Daily Temperatures

1. Clarify the problem: Before diving into solving the problem, let's clarify the requirements:

• We are given an array temperatures representing the daily temperatures.
• For each day, we want to find the number of days we must wait until a warmer temperature occurs.
• The goal is to return an array where each element represents the number of days we must wait for a warmer temperature.

2. Analyze the problem: To solve this problem, we can use a stack to keep track of the indices of the temperatures. By iterating through the array of temperatures, we can compare the current temperature with the temperatures at the indices stored in the stack. If the current temperature is warmer, we can update the result array accordingly. This approach allows us to efficiently determine the number of days we must wait for a warmer temperature.

3. Design an algorithm: Here is the algorithm to find the number of days we must wait for a warmer temperature:

1. Create an empty stack to store the indices of the temperatures.
2. Create a result array of the same length as the input array, initialized with zeros.
3. Iterate through the input array of temperatures.
   • While the stack is not empty and the current temperature is greater than the temperature at the index at the top of the stack:
     • Pop the top index from the stack.
     • Calculate the number of days by subtracting the popped index from the current index.
     • Update the result array at the popped index with the number of days.
   • Push the current index onto the stack.
4. Return the result array.

4. Explain your approach: The approach involves using a stack to keep track of the indices of the temperatures. By comparing the current temperature with the temperatures at the indices stored in the stack, we can determine the number of days we must wait for a warmer temperature. We iterate through the input array of temperatures and maintain the stack in a decreasing order of temperatures. Whenever we find a warmer temperature, we update the result array by calculating the number of days and storing it at the corresponding index.

5. Write clean and readable code:

python

def dailyTemperatures(temperatures):
    n = len(temperatures)
    result = [0] * n
    stack = []

    for i in range(n):
        while stack and temperatures[i] > temperatures[stack[-1]]:
            prev_index = stack.pop()
            result[prev_index] = i - prev_index
        stack.append(i)

    return result

6. Test your code:

python

# Test case 1
temperatures1 = [73, 74, 75, 71, 69, 72, 76, 73]
print(dailyTemperatures(temperatures1))  # Output: [1, 1, 4, 2, 1, 1, 0, 0]

# Test case 2
temperatures2 = [30, 40, 50, 60]
print(dailyTemperatures(temperatures2))  # Output: [1, 1, 1, 0]

# Test case 3
temperatures3 = [30, 60, 90]
print(dailyTemperatures(temperatures3))  # Output: [1, 1, 0]

7. Optimize if necessary: The provided solution already has an optimal time complexity of O(n), where n is the length of the input array temperatures. We iterate through the array once, and for each element, we perform a constant amount of operations. There is no need for further optimization.

8. Handle error cases: The code assumes that the input array temperatures is valid and contains integers. It does not handle invalid input or error cases explicitly. If the input array is empty or contains non-integer values, the behavior of the code may be unpredictable.

9. Discuss complexity analysis: The time complexity of the solution is O(n), where n is the length of the input array temperatures. This is because we iterate through the array once. The space complexity is O(n) as we use a stack to store the indices of the temperatures, which can potentially contain all elements in the input array.