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Minimum Jumps to Reach the End

Explore how to solve the problem of reaching the end of an array with the fewest jumps. Learn to optimize naive recursive solutions using dynamic programming techniques, including memoization and tabulation, and master a linear time approach that reduces complexity.

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 ...