: ");
console.log(arr2)
if(check(arr2) == true){
console.log("Yes, after some rotations given array can be transformed into an increasing or decreasing array");
}
else{
console.log("No, after some rotations given array cannot be transformed into an increasing or decreasing array");
}
输出
The given array is: [ 3, 4, 5, 6, 1, 2 ] Yes, after some rotations given array can be transformed into an increasing or decreasing array The given array is: [ 5, 1, 6, 2, 5, 3 ] No, after some rotations given array cannot be transformed into an increasing or decreasing array
上述代码的时间复杂度为O(N*N)，空间复杂度为O(1)。
高效的方法
在前面的数组中，我们检查了每次旋转数组是否增加或减少，在这种方法中，我们将部分检查增加或减少的数组。
示例
// function to check if the given array is increasing or not
function increasing(arr){
// getting the size of array
var len = arr.length
// traversing over the array
var i = 0;
for(var i = 1; i < len; i++){
if(arr[i] < arr[i-1]){
break;
}
}
if(i == len) return true;
i++;
for(; i< len; i++){
if(arr[i] < arr[i-1]){
return false;
}
}
return arr[len-1] <= arr[0];
}
// function to check if the given array is decreasing or not
function decreasing(arr){
// getting the size of array
var len = arr.length
// traversing over the array
var i = 0;
for(var i = 1; i < len; i++){
if(arr[i] > arr[i-1]){
break;
}
}
if(i == len) return true;
i++;
for(; i< len; i++){
if(arr[i] > arr[i-1]){
return false;
}
}
return arr[len-1] >= arr[0];
}
// function to check whether the given array can become increasing or decreasing after certain rotations
function check(arr){
if(increasing(arr) || decreasing(arr)){
return true;
}
else{
return false;
}
}
// defining the arr's
var arr1 = [3, 4, 7, 6, 1, 2]
var arr2 = [5, 1, 6, 2, 5, 3]
console.log("The given array is: ");
console.log(arr1)
if(check(arr1) == true){
console.log("Yes, after some rotations given array can be transformed into an increasing or decreasing array");
}
else{
console.log("No, after some rotations given array cannot be transformed into an increasing or decreasing array");
}
console.log("The given array is: ");
console.log(arr2)
if(check(arr2) == true){
console.log("Yes, after some rotations given array can be transformed into an increasing or decreasing array");
}
else{
console.log("No, after some rotations given array cannot be transformed into an increasing or decreasing array");
}
输出
The given array is: [ 3, 4, 7, 6, 1, 2 ] No, after some rotations given array cannot be transformed into an increasing or decreasing array The given array is: [ 5, 1, 6, 2, 5, 3 ] No, after some rotations given array cannot be transformed into an increasing or decreasing array
上述代码的时间复杂度为O(N)，空间复杂度为O(1)。
结论
在本教程中，我们实现了一个 JavaScript 程序，用于检查是否可以通过旋转给定数组来增加或减少它。我们实现了两种时间复杂度为 O(N*N) 和 O(N) 的方法，并且空间复杂度均为 O(1)。
