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Algorithms
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      • Find Numbers with Even Number of Digits
    • Two Pointers
      • Remove Element
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    • Untitled
  • Recursion
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  • Dynamic Programming
    • Introduction
    • Minimum (Maximum) Path to Reach a Target
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      • Coin Change
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      • Triangle
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    • Distinct Ways
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      • Number of Dice Rolls with Target Sum
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    • Introduction
      • First Bad Version
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      • Minimum Number of Days to Make m Bouquets
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      • Find K-th Smallest Pair Distance
      • Ugly Number 3
      • Find the Smallest Divisor Given a Threshold
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  • Graphs
    • Binary Trees
      • Merging Binary Trees
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      • Populating Next Right Pointers in Each Node II
      • 106. Construct Binary Tree from Inorder and Postorder Traversal
      • Serialise and Deserialise a Linked List
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      • Lowest Common Ancestor of a Binary Tree
    • n-ary Trees
      • Untitled
      • Minimum Height Trees
    • Binary Search Trees
      • Counting Maximal Value Roots in Binary Tree
      • Count BST nodes in a range
      • Invert a Binary Tree
      • Maximum Difference Between Node and Ancestor
      • Binary Tree Tilt
  • Practice
  • Linked Lists
    • What is a Linked List?
    • Add Two Numbers
      • Add Two Numbers 2
    • Reverse a Linked List
    • Tortoise & Hare Algorithm
      • Middle of the Linked List
  • Bitshifting
    • Introduction
  • Not Done Yet
    • Uncompleted
    • Minimum Cost For Tickets
    • Minimum Falling Path Sum
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  1. Dynamic Programming

Distinct Ways

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Last updated 4 years ago

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Given a target find a number of distinct ways to reach the target. We do this by summing all possible ways to reach the current state.

routes[i]=routes[iāˆ’1]+routes[iāˆ’2],...,+routes[iāˆ’k]routes[i] = routes[i-1] + routes[i-2], ... , + routes[i-k] routes[i]=routes[iāˆ’1]+routes[iāˆ’2],...,+routes[iāˆ’k]

An example is:

d = [float("inf") for i in range(n)]
d[0] = 1
d[1] = 2
for i in range(2, n):
    d[i] = d[i - 1] + d[i - 2]
return d[-1]