mirror of
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feat(chapter_backtracking): Add js and ts codes for chapter 13.3 (#667)
* feat(chapter_dynamic_programming): Add js and ts codes for chapter 14.1 * style(chapter_dynamic_programming): format code * refactor(chapter_dynamic_programming): remove main definition and add type * feat(chapter_backtracking): Add js and ts codes for chapter 13.3 * feat(chapter_divide_and_conquer): Add js and ts codes for chapter 12.2 * feat(chapter_divide_and_conquer): Add js and ts codes for chapter 12.3 * feat(chapter_divide_and_conquer): Add js and ts codes for chapter 12.4 * style(chapter_divide_and_conquer): fix typo * refactor: Use === instead of == in js and ts
This commit is contained in:
parent
c7c33f19ac
commit
70784a1ec3
31 changed files with 610 additions and 25 deletions
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@ -61,7 +61,7 @@ function traverse(nums) {
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/* 在数组中查找指定元素 */
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function find(nums, target) {
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for (let i = 0; i < nums.length; i++) {
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if (nums[i] == target) return i;
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if (nums[i] === target) return i;
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}
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return -1;
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}
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46
codes/javascript/chapter_backtracking/subset_sum_i.js
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46
codes/javascript/chapter_backtracking/subset_sum_i.js
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@ -0,0 +1,46 @@
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/**
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* File: subset_sum_i.js
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* Created Time: 2023-07-30
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* Author: yuan0221 (yl1452491917@gmail.com)
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*/
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/* 回溯算法:子集和 I */
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function backtrack(state, target, choices, start, res) {
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// 子集和等于 target 时,记录解
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if (target === 0) {
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res.push([...state]);
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return;
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}
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// 遍历所有选择
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// 剪枝二:从 start 开始遍历,避免生成重复子集
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for (let i = start; i < choices.length; i++) {
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// 剪枝一:若子集和超过 target ,则直接结束循环
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// 这是因为数组已排序,后边元素更大,子集和一定超过 target
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if (target - choices[i] < 0) {
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break;
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}
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// 尝试:做出选择,更新 target, start
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state.push(choices[i]);
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// 进行下一轮选择
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backtrack(state, target - choices[i], choices, i, res);
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// 回退:撤销选择,恢复到之前的状态
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state.pop();
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}
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}
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/* 求解子集和 I */
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function subsetSumI(nums, target) {
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const state = []; // 状态(子集)
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nums.sort(); // 对 nums 进行排序
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const start = 0; // 遍历起始点
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const res = []; // 结果列表(子集列表)
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backtrack(state, target, nums, start, res);
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return res;
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}
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/* Driver Code */
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const nums = [3, 4, 5];
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const target = 9;
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const res = subsetSumI(nums, target);
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console.log(`输入数组 nums = ${JSON.stringify(nums)}, target = ${target}`);
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console.log(`所有和等于 ${target} 的子集 res = ${JSON.stringify(res)}`);
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44
codes/javascript/chapter_backtracking/subset_sum_i_naive.js
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44
