Minimum Jumps to Reach the End
Explore how to determine the minimum number of jumps needed to reach the last index of an array, where each element dictates the maximum jump length. Understand naive recursive solutions, then optimize them using dynamic programming patterns such as top-down memoization and bottom-up tabulation. Discover how to improve time and space complexity and apply these techniques confidently in coding interviews.
Statement
Given an array nums of positive numbers, start from the first index and reach the last index with the minimum number of jumps, where a number at an index represents the maximum jump from that index.
For example, if the value at the current index is , then a maximum of and a minimum of a step jump can be taken in the direction of the last index of the array. You cannot move in the opposite direction, that is, away from the last index.
Let’s say you have an array of , starting from the index. It requires only two jumps to reach the last index. The first jump will be from the index to the index, i.e., only a one-step jump, and the next jump will be from the ...