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41 lines
1.2 KiB
JavaScript
41 lines
1.2 KiB
JavaScript
/*
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*
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* Unique Paths
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*
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* There is a robot on an `m x n` grid.
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* The robot is initially located at the top-left corner.
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* The robot tries to move to the bottom-right corner.
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* The robot can only move either down or right at any point in time.
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*
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* Given the two integers `m` and `n`,
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* return the number of possible unique paths that the robot can take to reach the bottom-right corner.
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* More info: https://leetcode.com/problems/unique-paths/
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*/
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/*
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* @param {number} m
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* @param {number} n
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* @return {number}
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*/
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const uniquePaths = (m, n) => {
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// only one way to reach end
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if (m === 1 || n === 1) return 1
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// build a linear grid of size m
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// base case, position 1 has only 1 move
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const paths = new Array(m).fill(1)
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for (let i = 1; i < n; i++) {
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for (let j = 1; j < m; j++) {
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// paths[j] in RHS represents the cell value stored above the current cell
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// paths[j-1] in RHS represents the cell value stored to the left of the current cell
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// paths [j] on the LHS represents the number of distinct pathways to the cell (i,j)
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paths[j] = paths[j - 1] + paths[j]
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}
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}
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return paths[m - 1]
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}
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export { uniquePaths }
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