JavaScript 检查通过旋转数组是否可能使数组递增或递减

数组的旋转意味着将数组视为一个循环数组，每次旋转将数组元素向左或向右移动一个索引位置，并且一个端点的元素可能取另一个端点的值。递增数组意味着每个元素都大于或等于其前一个元素，递减数组意味着每个元素都小于或等于前一个元素。

在这个问题中，我们给定一个数组，我们可以将数组向左或向右旋转，我们需要找到在旋转后（可能是零次）是否可以使数组递增或递减。

原生方法

在这种方法中，我们将旋转数组，并对每次旋转都检查当前数组是否递增或递减。

示例

在下面的示例中，我们检查通过旋转给定数组是否可能将数组递增或递减。以下是输入和预期输出。

输入：arr = [3, 4, 5, 6, 1, 2]

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

上面代码的时间复杂度是O(N*N)，空间复杂度是O(1)。

高效方法

在之前的数组中，我们每次旋转都会检查数组是递增还是递减，这种方法中我们将部分检查是否是递增或递减的数组。

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)。