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Yudong Jin
d7b2277d2b
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50 lines
1.2 KiB
C++
50 lines
1.2 KiB
C++
/**
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* File: climbing_stairs_dp.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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/* 階段登り：動的計画法 */
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int climbingStairsDP(int n) {
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if (n == 1 || n == 2)
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return n;
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// 部分問題の解を保存するために dp テーブルを初期化
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vector<int> dp(n + 1);
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// 初期状態：最小部分問題の解をあらかじめ設定
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dp[1] = 1;
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dp[2] = 2;
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// 状態遷移：小さい部分問題から大きい部分問題へ順に解く
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for (int i = 3; i <= n; i++) {
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dp[i] = dp[i - 1] + dp[i - 2];
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}
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return dp[n];
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}
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/* 階段登り：空間最適化した動的計画法 */
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int climbingStairsDPComp(int n) {
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if (n == 1 || n == 2)
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return n;
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int a = 1, b = 2;
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for (int i = 3; i <= n; i++) {
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int tmp = b;
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b = a + b;
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a = tmp;
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}
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return b;
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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 = climbingStairsDP(n);
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cout << "階段を " << n << " 段上る方法は全部で " << res << " 通り" << endl;
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res = climbingStairsDPComp(n);
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cout << "階段を " << n << " 段上る方法は全部で " << res << " 通り" << endl;
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return 0;
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}
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