Given a sorted array of integers nums and integer values a, b and c. Apply a function of the form f(x) = ax2 + bx + c to each element x in the array.
The returned array must be in sorted order.
Expected time complexity: O(n)
Example:
nums = [-4, -2, 2, 4], a = 1, b = 3, c = 5, Result: [3, 9, 15, 33] nums = [-4, -2, 2, 4], a = -1, b = 3, c = 5 Result: [-23, -5, 1, 7]
Credits:
Special thanks to @elmirap for adding this problem and creating all test cases.
解法1：把每一个数带入方程计算结果，然后对结果排序。Time: O(nlogn)，不是题目想要的
解法2：根据抛物线方程式的特点，a>0则抛物线开口朝上，两端的值比中间的大，a<0则抛物线开口朝下，则两端的值比中间的小，a=0时，则为直线方法，是单调递增或递减的。同时因为给定数组nums是有序的，所以才有O(n)的解法。
当a>0，两端的值比中间的大，从后边往中间填数，用两个指针分别指向数组的开头和结尾，比较两个数，将其中较大的数存入res，然后该指针向中间移，重复比较过程，直到把res都填满。
当a<0，两端的值比中间的小，从前边往中间填数，用两个指针分别指向数组的开头和结尾，比较两个数，将其中较小的数存入res，然后该指针向中间移，重复比较过程，直到把res都填满。
当a=0，函数是单调递增或递减的，那么从前往后填和从后往前填都可以，也可以将这种情况和a>0合并。
Java:
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public class Solution {
private int calcu(int x, int a, int b, int c){
return a*x*x + b*x + c;
}
public int[] sortTransformedArray(int[] nums, int a, int b, int c) {
int index;
if(a > 0){
index = nums.length - 1 ;
} else {
index = 0;
}
int result[] = new int[nums.length];
int i = 0;
int j = nums.length - 1;
if(a > 0){
while(i <= j){
result[index--] = calcu(nums[i],a,b,c) > calcu(nums[j],a,b,c) ? calcu(nums[i++],a,b,c):calcu(nums[j--],a,b,c);
}
}else{
while(i <= j){
result[index++] = calcu(nums[i],a,b,c) < calcu(nums[j],a,b,c) ? calcu(nums[i++],a,b,c):calcu(nums[j--],a,b,c);
}
}
return result;
}
}
Python: wo
class Solution():
def sortTransformedArray(self, nums, a, b, c):
if not nums:
return []
res = [0] * len(nums)
i, j = 0, len(nums) - 1
index = len(nums) - 1 if a >= 0 else 0
while i <= j:
if a >= 0:
calc_i = self.calc(nums[i], a, b, c)
calc_j = self.calc(nums[j], a, b, c)
if calc_i >= calc_j:
res[index] = calc_i
i += 1
else:
res[index] = calc_j
j -= 1
index -= 1
else:
calc_i = self.calc(nums[i], a, b, c)
calc_j = self.calc(nums[j], a, b, c)
if calc_i <= calc_j:
res[index] = calc_i
i += 1
else:
res[index] = calc_j
j -= 1
index += 1
return res
def calc(self, x, a, b, c):
return a * x * x + b * x + c
if __name__ == '__main__':
print Solution().sortTransformedArray([], 1, 3, 5)
print Solution().sortTransformedArray([2], 1, 3, 5)
print Solution().sortTransformedArray([-4, -2, 2, 4], 1, 3, 5)
print Solution().sortTransformedArray([-4, -2, 2, 4], -1, 3, 5)
print Solution().sortTransformedArray([-4, -2, 2, 4], 0, 3, 5)
C++:
class Solution {
public:
vector<int> sortTransformedArray(vector<int>& nums, int a, int b, int c) {
int n = nums.size(), i = 0, j = n - 1;
vector<int> res(n);
int idx = a >= 0 ? n - 1 : 0;
while (i <= j) {
if (a >= 0) {
res[idx--] = cal(nums[i], a, b, c) >= cal(nums[j], a, b, c) ? cal(nums[i++], a, b, c) : cal(nums[j--], a, b, c);
} else {
res[idx++] = cal(nums[i], a, b, c) >= cal(nums[j], a, b, c) ? cal(nums[j--], a, b, c) : cal(nums[i++], a, b, c);
}
}
return res;
}
int cal(int x, int a, int b, int c) {
return a * x * x + b * x + c;
}
};
C++:
class Solution {
public:
vector<int> sortTransformedArray(vector<int>& nums, int a, int b, int c) {
if(nums.size() ==0) return {};
vector<int> result;
int left = 0, right = nums.size()-1;
auto func = [=](int x) { return a*x*x + b*x + c; };
while(left <= right)
{
int val1 = func(nums[left]), val2 = func(nums[right]);
if(a > 0) result.push_back(val1>=val2?val1:val2);
if(a > 0) val1>val2?left++:right--;
if(a <= 0) result.push_back(val1>=val2?val2:val1);
if(a <= 0) val1>val2?right--:left++;
}
if(a > 0) reverse(result.begin(), result.end());
return result;
}
};
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