Range Caching

Range caching refers to storing the results of operations on a range of elements in an array or collection. This avoids repeated computations by caching the results for a range that can be reused.

Java example:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16

int[] nums = {1, 2, 3, 4, 5};

// Cache sum of first 3 elements
int cache = 0;
for (int i = 0; i < 3; i++) {
  cache += nums[i]; 
}

// Reuse cache instead of recomputing sum
int sum1 = cache; 

// Compute sum of last 3 elements
int sum2 = 0;
for (int i = 3; i < nums.length; i++) {
  sum2 += nums[i];
}

C++ example:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16

vector<int> nums {1, 2, 3, 4, 5};

// Cache sum of first 3 elements
int cache = 0;
for (int i = 0; i < 3; i++) {
  cache += nums[i];
}

// Reuse cache instead of recomputing 
int sum1 = cache;

// Compute sum of last 3 elements
int sum2 = 0; 
for (int i = 3; i < nums.size(); i++) {
  sum2 += nums[i]; 
}

Python example:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14

nums = [1, 2, 3, 4, 5]

# Cache sum of first 3 elements
cache = 0
for i in range(3):
  cache += nums[i]

# Reuse cache  
sum1 = cache

# Compute sum of last 3 elements
sum2 = 0
for i in range(3, len(nums)):
  sum2 += nums[i]

The key ideas are:

• Compute result for a range once and store in cache
• Reuse cache to avoid recomputing range results
• Apply to common ops like sum, min/max, product etc.

This speeds up repeated operations on the same range.

Description

Range Caching is a method to store the results of calculations in a defined range. Instead of recalculating values, a program can quickly retrieve the cached result, saving time and computational resources. This technique is useful in scenarios where the same calculations are performed repeatedly within a specific range.

Solution

Java

In Java, you can implement range caching using a HashMap to store previously computed results.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19

import java.util.HashMap;

public class RangeCache {
  private HashMap<Integer, Integer> cache;

  public RangeCache() {
    cache = new HashMap<>();
  }

  public int compute(int x) {
    if (cache.containsKey(x)) {
      return cache.get(x);
    }

    int result = x * x; // Example computation
    cache.put(x, result);
    return result;
  }
}

This class defines a simple range cache that stores the square of integers. It uses the HashMap to keep track of computed values.

C++

In C++, you can utilize the std::unordered_map for a similar approach.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16

#include <unordered_map>

class RangeCache {
  std::unordered_map<int, int> cache;

public:
  int compute(int x) {
    if (cache.find(x) != cache.end()) {
      return cache[x];
    }

    int result = x * x; // Example computation
    cache[x] = result;
    return result;
  }
};

Here, the std::unordered_map helps in storing previously computed results for fast retrieval.

Python

In Python, you can use a dictionary to implement range caching.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11

class RangeCache:
  def __init__(self):
    self.cache = {}

  def compute(self, x):
    if x in self.cache:
      return self.cache[x]

    result = x * x # Example computation
    self.cache[x] = result
    return result

This code defines a class that similarly stores the square of integers in a dictionary, providing an efficient way to cache the results for a given range.

Key Takeaways

• Range caching optimizes computations by storing previously calculated results.
• You can use data structures like HashMap in Java, std::unordered_map in C++, and dictionary in Python to efficiently implement range caching.
• This technique is particularly useful when the same calculations are performed repeatedly within a specific range.

Imagine a sequence of numbers for which you want to calculate the square, and the range is from 1 to 5.

Without Range Caching

• Every time a calculation is requested for a number within the range, the function calculates it anew.
• If you ask for the square of 3 three times, it will calculate 3 * 3 = 9 all three times.

With Range Caching

• The first time you ask for the square of 3, it calculates 3 * 3 = 9 and stores it in the cache.
• The next time you ask for the square of 3, it retrieves the answer 9 from the cache without recalculating.
• If you ask for the square of 3 three times, it calculates once and retrieves from the cache twice.

You can visualize the cache as a table:

As the function is called with different inputs, the corresponding results are added to the table, and subsequent calls with the same inputs will simply look up the results in the table rather than recalculating them.

This visual representation showcases the efficiency of range caching by storing previously computed results and retrieving them when needed, rather than recalculating them.

Why is it called Range Caching?

Range caching refers to the practice of caching results specifically within a defined range of input values. The term “range” emphasizes that the caching is applied to a particular interval or set of values, rather than to all possible inputs.

How is it different from Caching?

1. Caching:

   • Caching is a general term that refers to the practice of storing and reusing previously computed results or data.
   • It can be applied to any type of data, regardless of the range or context.
   • Caching is used to speed up access to frequently requested data or computations.

2. Range Caching:

   • Range caching is a specific type of caching where the caching mechanism is applied to a defined range of values.
   • It’s particularly useful when you know that certain values within a specific range will be requested repeatedly.
   • By focusing on a specific range, you can optimize the caching strategy for that subset of values, potentially saving space and improving efficiency.

Key Takeaways

• While general caching can be applied to any data or computation, range caching specifically targets a subset or range of values.
• Range caching may be a strategic choice when you know that a particular range of values will be accessed frequently.
• The term “range” in range caching highlights the focus on a specific interval or set of values.