codes/javascript/chapter_backtracking/subset_sum_i_naive.js
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@ -0,0 +1,44 @@
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/**
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* File: subset_sum_i_naive.js
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* Created Time: 2023-07-30
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* Author: yuan0221 (yl1452491917@gmail.com)
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*/
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/* 回溯算法:子集和 I */
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function backtrack(state, target, total, choices, res) {
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// 子集和等于 target 时,记录解
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if (total === target) {
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res.push([...state]);
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return;
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}
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// 遍历所有选择
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for (let i = 0; i < choices.length; i++) {
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// 剪枝:若子集和超过 target ,则跳过该选择
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if (total + choices[i] > target) {
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continue;
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}
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// 尝试:做出选择,更新元素和 total
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state.push(choices[i]);
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// 进行下一轮选择
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backtrack(state, target, total + choices[i], choices, res);
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// 回退:撤销选择,恢复到之前的状态
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state.pop();
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}
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}
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/* 求解子集和 I(包含重复子集) */
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function subsetSumINaive(nums, target) {
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const state = []; // 状态(子集)
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const total = 0; // 子集和
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const res = []; // 结果列表(子集列表)
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backtrack(state, target, total, nums, res);
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return res;
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}
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/* Driver Code */
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const nums = [3, 4, 5];
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const target = 9;
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const res = subsetSumINaive(nums, target);
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console.log(`输入数组 nums = ${JSON.stringify(nums)}, target = ${target}`);
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console.log(`所有和等于 ${target} 的子集 res = ${JSON.stringify(res)}`);
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console.log('请注意,该方法输出的结果包含重复集合');
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51
codes/javascript/chapter_backtracking/subset_sum_ii.js
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51
codes/javascript/chapter_backtracking/subset_sum_ii.js
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/**
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* File: subset_sum_ii.js
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* Created Time: 2023-07-30
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* Author: yuan0221 (yl1452491917@gmail.com)
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*/
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/* 回溯算法:子集和 II */
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function backtrack(state, target, choices, start, res) {
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// 子集和等于 target 时,记录解
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if (target === 0) {
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res.push([...state]);
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return;
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}
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// 遍历所有选择
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// 剪枝二:从 start 开始遍历,避免生成重复子集
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// 剪枝三:从 start 开始遍历,避免重复选择同一元素
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for (let i = start; i < choices.length; i++) {
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// 剪枝一:若子集和超过 target ,则直接结束循环
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// 这是因为数组已排序,后边元素更大,子集和一定超过 target
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if (target - choices[i] < 0) {
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break;
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}
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// 剪枝四:如果该元素与左边元素相等,说明该搜索分支重复,直接跳过
