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Minimum Jumps to Reach the End

Explore how to solve the minimum jumps problem by applying recursive and dynamic programming patterns. Understand naive, top-down, and bottom-up approaches, and learn to optimize solutions for better time and space efficiency, enabling you to tackle similar coding interview challenges confidently.

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 33, then a maximum of 33 and a minimum of a 11 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 [2,3,1,5,7][2, 3, 1, 5, 7], starting from the 0th0^{th} index. It requires only two jumps to reach the last index. The first jump will be from the 0th0^{th} index to the 1st1^{st} index, i.e., only a one-step jump, and the next jump will be from the ...