35 lines
1.1 KiB
JavaScript
35 lines
1.1 KiB
JavaScript
/**
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* File: climbing_stairs_backtrack.js
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* Created Time: 2023-07-26
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* Author: yuan0221 (yl1452491917@gmail.com)
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*/
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/* Backtracking */
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function backtrack(choices, state, n, res) {
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// When climbing to the nth step, add 1 to the number of solutions
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if (state === n) res.set(0, res.get(0) + 1);
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// Traverse all choices
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for (const choice of choices) {
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// Pruning: do not allow climbing beyond the nth step
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if (state + choice > n) continue;
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// Attempt: make a choice, update the state
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backtrack(choices, state + choice, n, res);
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// Retract
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}
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}
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/* Climbing stairs: Backtracking */
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function climbingStairsBacktrack(n) {
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const choices = [1, 2]; // Can choose to climb up 1 step or 2 steps
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const state = 0; // Start climbing from the 0th step
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const res = new Map();
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res.set(0, 0); // Use res[0] to record the number of solutions
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backtrack(choices, state, n, res);
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return res.get(0);
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}
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/* Driver Code */
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const n = 9;
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const res = climbingStairsBacktrack(n);
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console.log(`爬 ${n} 阶楼梯共有 ${res} 种方案`);
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