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if (i > start && choices[i] === choices[i - 1]) {
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continue;
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}
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// 尝试:做出选择,更新 target, start
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state.push(choices[i]);
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// 进行下一轮选择
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backtrack(state, target - choices[i], choices, i + 1, res);
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// 回退:撤销选择,恢复到之前的状态
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state.pop();
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}
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}
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/* 求解子集和 II */
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function subsetSumII(nums, target) {
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const state = []; // 状态(子集)
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nums.sort(); // 对 nums 进行排序
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const start = 0; // 遍历起始点
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const res = []; // 结果列表(子集列表)
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backtrack(state, target, nums, start, res);
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return res;
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}
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/* Driver Code */
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const nums = [4, 4, 5];
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const target = 9;
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const res = subsetSumII(nums, target);
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console.log(`输入数组 nums = ${JSON.stringify(nums)}, target = ${target}`);
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console.log(`所有和等于 ${target} 的子集 res = ${JSON.stringify(res)}`);
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@ -77,7 +77,7 @@ function exponential(n) {
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/* 指数阶(递归实现) */
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function expRecur(n) {
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if (n == 1) return 1;
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if (n === 1) return 1;
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return expRecur(n - 1) + expRecur(n - 1) + 1;
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}
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@ -109,7 +109,7 @@ function linearLogRecur(n) {
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/* 阶乘阶(递归实现) */
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function factorialRecur(n) {
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if (n == 0) return 1;
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if (n === 0) return 1;
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let count = 0;
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// 从 1 个分裂出 n 个
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for (let i = 0; i < n; i++) {
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/**
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* File: binary_search_recur.js
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* Created Time: 2023-07-30
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* Author: yuan0221 (yl1452491917@gmail.com)
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*/
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/* 二分查找:问题 f(i, j) */
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function dfs(nums, target, i, j) {
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// 若区间为空,代表无目标元素,则返回 -1
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if (i > j) {
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return -1;
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}
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// 计算中点索引 m
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const m = i + ((j - i) >> 1);
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if (nums[m] < target) {
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// 递归子问题 f(m+1, j)
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return dfs(nums, target, m + 1, j);
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} else if (nums[m] > target) {
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// 递归子问题 f(i, m-1)
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return dfs(nums, target, i, m - 1);
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} else {
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// 找到目标元素,返回其索引
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return m;
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}
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}
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/* 二分查找 */
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function binarySearch(nums, target) {
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const n = nums.length;
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// 求解问题 f(0, n-1)
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return dfs(nums, target, 0, n - 1);
