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Range Sum

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to count the number of range sums that lie in a given range [lower, upper] inclusive. Given an integer array nums and two integers lower and upper, return the number of range sums that lie in [lower, upper] inclusive. Range sum S(i, j) is defined as the sum of the elements in nums from indices i to j inclusive, where i <= j.

Example 1
    
      
  • Input: nums = [-2,5,-1], lower = -2, upper = 2
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  • Output: 3
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  • Explanation: 
     Step 1: Calculate all possible range sums

     Step 2: S(0,0) = -2, S(0,1) = 3, S(0,2) = 2, S(1,1) = 5, S(1,2) = 4, S(2,2) = -1

     Step 3: Range sums in [-2, 2]: S(0,0) = -2, S(0,2) = 2, S(2,2) = -1

     Step 4: Therefore, count = 3
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Example 2
    
      
  • Input: nums = [0], lower = 0, upper = 0
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  • Output: 1
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  • Explanation: 
     Step 1: Only one element in array

     Step 2: S(0,0) = 0

     Step 3: 0 lies within range [0, 0]
     Step 4: Therefore, count = 1
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Constraints
    
      
  • 1 <= nums.length <= 10^5
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  • -2^31 <= nums[i] <= 2^31 - 1
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  • -10^5 <= lower <= upper <= 10^5
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  • Time Complexity: O(n^2) for brute force approach
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  • Space Complexity: O(1)
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ArraysControl StructuresAccentureZomato
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Hint
Solution

Solution Hints

    
      
  • Use nested loops to generate all possible range sums
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  • For each starting index i, calculate cumulative sum to all ending indices j >= i
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  • Check if each range sum falls within [lower, upper]
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  • Keep a counter for valid range sums
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  • Use long long to avoid integer overflow during sum calculations
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Steps to solve by this approach:

 Step 1: Initialize a counter variable to keep track of valid range sums
 Step 2: Use outer loop to iterate through each starting index i from 0 to numsSize-1
 Step 3: For each starting index i, initialize sum to 0 and use inner loop for ending index j from i to numsSize-1
 Step 4: Add nums[j] to current sum to get range sum from index i to j
 Step 5: Check if current range sum falls within [lower, upper] bounds
 Step 6: If range sum is valid, increment the counter
 Step 7: Return the final count of valid range sums

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