【LeetCode】动态规划入门（专项打卡21天合集）

下图为证

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Day1

斐波拉契数

509. 斐波那契数

class Solution {public int fib(int n) {int[] dp = new int[31];dp[1] = 1;for (int i = 2; i <= n; i++) {dp[i] = dp[i - 1] + dp[i - 2];}return dp[n];}
}

第 N 个泰波那契数

1137. 第 N 个泰波那契数

class Solution {public int tribonacci(int n) {int[] dp = new int[38];dp[1] = dp[2] = 1;for (int i = 3; i <= n; i++) {dp[i] = dp[i - 1] + dp[i - 2] + dp[i - 3];}return dp[n];}
}

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Day2

爬楼梯

70. 爬楼梯

class Solution {public int climbStairs(int n) {if (n < 3) return n;int cur = 2, pre = 1;for (int i = 3; i <= n; i++) {int temp = cur;cur += pre;pre = temp;}return cur;}
}

使用最小花费爬楼梯

746. 使用最小花费爬楼梯

class Solution {public int minCostClimbingStairs(int[] cost) {int n = cost.length;int[] dp = new int[n];dp[0] = cost[0];dp[1] = cost[1];for (int i = 2; i < n; i++) {dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];}return Math.min(dp[n - 2], dp[n - 1]);}
}

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Day3

打家劫舍

198. 打家劫舍

class Solution {public int rob(int[] nums) {int n = nums.length;int[] dp = new int[n + 1];dp[1] = nums[0];for (int i = 1; i < n; i++) {dp[i + 1] = Math.max(dp[i], dp[i - 1] + nums[i]);}return dp[n];}
}

打家劫舍 II

213. 打家劫舍 II

class Solution {public int rob(int[] nums) {if (nums == null || nums.length == 0) return 0;if (nums.length == 1) return nums[0];int val1 = rob1(nums);reverse(nums);int val2 = rob1(nums);return Math.max(val1, val2);}public int rob1(int[] nums) {int n = nums.length;int[] dp = new int[n + 1];dp[1] = nums[0];for (int i = 1; i < n; i++) {dp[i + 1] = Math.max(dp[i], dp[i - 1] + nums[i]);}return dp[n - 1];}private void reverse(int[] nums) {int n = nums.length, i = 0;while (i < n / 2) {int t = nums[i];nums[i] = nums[n - i - 1];nums[n - i - 1] = t;i++;}}
}

删除并获得点数

740. 删除并获得点数

class Solution {public int deleteAndEarn(int[] nums) {int n = 10000;int[] mark = new int[n + 1];for (int num : nums) mark[num] += num;int[] dp = new int[n + 2];dp[1] = mark[0];for (int i = 1; i < n + 1; i++) {dp[i + 1] = Math.max(dp[i], dp[i - 1] + mark[i]);}return dp[n + 1];}
}

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Day4

跳跃游戏

55. 跳跃游戏

前向遍历

class Solution {public boolean canJump(int[] nums) {int ri = 0;for (int i = 0; i < nums.length; i++) {if (ri >= i) {ri = Math.max(ri, i + nums[i]);} else {return false;}}return true;}
}

后向遍历

class Solution {public boolean canJump(int[] nums) {if(nums == null || nums.length < 2) return true;int le = nums.length - 1;for(int i = nums.length - 2; i >= 0; i--) {if(i + nums[i] >= le) le = i;}return le == 0;}
}

跳跃游戏 II

45. 跳跃游戏 II

动态规划法

class Solution {public int jump(int[] nums) {int n = nums.length;int[] dp = new int[n + 1];for (int i = 0; i < nums.length; i++) {for (int j = 1; j <= nums[i] && i + j < n; j++) {dp[i + j] = dp[i + j] == 0 ? dp[i] + 1 : Math.min(dp[i + j], dp[i] + 1);}}return dp[n - 1];}
}

贪心法

class Solution {public int jump(int[] nums) {int steps = 0;int reach = 0, nextreach = 0;for (int i = 0; i < nums.length - 1; i++) {nextreach = Math.max(nextreach, i + nums[i]);if (reach == i) {reach = nextreach;steps++;}}return steps;}
}

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Day5

最大子序和

53. 最大子序和

class Solution {public int maxSubArray(int[] nums) {int res = nums[0], cur = nums[0];for (int i = 1; i < nums.length; i++) {cur = cur > 0 ? cur + nums[i] : nums[i];res = Math.max(res, cur);}return res;}
}

环形子数组的最大和

918. 环形子数组的最大和

class Solution {public int maxSubarraySumCircular(int[] nums) {int max, min, curMax, curMin, sum;max = min = curMax = curMin = sum = nums[0];for (int i = 1; i < nums.length; i++) {sum += nums[i];curMax = curMax > 0 ? curMax + nums[i] : nums[i];max = Math.max(max, curMax);curMin = curMin < 0 ? curMin + nums[i] : nums[i];min = Math.min(min, curMin);}return max < 0 ? max : Math.max(max, sum - min);}
}

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Day6

乘积最大子数组

152. 乘积最大子数组

class Solution {public int maxProduct(int[] nums) {int res, max, min;res = max = min = nums[0];for (int i = 1; i < nums.length; i++) {int mx = max, mn = min;max = Math.max(mx * nums[i], Math.max(mn * nums[i], nums[i]));min = Math.min(mx * nums[i], Math.min(mn * nums[i], nums[i]));res = Math.max(res, max);} return res;}
}

乘积为正数的最长子数组长度

1567. 乘积为正数的最长子数组长度

class Solution {public int getMaxLen(int[] nums) {int res = 0, p = 0, q = 0;for (int num : nums) {if (num == 0) {p = q = 0;    //乘积为正负的长度} else {if (num > 0) {p++;if (q > 0) q++;} else {int t = p;p = q;q = t;q++;if (p > 0) p++;}}res = Math.max(res, p);}return res;}
}

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Day7

最佳观光组合

1014. 最佳观光组合

class Solution {public int maxScoreSightseeingPair(int[] values) {int res = 0, leftMax = 0;for (int i = 0; i < values.length; i++) {res = Math.max(res, leftMax + values[i] - i);leftMax = Math.max(leftMax, values[i] + i);}return res;}
}

买卖股票的最佳时机

121. 买卖股票的最佳时机

class Solution {public int maxProfit(int[] prices) {int profit = 0, minPrice = 10001;for (int price : prices) {minPrice = Math.min(minPrice, price);profit = Math.max(profit, price - minPrice);}return profit;}
}

买卖股票的最佳时机 II

122. 买卖股票的最佳时机 II

方法一：动态规划法

class Solution {public int maxProfit(int[] prices) {int n = prices.length;int[][] dp = new int[n][2];  //0不持有1持有dp[0][1] = -prices[0];for (int i = 1; i < n; i++) {dp[i][0] = Math.max(dp[i - 1][0], dp[i - 1][1] + prices[i]);dp[i][1] = Math.max(dp[i - 1][1], dp[i - 1][0] - prices[i]);}return dp[n - 1][0];}
}

方法二：贪心法

class Solution {public int maxProfit(int[] prices) {int res = 0;for (int i = 1; i < prices.length; i++) {res += Math.max(0, prices[i] - prices[i - 1]);}return res;}
}

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Day8

最佳买卖股票时机含冷冻期

309. 最佳买卖股票时机含冷冻期

class Solution {public int maxProfit(int[] prices) {int n = prices.length;int[][] dp = new int[n + 2][2];  //0不持有1持有dp[0][1] = dp[1][1] = Integer.MIN_VALUE;for (int i = 0; i < n; i++) {dp[i + 2][0] = Math.max(dp[i + 1][0], dp[i + 1][1] + prices[i]);dp[i + 2][1] = Math.max(dp[i + 1][1], dp[i][0] - prices[i]);}return dp[n + 1][0];}
}

买卖股票的最佳时机含手续费

714. 买卖股票的最佳时机含手续费

方法一：

class Solution {public int maxProfit(int[] prices, int fee) {int n = prices.length;int[][] dp = new int[n][2];dp[0][1] = -prices[0] - fee;for (int i = 1; i < n; i++) {dp[i][0] = Math.max(dp[i - 1][0], dp[i - 1][1] + prices[i]);dp[i][1] = Math.max(dp[i - 1][1], dp[i - 1][0] - prices[i] - fee);}return dp[n - 1][0];}
}

方法二：

class Solution {public int maxProfit(int[] prices, int fee) {if (prices.length < 2) return 0;int buy = -prices[0], sell = 0;for (int i = 1; i < prices.length; i++) {buy = Math.max(buy, sell - prices[i]);sell = Math.max(sell, buy + prices[i] - fee);}return sell;}
}

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Day9

单词拆分

139. 单词拆分

class Solution {public boolean wordBreak(String s, List<String> wordDict) {int n = s.length(), len = 0;Set<String> set = new HashSet<>();for (String word : wordDict) {set.add(word);len = Math.max(len, word.length());}boolean[] dp = new boolean[n + 1];dp[0] = true;for (int i = 1; i <= n; i++) {for (int j = Math.max(0, i - len); j < i; j++) {if (dp[j] && set.contains(s.substring(j, i))) {dp[i] = true;break;}}}return dp[n];}
}

接雨水

42. 接雨水

class Solution {public int trap(int[] height) {if (height == null || height.length < 3) return 0;int res = 0;int L = 1, R = height.length - 2;int leftMax = height[0], rightMax = height[height.length - 1];while(L <= R) {if (leftMax < rightMax) {res += Math.max(0, leftMax - height[L]);leftMax = Math.max(leftMax, height[L++]);} else {res += Math.max(0, rightMax - height[R]);rightMax = Math.max(rightMax, height[R--]);}}return res;}
}

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Day10

等差数列划分

413. 等差数列划分

class Solution {public int numberOfArithmeticSlices(int[] nums) {if (nums.length < 3) return 0;int n = nums.length, res = 0;int[] dp = new int[n];for (int i = 2; i < n; i++) {if (nums[i] - nums[i - 1] == nums[i - 1] - nums[i - 2]) {dp[i] = dp[i - 1] + 1;}res += dp[i];}return res;}
}

优化版

class Solution {public int numberOfArithmeticSlices(int[] nums) {if (nums.length < 3) return 0;int res = 0, pre = 0;for (int i = 2; i < nums.length; i++) {if (nums[i] - nums[i - 1] == nums[i - 1] - nums[i - 2]) {pre += 1;res += pre;} else {pre = 0;}}return res;}
}

解码方法

91. 解码方法

class Solution {public int numDecodings(String s) {if (s.charAt(0) == '0') return 0;int n = s.length();int[] dp = new int[n + 1];dp[0] = 1;for (int i = 0; i < n; i++) {dp[i + 1] = s.charAt(i) == '0' ? 0 : dp[i];if (i > 0 && (s.charAt(i - 1) == '1' || s.charAt(i - 1) == '2' && s.charAt(i) < '7')) {dp[i + 1] += dp[i - 1];}}return dp[n];}
}

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Day11

丑数 II

264. 丑数 II

class Solution {public int nthUglyNumber(int n) {int two, three, five;two = three = five = 0;int[] dp = new int[n];dp[0] = 1;for (int i = 1; i < n; i++) {dp[i] = Math.min(dp[two] * 2, Math.min(dp[three] * 3, dp[five] * 5));if (dp[i] == dp[two] * 2) two++;if (dp[i] == dp[three] * 3) three++;if (dp[i] == dp[five] * 5) five++;}return dp[n - 1];}
}

不同的二叉搜索树

96. 不同的二叉搜索树

class Solution {public int numTrees(int n) {int[] dp = new int[n + 1];dp[0] = dp[1] = 1;for (int i = 2; i <= n; i++) {for (int j = 1; j <= i; j++) {dp[i] += dp[j - 1] * dp[i - j];}}return dp[n];}
}

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Day12

杨辉三角

118. 杨辉三角

class Solution {public List<List<Integer>> generate(int numRows) {List<List<Integer>> res = new ArrayList<>();if (numRows == 0) return res;List<Integer> temp = new ArrayList<>();temp.add(1);res.add(temp);for (int i = 1; i < numRows; i++) {List<Integer> list = new ArrayList<>();temp = res.get(i - 1);for (int j = 0; j <= i; j++) {if (j == 0 || i == j) {list.add(1);} else {list.add(temp.get(j - 1) + temp.get(j));}}res.add(list);}return res;}
}

杨辉三角 II

119. 杨辉三角 II

class Solution {public List<Integer> getRow(int rowIndex) {Integer[] dp = new Integer[rowIndex + 1];Arrays.fill(dp, 1);for (int i = 1; i <= rowIndex; i++) {for (int j = i - 1; j > 0; j--) {dp[j] = dp[j] + dp[j - 1];}}List<Integer> res = Arrays.asList(dp);return res;}
}

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Day13

下降路径最小和

931. 下降路径最小和

class Solution {public int minFallingPathSum(int[][] matrix) {int m = matrix.length, n = matrix[0].length;int minVal;for (int i = 1; i < m; i++) {for (int j = 0; j < n; j++) {minVal = 10000;if (j > 0) minVal = Math.min(minVal, matrix[i - 1][j - 1]);if (j < n - 1) minVal = Math.min(minVal, matrix[i - 1][j + 1]);minVal = Math.min(minVal, matrix[i - 1][j]);matrix[i][j] += minVal;}}int res = 10000;for (int i = 0; i < n; i++) {res = Math.min(res, matrix[m - 1][i]);}return res;}
}

三角形最小路径和

120. 三角形最小路径和

class Solution {public int minimumTotal(List<List<Integer>> triangle) {for(int i = triangle.size() - 2; i >= 0; i--) {for(int j = 0; j < triangle.get(i).size(); j++) {triangle.get(i).set(j, Math.min(triangle.get(i + 1).get(j), triangle.get(i + 1).get(j + 1)) + triangle.get(i).get(j));}}return triangle.get(0).get(0);}
}

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Day14

矩阵区域和

1314. 矩阵区域和

class Solution {public int[][] matrixBlockSum(int[][] mat, int k) {int m = mat.length, n = mat[0].length;int[][] pre = new int[m + 1][n + 1];for (int i = 0; i < m; i++) {for (int j = 0; j < n; j++) {pre[i + 1][j + 1] = pre[i + 1][j] + pre[i][j + 1] - pre[i][j] + mat[i][j];}}int[][] ans = new int[m][n];for (int i = 0; i < m; i++) {for (int j = 0; j < n; j++) {int to = Math.max(0, i - k);int bo = Math.min(m - 1, i + k) + 1;int le = Math.max(0, j - k);int ri = Math.min(n - 1, j + k) + 1;ans[i][j] = pre[bo][ri] - pre[to][ri] - pre[bo][le] + pre[to][le];}}return ans;}
}

二维区域和检索 - 矩阵不可变

304. 二维区域和检索 - 矩阵不可变

class NumMatrix {int[][] pre;public NumMatrix(int[][] matrix) {int m = matrix.length, n = matrix[0].length;pre = new int[m + 1][n + 1];for (int i = 0; i < m; i++) {for (int j = 0; j < n; j++) {pre[i + 1][j + 1] = pre[i][j + 1] + pre[i + 1][j] - pre[i][j] + matrix[i][j];}}}public int sumRegion(int row1, int col1, int row2, int col2) {row2 += 1;col2 += 1;return pre[row2][col2] - pre[row2][col1] - pre[row1][col2] + pre[row1][col1];}
}

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Day15

不同路径

62. 不同路径

方法一：动态规划

class Solution {public int uniquePaths(int m, int n) {int[][] dp = new int[m][n];for (int i = 0; i < m; i++) {for (int j = 0; j < n; j++) {if (i == 0 || j == 0) {dp[i][j] = 1;} else {dp[i][j] = dp[i - 1][j] + dp[i][j - 1];}}}return dp[m - 1][n - 1];}
}

方法二：组合

class Solution {public int uniquePaths(int m, int n) {int C = m + n - 2;int K = (m > n ? n : m) - 1;double res = 1;for (int i = 1; i <= K; i++) {res = res * (C - i + 1) / i;}return (int)res;}
}

不同路径 II

63. 不同路径 II

class Solution {public int uniquePathsWithObstacles(int[][] obstacleGrid) {int m = obstacleGrid.length, n = obstacleGrid[0].length;int[] dp = new int[n];dp[0] = obstacleGrid[0][0] == 0 ? 1: 0;for (int i = 0; i < m; i++) {for (int j = 0; j < n; j++) {if (obstacleGrid[i][j] == 1) {dp[j] = 0;continue;}if (j >= 1 && obstacleGrid[i][j - 1] == 0) {dp[j] += dp[j - 1];}}}return dp[n - 1];}
}

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Day16

最小路径和

64. 最小路径和

class Solution {public int minPathSum(int[][] grid) {int r = grid.length, c = grid[0].length;int[] dp = new int[c];for (int i = 0; i < r; i++) {for (int j = 0; j < c; j++) {if (i == 0 && j > 0) {dp[j] = dp[j - 1] + grid[i][j];} else if (j == 0) {dp[j] += grid[i][j];} else {dp[j] = Math.min(dp[j], dp[j - 1]) + grid[i][j];}}}return dp[c - 1];}
}

最大正方形

221. 最大正方形

class Solution {public int maximalSquare(char[][] matrix) {int m = matrix.length, n = matrix[0].length;int[][] dp = new int[m + 1][n + 1];int res = 0;for (int i = 0; i < m; i++) {for (int j = 0; j < n; j++) {if (matrix[i][j] == '1') {dp[i + 1][j + 1] = 1 + Math.min(dp[i][j], Math.min(dp[i + 1][j], dp[i][j + 1]));res = Math.max(res, dp[i + 1][j + 1]);}}}return res * res;}
}

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Day17

最长回文子串

5. 最长回文子串

方法一：动态规划

class Solution {public String longestPalindrome(String s) {if (s.length() < 2) return s;int n = s.length();boolean[][] dp = new boolean[n][n];for (int i = 0; i < n; i++) dp[i][i] = true;int begin = 0, maxLen = 1;for (int L = 2; L <= n; L++) {for (int i = 0; i < n; i++) {int j = L + i - 1;if (j >= n) break;if (s.charAt(i) != s.charAt(j)) {dp[i][j] = false;} else {if (j - i + 1 < 3) {dp[i][j] = true;} else {dp[i][j] = dp[i + 1][j - 1];}}if (dp[i][j] && j - i + 1 > maxLen) {begin = i;maxLen = j - i + 1;}}}return s.substring(begin, begin + maxLen);}
}

方法二：中心扩展法

class Solution {public String longestPalindrome(String s) {//中心扩展法int start = 0, maxLen = 0;for (int i = 0; i < s.length(); i++) {int len1 = expandAroundCentor(s, i, i);int len2 = expandAroundCentor(s, i, i + 1);int len = Math.max(len1, len2);if (len > maxLen) {start = i - (len - 1) / 2;maxLen = len;}}return s.substring(start, start + maxLen);}private int expandAroundCentor(String s, int left, int right) {while (left >= 0 && right < s.length() && s.charAt(left) == s.charAt(right)) {left--;right++;}return right - left - 1;}
}

最长回文子序列

516. 最长回文子序列

class Solution {public int longestPalindromeSubseq(String s) {int n = s.length();int[][] dp = new int[n + 1][n + 1];//最长公共子序列for (int i = 0; i < n; i++) {for (int j = 0; j < n; j++) {char a = s.charAt(i);char b = s.charAt(n - j - 1);if (a == b) {dp[i + 1][j + 1] = dp[i][j] + 1;} else {dp[i + 1][j + 1] = Math.max(dp[i + 1][j], dp[i][j + 1]);}}}return dp[n][n];}
}