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}
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/* Driver Code */
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const target = 6;
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const nums = [1, 3, 6, 8, 12, 15, 23, 26, 31, 35];
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// 二分查找(双闭区间)
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const index = binarySearch(nums, target);
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console.log(`目标元素 6 的索引 = ${index}`);
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codes/javascript/chapter_divide_and_conquer/build_tree.js
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codes/javascript/chapter_divide_and_conquer/build_tree.js
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/**
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* File: build_tree.js
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* Created Time: 2023-07-30
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* Author: yuan0221 (yl1452491917@gmail.com)
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*/
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const { printTree } = require('../modules/PrintUtil');
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const { TreeNode } = require('../modules/TreeNode');
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/* 构建二叉树:分治 */
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function dfs(preorder, inorder, hmap, i, l, r) {
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// 子树区间为空时终止
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if (r - l < 0) return null;
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// 初始化根节点
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const root = new TreeNode(preorder[i]);
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// 查询 m ,从而划分左右子树
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const m = hmap.get(preorder[i]);
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// 子问题:构建左子树
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root.left = dfs(preorder, inorder, hmap, i + 1, l, m - 1);
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// 子问题:构建右子树
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root.right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r);
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// 返回根节点
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return root;
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}
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/* 构建二叉树 */
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function buildTree(preorder, inorder) {
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// 初始化哈希表,存储 inorder 元素到索引的映射
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let hmap = new Map();
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for (let i = 0; i < inorder.length; i++) {
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hmap.set(inorder[i], i);
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}
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const root = dfs(preorder, inorder, hmap, 0, 0, inorder.length - 1);
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return root;
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}
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/* Driver Code */
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const preorder = [3, 9, 2, 1, 7];
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const inorder = [9, 3, 1, 2, 7];
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console.log('前序遍历 = ' + JSON.stringify(preorder));
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console.log('中序遍历 = ' + JSON.stringify(inorder));
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const root = buildTree(preorder, inorder);
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console.log('构建的二叉树为:');
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printTree(root);
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52
codes/javascript/chapter_divide_and_conquer/hanota.js
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52
codes/javascript/chapter_divide_and_conquer/hanota.js
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/**
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* File: hanota.js
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* Created Time: 2023-07-30
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* Author: yuan0221 (yl1452491917@gmail.com)
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*/
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/* 移动一个圆盘 */
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function move(src, tar) {
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// 从 src 顶部拿出一个圆盘
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const pan = src.pop();
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// 将圆盘放入 tar 顶部
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tar.push(pan);
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}
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/* 求解汉诺塔:问题 f(i) */
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function dfs(i, src, buf, tar) {
