Dynamic Programming (DP) is a powerful technique used in computer science to solve complex problems by breaking them down into simpler overlapping subproblems. It is widely used for optimization problems like finding the shortest path, computing maximum profit, or counting possibilities efficiently.
Dynamic Programming is a method of solving problems by storing the results of already solved subproblems and reusing them when needed instead of recomputing them.
“Divide the problem into smaller overlapping subproblems and store their results to avoid redundant work.”
# Recursive (inefficient)
def fib(n):
if n <= 1:
return n
return fib(n-1) + fib(n-2)
# Dynamic Programming (efficient)
def fib_dp(n):
dp = [0, 1]
for i in range(2, n+1):
dp.append(dp[i-1] + dp[i-2])
return dp[n]
Time Complexity: O(n) for DP vs O(2ⁿ) for simple recursion.
Dynamic Programming is an essential technique for optimizing recursive algorithms. Understanding how to identify overlapping subproblems and optimal substructure is key to mastering DP-based problem solving.
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