Skip to content

solution19.md

Latest commit

 

History

History
55 lines (47 loc) · 1.8 KB

solution19.md

File metadata and controls

55 lines (47 loc) · 1.8 KB

Solution 19: Watershed Convergence (Pacific Atlantic Water Flow)

Approach Explanation

Instead of checking where water flows to, we check where water can flow from the oceans (reverse flow).

  1. Start DFS from Pacific borders (top and left) and find all reachable cells.
  2. Start DFS from Atlantic borders (bottom and right) and find all reachable cells.
  3. The intersection of these two sets of reachable cells is the answer.

Step-by-Step Logic

  1. pacific_reachable = set(), atlantic_reachable = set().
  2. dfs(r, c, reachable_set, prev_height):
    • If out of bounds or (r, c) already in set or height < prev_height, return.
    • Add (r, c) to set.
    • Recurse on 4 neighbors.
  3. Call dfs for all boundary cells.
  4. Return cells present in both sets.

Complexity

  • Time Complexity: O(M * N).
  • Space Complexity: O(M * N).

Code

def pacific_atlantic(heights):
    if not heights: return []
    rows, cols = len(heights), len(heights[0])
    pac, atl = set(), set()
    
    def dfs(r, c, visit, prevH):
        if (r < 0 or r >= rows or 
            c < 0 or c >= cols or 
            (r, c) in visit or 
            heights[r][c] < prevH):
            return
        visit.add((r, c))
        dfs(r + 1, c, visit, heights[r][c])
        dfs(r - 1, c, visit, heights[r][c])
        dfs(r, c + 1, visit, heights[r][c])
        dfs(r, c - 1, visit, heights[r][c])
        
    for c in range(cols):
        dfs(0, c, pac, heights[0][c])
        dfs(rows - 1, c, atl, heights[rows-1][c])
        
    for r in range(rows):
        dfs(r, 0, pac, heights[r][0])
        dfs(r, cols - 1, atl, heights[r][cols-1])
        
    res = []
    for r in range(rows):
        for c in range(cols):
            if (r, c) in pac and (r, c) in atl:
                res.append([r, c])
    return res