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// 若 src 只剩下一个圆盘,则直接将其移到 tar
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if (i === 1) {
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move(src, tar);
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return;
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}
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// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf
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dfs(i - 1, src, tar, buf);
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// 子问题 f(1) :将 src 剩余一个圆盘移到 tar
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move(src, tar);
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// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar
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dfs(i - 1, buf, src, tar);
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}
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/* 求解汉诺塔 */
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function solveHanota(A, B, C) {
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const n = A.length;
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// 将 A 顶部 n 个圆盘借助 B 移到 C
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dfs(n, A, B, C);
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}
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/* Driver Code */
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// 列表尾部是柱子顶部
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const A = [5, 4, 3, 2, 1];
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const B = [];
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const C = [];
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console.log('初始状态下:');
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console.log(`A = ${JSON.stringify(A)}`);
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console.log(`B = ${JSON.stringify(B)}`);
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console.log(`C = ${JSON.stringify(C)}`);
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solveHanota(A, B, C);
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console.log('圆盘移动完成后:');
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console.log(`A = ${JSON.stringify(A)}`);
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console.log(`B = ${JSON.stringify(B)}`);
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console.log(`C = ${JSON.stringify(C)}`);
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/* 搜索 */
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function dfs(i) {
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// 已知 dp[1] 和 dp[2] ,返回之
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if (i == 1 || i == 2) return i;
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if (i === 1 || i === 2) return i;
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// dp[i] = dp[i-1] + dp[i-2]
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const count = dfs(i - 1) + dfs(i - 2);
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return count;
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@ -7,7 +7,7 @@
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/* 记忆化搜索 */
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function dfs(i, mem) {
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// 已知 dp[1] 和 dp[2] ,返回之
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if (i == 1 || i == 2) return i;
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if (i === 1 || i === 2) return i;
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// 若存在记录 dp[i] ,则直接返回之
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if (mem[i] != -1) return mem[i];
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// dp[i] = dp[i-1] + dp[i-2]
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/* 爬楼梯:动态规划 */
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function climbingStairsDP(n) {
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if (n == 1 || n == 2) return n;
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if (n === 1 || n === 2) return n;
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// 初始化 dp 表,用于存储子问题的解
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const dp = new Array(n + 1).fill(-1);
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// 初始状态:预设最小子问题的解
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@ -21,7 +21,7 @@ function climbingStairsDP(n) {
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/* 爬楼梯:状态压缩后的动态规划 */
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function climbingStairsDPComp(n) {
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if (n == 1 || n == 2) return n;
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if (n === 1 || n === 2) return n;
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let a = 1,
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b = 2;
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for (let i = 3; i <= n; i++) {
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@ -69,7 +69,7 @@ class GraphAdjMat {
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if (i < 0 || j < 0 || i >= this.size() || j >= this.size() || i === j) {
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throw new RangeError('Index Out Of Bounds Exception');
