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44 lines
1.2 KiB
44 lines
1.2 KiB
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/**
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* File: climbing_stairs_backtrack.cpp
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* Created Time: 2023-06-30
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* Author: krahets (krahets@163.com)
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*/
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#include "../utils/common.hpp"
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/* Backtracking */
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void backtrack(vector<int> &choices, int state, int n, vector<int> &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)
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res[0]++;
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// Traverse all choices
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for (auto &choice : choices) {
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// Pruning: do not allow climbing beyond the nth step
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if (state + choice > n)
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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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int climbingStairsBacktrack(int n) {
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vector<int> choices = {1, 2}; // Can choose to climb up 1 step or 2 steps
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int state = 0; // Start climbing from the 0th step
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vector<int> res = {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[0];
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}
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/* Driver Code */
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int main() {
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int n = 9;
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int res = climbingStairsBacktrack(n);
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cout << "There are " << res << " solutions to climb " << n << " stairs" << endl;
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return 0;
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}
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