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Number of Taps to Water Garden

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

Write a C program to find the minimum number of taps needed to water a garden. There is a one-dimensional garden on the x-axis. The garden starts at x = 0 and ends at x = n. There are n + 1 taps located at points [0, 1, 2, ..., n] on the x-axis. Given an integer n and an integer array ranges of length n + 1 where ranges[i] (0-indexed) means the i-th tap can water the area [i - ranges[i], i + ranges[i]] if it was open. Return the minimum number of taps that should be open to water the whole garden, If the garden cannot be watered return -1.

Example 1
    
      
  • Input: n = 5, ranges = [3,4,1,1,0,0]
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  • Output: 1
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  • Explanation: 
    The tap at point 0 can cover range [-3, 3]. 
    The tap at point 1 can cover range [-3, 5]. 
    Since tap at point 1 covers [0, 5] completely, only 1 tap is needed. 
    Therefore, minimum taps needed = 1.
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Example 2
    
      
  • Input: n = 3, ranges = [0,0,0,0]
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  • Output: -1
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  • Explanation: 
    All taps have range 0, so each can only water their own point. 
    Tap 0 covers [0,0], tap 1 covers [1,1], tap 2 covers [2,2], tap 3 covers [3,3]. 
    No tap can cover multiple points, impossible to water entire garden [0,3]. 
    Therefore, return -1.
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Constraints
    
      
  • 1 ≤ n ≤ 10^4
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  • ranges.length == n + 1
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  • 0 ≤ ranges[i] ≤ 100
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  • Time Complexity: O(n^2)
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  • Space Complexity: O(n)
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Hint
Solution

Solution Hints

    
      
  • Convert the tap ranges into intervals that each tap can cover
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  • Use greedy approach to select minimum taps
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  • For each position, find the tap that extends the farthest
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  • Keep track of current coverage and next possible coverage
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  • If at any point coverage gap exists, return -1
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  • Count the number of taps used during the process
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Steps to solve by this approach:

 Step 1: Convert tap positions and ranges into maximum reachable positions from each point
 Step 2: Create an array to store the farthest point reachable from each position
 Step 3: Iterate through each position and update the maximum reach possible
 Step 4: Use greedy approach to select minimum taps by always choosing the tap that extends coverage the farthest
 Step 5: Keep track of current coverage end and farthest possible reach
 Step 6: If at any point we cannot extend coverage, return -1
 Step 7: Count and return the total number of taps used

Submitted Code :