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}
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// 在无向图中,邻接矩阵沿主对角线对称,即满足 (i, j) == (j, i)
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// 在无向图中,邻接矩阵沿主对角线对称,即满足 (i, j) === (j, i)
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this.adjMat[i][j] = 1;
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this.adjMat[j][i] = 1;
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}
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@ -103,7 +103,7 @@ class MaxHeap {
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if (l < this.size() && this.#maxHeap[l] > this.#maxHeap[ma]) ma = l;
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if (r < this.size() && this.#maxHeap[r] > this.#maxHeap[ma]) ma = r;
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// 若节点 i 最大或索引 l, r 越界,则无需继续堆化,跳出
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if (ma == i) break;
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if (ma === i) break;
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// 交换两节点
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this.#swap(i, ma);
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// 循环向下堆化
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@ -18,7 +18,7 @@ function binarySearchLeftEdge(nums, target) {
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j = m - 1; // 首个小于 target 的元素在区间 [i, m-1] 中
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}
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}
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if (i == nums.length || nums[i] != target) {
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if (i === nums.length || nums[i] != target) {
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return -1; // 未找到目标元素,返回 -1
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}
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return i;
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@ -26,12 +26,12 @@ class ArrayQueue {
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|
||||
/* 判断队列是否为空 */
|
||||
empty() {
|
||||
return this.#queSize == 0;
|
||||
return this.#queSize === 0;
|
||||
}
|
||||
|
||||
/* 入队 */
|
||||
push(num) {
|
||||
if (this.size == this.capacity) {
|
||||
if (this.size === this.capacity) {
|
||||
console.log('队列已满');
|
||||
return;
|
||||
}
|
||||
|
|
|
@ -22,7 +22,7 @@ class LinkedListStack {
|
|||
|
||||
/* 判断栈是否为空 */
|
||||
isEmpty() {
|
||||
return this.size == 0;
|
||||
return this.size === 0;
|
||||
}
|
||||
|
||||
/* 入栈 */
|
||||
|
|
54
codes/typescript/chapter_backtracking/subset_sum_i.ts
Normal file
54
codes/typescript/chapter_backtracking/subset_sum_i.ts
Normal file
|
@ -0,0 +1,54 @@
|
|||
/**
|
||||
* File: subset_sum_i.ts
|
||||
* Created Time: 2023-07-30
|
||||
* Author: yuan0221 (yl1452491917@gmail.com)
|
||||
*/
|
||||
|
||||
/* 回溯算法:子集和 I */
|
||||
function backtrack(
|
||||
state: number[],
|
||||
target: number,
|
||||
choices: number[],
|
||||
start: number,
|
||||
res: number[][]
|
||||
): void {
|
||||
// 子集和等于 target 时,记录解
|
||||
if (target === 0) {
|
||||
res.push([...state]);
|
||||
return;
|
||||
}
|
||||
// 遍历所有选择
|
||||
// 剪枝二:从 start 开始遍历,避免生成重复子集
|
||||
for (let i = start; i < choices.length; i++) {
|
||||
// 剪枝一:若子集和超过 target ,则直接结束循环
|
||||
// 这是因为数组已排序,后边元素更大,子集和一定超过 target
|
||||
if (target - choices[i] < 0) {
|
||||
break;
|
||||
}
|
||||
// 尝试:做出选择,更新 target, start
|
||||
state.push(choices[i]);
|
||||
// 进行下一轮选择
|
||||
backtrack(state, target - choices[i], choices, i, res);
|
||||
// 回退:撤销选择,恢复到之前的状态
|
||||
state.pop();
|
||||
}
|
||||
}
|
||||
|
||||
/* 求解子集和 I */
|
||||
function subsetSumI(nums: number[], target: number): number[][] {
|
||||
const state = []; // 状态(子集)
|
||||
nums.sort(); // 对 nums 进行排序
|
||||
const start = 0; // 遍历起始点
|
||||
const res = []; // 结果列表(子集列表)
|
||||
backtrack(state, target, nums, start, res);
|
||||
return res;
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
const nums = [3, 4, 5];
|
||||
const target = 9;
|
||||
const res = subsetSumI(nums, target);
|
||||
console.log(`输入数组 nums = ${JSON.stringify(nums)}, target = ${target}`);
|
||||
console.log(`所有和等于 ${target} 的子集 res = ${JSON.stringify(res)}`);
|
||||
|
||||
export {};
|
52
codes/typescript/chapter_backtracking/subset_sum_i_naive.ts
Normal file
52
codes/typescript/chapter_backtracking/subset_sum_i_naive.ts
Normal file
|
@ -0,0 +1,52 @@
|
|||
/**
|
||||
* File: subset_sum_i_naive.ts
|
||||
* Created Time: 2023-07-30
|
||||
* Author: yuan0221 (yl1452491917@gmail.com)
|
||||
*/
|
||||
|
||||
/* 回溯算法:子集和 I */
|
||||
function backtrack(
|
||||
state: number[],
|
||||
target: number,
|
||||
total: number,
|
||||
choices: number[],
|
||||
res: number[][]
|
||||
): void {
|
||||
// 子集和等于 target 时,记录解
|
||||
if (total === target) {
|
||||
res.push([...state]);
|
||||
return;
|
||||
}
|
||||
// 遍历所有选择
|
||||
for (let i = 0; i < choices.length; i++) {
|
||||
// 剪枝:若子集和超过 target ,则跳过该选择
|
||||
if (total + choices[i] > target) {
|
||||
continue;
|
||||
}
|
||||
// 尝试:做出选择,更新元素和 total
|
||||
state.push(choices[i]);
|
||||
// 进行下一轮选择
|
||||
backtrack(state, target, total + choices[i], choices, res);
|
||||
// 回退:撤销选择,恢复到之前的状态
|
||||
state.pop();
|
||||
}
|
||||
}
|
||||
|
||||
/* 求解子集和 I(包含重复子集) */
|
||||
function subsetSumINaive(nums: number[], target: number): number[][] {
|
||||
const state = []; // 状态(子集)
|
||||
const total = 0; // 子集和
|
||||
const res = []; // 结果列表(子集列表)
|
||||
backtrack(state, target, total, nums, res);
|
||||
return res;
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
const nums = [3, 4, 5];
|
||||
const target = 9;
|
||||
const res = subsetSumINaive(nums, target);
|
||||
console.log(`输入数组 nums = ${JSON.stringify(nums)}, target = ${target}`);
|
||||
console.log(`所有和等于 ${target} 的子集 res = ${JSON.stringify(res)}`);
|
||||
console.log('请注意,该方法输出的结果包含重复集合');
|
||||
|
||||
export {};
|
59
codes/typescript/chapter_backtracking/subset_sum_ii.ts
Normal file
59
codes/typescript/chapter_backtracking/subset_sum_ii.ts
Normal file
|
@ -0,0 +1,59 @@
|
|||
/**
|
||||
* File: subset_sum_ii.ts
|
||||
* Created Time: 2023-07-30
|
||||
* Author: yuan0221 (yl1452491917@gmail.com)
|
||||
*/
|
||||
|
||||
/* 回溯算法:子集和 II */
|
||||
function backtrack(
|
||||
state: number[],
|
||||
target: number,
|
||||
choices: number[],
|
||||
start: number,
|
||||
res: number[][]
|
||||
): void {
|
||||
// 子集和等于 target 时,记录解
|
||||
if (target === 0) {
|
||||
res.push([...state]);
|
||||
return;
|
||||
}
|
||||
// 遍历所有选择
|
||||
// 剪枝二:从 start 开始遍历,避免生成重复子集
|
||||
// 剪枝三:从 start 开始遍历,避免重复选择同一元素
|
||||
for (let i = start; i < choices.length; i++) {
|
||||
// 剪枝一:若子集和超过 target ,则直接结束循环
|
||||
// 这是因为数组已排序,后边元素更大,子集和一定超过 target
|
||||
if (target - choices[i] < 0) {
|
||||
break;
|
||||
}
|
||||
// 剪枝四:如果该元素与左边元素相等,说明该搜索分支重复,直接跳过
|
||||
if (i > start && choices[i] === choices[i - 1]) {
|
||||
continue;
|
||||
}
|
||||
// 尝试:做出选择,更新 target, start
|
||||
state.push(choices[i]);
|
||||
// 进行下一轮选择
|
||||
backtrack(state, target - choices[i], choices, i + 1, res);
|
||||
// 回退:撤销选择,恢复到之前的状态
|
||||
state.pop();
|
||||
}
|
||||
}
|
||||
|
||||
/* 求解子集和 II */
|
||||
function subsetSumII(nums: number[], target: number): number[][] {
|
||||
const state = []; // 状态(子集)
|
||||
nums.sort(); // 对 nums 进行排序
|
||||
const start = 0; // 遍历起始点
|
||||
const res = []; // 结果列表(子集列表)
|
||||
backtrack(state, target, nums, start, res);
|
||||
return res;
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
const nums = [4, 4, 5];
|
||||
const target = 9;
|
||||
const res = subsetSumII(nums, target);
|
||||
console.log(`输入数组 nums = ${JSON.stringify(nums)}, target = ${target}`);
|
||||
console.log(`所有和等于 ${target} 的子集 res = ${JSON.stringify(res)}`);
|
||||
|
||||
export {};
|
|
@ -77,7 +77,7 @@ function exponential(n: number): number {
|
|||
|
||||
/* 指数阶(递归实现) */
|
||||
function expRecur(n: number): number {
|
||||
if (n == 1) return 1;
|
||||
if (n === 1) return 1;
|
||||
return expRecur(n - 1) + expRecur(n - 1) + 1;
|
||||
}
|
||||
|
||||
|
@ -109,7 +109,7 @@ function linearLogRecur(n: number): number {
|
|||
|
||||
/* 阶乘阶(递归实现) */
|
||||
function factorialRecur(n: number): number {
|
||||
if (n == 0) return 1;
|
||||
if (n === 0) return 1;
|
||||
let count = 0;
|
||||
// 从 1 个分裂出 n 个
|
||||
for (let i = 0; i < n; i++) {
|
||||
|
|
|
@ -0,0 +1,41 @@
|
|||
/**
|
||||
* File: binary_search_recur.ts
|
||||
* Created Time: 2023-07-30
|
||||
* Author: yuan0221 (yl1452491917@gmail.com)
|
||||
*/
|
||||
|
||||
/* 二分查找:问题 f(i, j) */
|
||||
function dfs(nums: number[], target: number, i: number, j: number): number {
|
||||
// 若区间为空,代表无目标元素,则返回 -1
|
||||
if (i > j) {
|
||||
return -1;
|
||||
}
|
||||
// 计算中点索引 m
|
||||
const m = i + ((j - i) >> 1);
|
||||
if (nums[m] < target) {
|
||||
// 递归子问题 f(m+1, j)
|
||||
return dfs(nums, target, m + 1, j);
|
||||
} else if (nums[m] > target) {
|
||||
// 递归子问题 f(i, m-1)
|
||||
return dfs(nums, target, i, m - 1);
|
||||
} else {
|
||||
// 找到目标元素,返回其索引
|
||||
return m;
|
||||
}
|
||||
}
|
||||
|
||||
/* 二分查找 */
|
||||
function binarySearch(nums: number[], target: number): number {
|
||||
const n = nums.length;
|
||||
// 求解问题 f(0, n-1)
|
||||
return dfs(nums, target, 0, n - 1);
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
const target = 6;
|
||||
const nums = [1, 3, 6, 8, 12, 15, 23, 26, 31, 35];
|
||||
// 二分查找(双闭区间)
|
||||
const index = binarySearch(nums, target);
|
||||
console.log(`目标元素 6 的索引 = ${index}`);
|
||||
|
||||
export {};
|
51
codes/typescript/chapter_divide_and_conquer/build_tree.ts
Normal file
51
codes/typescript/chapter_divide_and_conquer/build_tree.ts
Normal file
|
@ -0,0 +1,51 @@
|
|||
/**
|
||||
* File: build_tree.ts
|
||||
* Created Time: 2023-07-30
|
||||
* Author: yuan0221 (yl1452491917@gmail.com)
|
||||
*/
|
||||
|
||||
import { printTree } from '../modules/PrintUtil';
|
||||
import { TreeNode } from '../modules/TreeNode';
|
||||
|
||||
/* 构建二叉树:分治 */
|
||||
function dfs(
|
||||
preorder: number[],
|
||||
inorder: number[],
|
||||
hmap: Map<number, number>,
|
||||
i: number,
|
||||
l: number,
|
||||
r: number
|
||||
): TreeNode | null {
|
||||
// 子树区间为空时终止
|
||||
if (r - l < 0) return null;
|
||||
// 初始化根节点
|
||||
const root: TreeNode = new TreeNode(preorder[i]);
|
||||
// 查询 m ,从而划分左右子树
|
||||
const m = hmap.get(preorder[i]);
|
||||
// 子问题:构建左子树
|
||||
root.left = dfs(preorder, inorder, hmap, i + 1, l, m - 1);
|
||||
// 子问题:构建右子树
|
||||
root.right = dfs(preorder, inorder, hmap, i + 1 + m - l, m + 1, r);
|
||||
// 返回根节点
|
||||
return root;
|
||||
}
|
||||
|
||||
/* 构建二叉树 */
|
||||
function buildTree(preorder: number[], inorder: number[]): TreeNode | null {
|
||||
// 初始化哈希表,存储 inorder 元素到索引的映射
|
||||
let hmap = new Map<number, number>();
|
||||
for (let i = 0; i < inorder.length; i++) {
|
||||
hmap.set(inorder[i], i);
|
||||
}
|
||||
const root = dfs(preorder, inorder, hmap, 0, 0, inorder.length - 1);
|
||||
return root;
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
const preorder = [3, 9, 2, 1, 7];
|
||||
const inorder = [9, 3, 1, 2, 7];
|
||||
console.log('前序遍历 = ' + JSON.stringify(preorder));
|
||||
console.log('中序遍历 = ' + JSON.stringify(inorder));
|
||||
const root = buildTree(preorder, inorder);
|
||||
console.log('构建的二叉树为:');
|
||||
printTree(root);
|
52
codes/typescript/chapter_divide_and_conquer/hanota.ts
Normal file
52
codes/typescript/chapter_divide_and_conquer/hanota.ts
Normal file
|
@ -0,0 +1,52 @@
|
|||
/**
|
||||
* File: hanota.ts
|
||||
* Created Time: 2023-07-30
|
||||
* Author: yuan0221 (yl1452491917@gmail.com)
|
||||
*/
|
||||
|
||||
/* 移动一个圆盘 */
|
||||
function move(src: number[], tar: number[]): void {
|
||||
// 从 src 顶部拿出一个圆盘
|
||||
const pan = src.pop();
|
||||
// 将圆盘放入 tar 顶部
|
||||
tar.push(pan);
|
||||
}
|
||||
|
||||
/* 求解汉诺塔:问题 f(i) */
|
||||
function dfs(i: number, src: number[], buf: number[], tar: number[]): void {
|
||||
// 若 src 只剩下一个圆盘,则直接将其移到 tar
|
||||
if (i === 1) {
|
||||
move(src, tar);
|
||||
return;
|
||||
}
|
||||
// 子问题 f(i-1) :将 src 顶部 i-1 个圆盘借助 tar 移到 buf
|
||||
dfs(i - 1, src, tar, buf);
|
||||
// 子问题 f(1) :将 src 剩余一个圆盘移到 tar
|
||||
move(src, tar);
|
||||
// 子问题 f(i-1) :将 buf 顶部 i-1 个圆盘借助 src 移到 tar
|
||||
dfs(i - 1, buf, src, tar);
|
||||
}
|
||||
|
||||
/* 求解汉诺塔 */
|
||||
function solveHanota(A: number[], B: number[], C: number[]): void {
|
||||
const n = A.length;
|
||||
// 将 A 顶部 n 个圆盘借助 B 移到 C
|
||||
dfs(n, A, B, C);
|
||||
}
|
||||
|
||||
/* Driver Code */
|
||||
// 列表尾部是柱子顶部
|
||||
const A = [5, 4, 3, 2, 1];
|
||||
const B = [];
|
||||
const C = [];
|
||||
console.log('初始状态下:');
|
||||
console.log(`A = ${JSON.stringify(A)}`);
|
||||
console.log(`B = ${JSON.stringify(B)}`);
|
||||
console.log(`C = ${JSON.stringify(C)}`);
|
||||
|
||||
solveHanota(A, B, C);
|
||||
|
||||
console.log('圆盘移动完成后:');
|
||||
console.log(`A = ${JSON.stringify(A)}`);
|
||||
console.log(`B = ${JSON.stringify(B)}`);
|
||||
console.log(`C = ${JSON.stringify(C)}`);
|
|
@ -7,7 +7,7 @@
|
|||
/* 搜索 */
|
||||
function dfs(i: number): number {
|
||||
// 已知 dp[1] 和 dp[2] ,返回之
|
||||
if (i == 1 || i == 2) return i;
|
||||
if (i === 1 || i === 2) return i;
|
||||
// dp[i] = dp[i-1] + dp[i-2]
|
||||
const count = dfs(i - 1) + dfs(i - 2);
|
||||
return count;
|
||||
|
|
|
@ -7,7 +7,7 @@
|
|||
/* 记忆化搜索 */
|
||||
function dfs(i: number, mem: number[]): number {
|
||||
// 已知 dp[1] 和 dp[2] ,返回之
|
||||
if (i == 1 || i == 2) return i;
|
||||
if (i === 1 || i === 2) return i;
|
||||
// 若存在记录 dp[i] ,则直接返回之
|
||||
if (mem[i] != -1) return mem[i];
|
||||
// dp[i] = dp[i-1] + dp[i-2]
|
||||
|
|
|
@ -6,7 +6,7 @@
|
|||
|
||||
/* 爬楼梯:动态规划 */
|
||||
function climbingStairsDP(n: number): number {
|
||||
if (n == 1 || n == 2) return n;
|
||||
if (n === 1 || n === 2) return n;
|
||||
// 初始化 dp 表,用于存储子问题的解
|
||||
const dp = new Array(n + 1).fill(-1);
|
||||
// 初始状态:预设最小子问题的解
|
||||
|
@ -21,7 +21,7 @@ function climbingStairsDP(n: number): number {
|
|||
|
||||
/* 爬楼梯:状态压缩后的动态规划 */
|
||||
function climbingStairsDPComp(n: number): number {
|
||||
if (n == 1 || n == 2) return n;
|
||||
if (n === 1 || n === 2) return n;
|
||||
let a = 1,
|
||||
b = 2;
|
||||
for (let i = 3; i <= n; i++) {
|
||||
|
|
|
@ -69,7 +69,7 @@ class GraphAdjMat {
|
|||
if (i < 0 || j < 0 || i >= this.size() || j >= this.size() || i === j) {
|
||||
throw new RangeError('Index Out Of Bounds Exception');
|
||||
}
|
||||
// 在无向图中,邻接矩阵沿主对角线对称,即满足 (i, j) == (j, i)
|
||||
// 在无向图中,邻接矩阵沿主对角线对称,即满足 (i, j) === (j, i)
|
||||
this.adjMat[i][j] = 1;
|
||||
this.adjMat[j][i] = 1;
|
||||
}
|
||||
|
|
|
@ -102,7 +102,7 @@ class MaxHeap {
|
|||
if (l < this.size() && this.maxHeap[l] > this.maxHeap[ma]) ma = l;
|
||||
if (r < this.size() && this.maxHeap[r] > this.maxHeap[ma]) ma = r;
|
||||
// 若节点 i 最大或索引 l, r 越界,则无需继续堆化,跳出
|
||||
if (ma == i) break;
|
||||
if (ma === i) break;
|
||||
// 交换两节点
|
||||
this.swap(i, ma);
|
||||
// 循环向下堆化
|
||||
|
|
|
@ -17,7 +17,7 @@ function binarySearchLeftEdge(nums: number[], target: number): number {
|
|||
j = m - 1; // 首个小于 target 的元素在区间 [i, m-1] 中
|
||||
}
|
||||
}
|
||||
if (i == nums.length || nums[i] != target) {
|
||||
if (i === nums.length || nums[i] != target) {
|
||||
return -1; // 未找到目标元素,返回 -1
|
||||
}
|
||||
return i;
|
||||
|
|
|
@ -27,12 +27,12 @@ class ArrayQueue {
|
|||
|
||||
/* 判断队列是否为空 */
|
||||
empty(): boolean {
|
||||
return this.queSize == 0;
|
||||
return this.queSize === 0;
|
||||
}
|
||||
|
||||
/* 入队 */
|
||||
push(num: number): void {
|
||||
if (this.size == this.capacity) {
|
||||
if (this.size === this.capacity) {
|
||||
console.log('队列已满');
|
||||
return;
|
||||
}
|
||||
|
|
|
@ -22,7 +22,7 @@ class LinkedListStack {
|
|||
|
||||
/* 判断栈是否为空 */
|
||||
isEmpty(): boolean {
|
||||
return this.size == 0;
|
||||
return this.size === 0;
|
||||
}
|
||||
|
||||
/* 入栈 */
|
||||
|
|
Loading…
Reference in a new issue