differences between space complexity and time complexity?

### Space Complexity

1. **Memory Usage**: Space complexity measures the amount of memory an algorithm uses in relation to the input size.

2. **Auxiliary Space**: It includes both the space needed for the input data and the auxiliary space required during the computation.

3. **Primary Focus**: Space complexity focuses on the storage requirements rather than the execution time.

4. **Memory Constraints**: It is crucial in environments with limited memory resources, such as embedded systems.

5. **Optimization**: Algorithms can be optimized for space to reduce memory footprint, sometimes at the cost of increased time complexity.

### Time Complexity

1. **Execution Time**: Time complexity measures the amount of time an algorithm takes to complete as a function of the input size.

2. **Growth Rate**: It describes how the execution time grows with increasing input size, often expressed using Big O notation.

3. **Primary Focus**: Time complexity focuses on the speed of execution rather than memory usage.

4. **Efficiency**: It is crucial in scenarios where the speed of processing is critical, such as real-time systems.

5. **Optimization**: Algorithms can be optimized for time to reduce execution duration, sometimes at the cost of increased space complexity.

Both space and time complexity are essential considerations in algorithm design, and often a trade-off is made between the two to achieve the desired performance and efficiency.