Frog Jump

arraydynamic programming

Problem Statement

A frog is crossing a river. The river is divided into some number of units, and at each unit, there may or may not exist a stone. The frog can jump on a stone, but it must not jump into the water.

Given a list of stones positions (in units) in sorted ascending order , determine if the frog can cross the river by landing on the last stone. Initially, the frog is on the first stone and assumes the first jump must be 1 unit.

If the frog's last jump was k units, its next jump must be either k - 1 , k , or k + 1 units. The frog can only jump in the forward direction.

Examples

Example 1

Input: stones = [0,1,3,5,6,8,12,17]
Output: true
The frog can jump to the last stone by jumping 1 unit to the 2nd stone, then 2 units to the 3rd stone, then 2 units to the 4th stone, then 3 units to the 6th stone, 4 units to the 7th stone, and 5 units to the 8th stone.

Example 2

Input: stones = [0,1,2,3,4,8,9,11]
Output: false
There is no way to jump to the last stone as the gap between the 5th and 6th stone is too large.

Constraints

2 <= stones.length <= 2000

0 <= stones[i] <= 2 ^31 - 1

stones[0] == 0

stones is sorted in a strictly increasing order.

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming