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  1. LeetCode Problem 778, "Swim in Rising Water", can be solved using Dijkstra's Algorithm. The problem involves finding the minimum time required to traverse a grid from the top-left to the bottom-right corner while adhering to elevation constraints. Here's how you can implement it in Python.

    Approach

    We treat the grid as a graph where each cell is a node, and edges exist between adjacent cells. The weight of an edge is determined by the maximum elevation encountered so far. Dijkstra's algorithm helps us find the path with the minimum "maximum elevation."

    Python Implementation

    import heapq

    def swimInWater(grid):
    n = len(grid)
    directions = [(0, 1), (1, 0), (0, -1), (-1, 0)] # Right, Down, Left, Up
    visited = [[False] * n for _ in range(n)]
    min_heap = [(grid[0][0], 0, 0)] # (elevation, row, col)
    visited[0][0] = True
    max_elevation = 0

    while min_heap:
    elevation, x, y = heapq.heappop(min_heap)
    max_elevation = max(max_elevation, elevation)

    # If we reach the bottom-right corner
    if x == n - 1 and y == n - 1:
    return max_elevation

    # Explore neighbors
    for dx, dy in directions:
    nx, ny = x + dx, y + dy
    if 0 <= nx < n and 0 <= ny < n and not visited[nx][ny]:
    visited[nx][ny] = True
    heapq.heappush(min_heap, (grid[nx][ny], nx, ny))
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