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Day18

最长递增子序列

300. 最长递增子序列

class Solution {public int lengthOfLIS(int[] nums) {int n = nums.length;int[] dp = new int[n];int k = 0;for (int num : nums) {if (k == 0 || num > dp[k - 1]) {dp[k++] = num;} else {int index = binarySearch(dp, k - 1, num);dp[index] = num;}}return k;}private int binarySearch(int[] nums, int k, int x) {int lo = 0, ri = k;while (lo <= ri) {int mid = lo + (ri - lo) / 2;if (x == nums[mid]) {return mid;} else if (x < nums[mid]) {ri = mid - 1;} else {lo = mid + 1;}}return lo;}
}

摆动序列

376. 摆动序列

class Solution {public int wiggleMaxLength(int[] nums) {if (nums.length < 2) return nums.length;int up = 1, down = 1;for (int i = 1; i < nums.length; i++) {if (nums[i] > nums[i - 1]) {up = down + 1;} else if (nums[i] < nums[i - 1]) {down = up + 1;}}return Math.max(up, down);}
}

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Day19

判断子序列

392. 判断子序列

class Solution {public boolean isSubsequence(String s, String t) {if (s.equals("")) return true;int k = 0;for (char c : t.toCharArray()) {if (k < s.length() && c == s.charAt(k)) {if (++k == s.length()) return true;}}return false;}
}

最长公共子序列

1143. 最长公共子序列

class Solution {public int longestCommonSubsequence(String text1, String text2) {int n1 = text1.length(), n2 = text2.length();int[][] dp = new int[n1 + 1][n2 + 2];for (int i = 0; i < n1; i++) {for (int j = 0; j < n2; j++) {if (text1.charAt(i) == text2.charAt(j)) {dp[i + 1][j + 1] = dp[i][j] + 1;} else {dp[i + 1][j + 1] = Math.max(dp[i + 1][j], dp[i][j + 1]);}}}return dp[n1][n2];}
}

编辑距离

72. 编辑距离

class Solution {public int minDistance(String word1, String word2) {int m = word1.length(), n = word2.length();int[][] cost = new int[m + 1][n + 1];for (int i = 0; i <= m; i++) cost[i][0] = i;for (int j = 0; j <= n; j++) cost[0][j] = j;for (int i = 0; i < m; i++) {for (int j = 0; j < n; j++) {if (word1.charAt(i) == word2.charAt(j)) {cost[i + 1][j + 1] = cost[i][j];} else {cost[i + 1][j + 1] = 1 + Math.min(cost[i][j], Math.min(cost[i][j + 1], cost[i + 1][j]));}}}return cost[m][n];}
}

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Day20

零钱兑换

322. 零钱兑换

class Solution {public int coinChange(int[] coins, int amount) {int[] dp = new int[amount + 1];Arrays.fill(dp, amount + 1);dp[0] = 0;for (int i = 0; i <= amount; i++) {for (int coin : coins) {if (i >= coin) dp[i] = Math.min(dp[i], dp[i - coin] + 1);}}return dp[amount] > amount ? -1 : dp[amount];}
}

零钱兑换 II

518. 零钱兑换 II

class Solution {public int change(int amount, int[] coins) {int[] dp = new int[amount + 1];dp[0] = 1;for (int coin : coins) {for (int i = 0; i <= amount; i++) {if (i + coin <= amount) {dp[i + coin] += dp[i];}}}return dp[amount];}
}

---

Day21

组合总和 Ⅳ

377. 组合总和 Ⅳ

class Solution {public int combinationSum4(int[] nums, int target) {int[] dp = new int[target + 1];dp[0] = 1;for (int i = 1; i <= target; i++) {for (int num : nums) {if (i - num >= 0) {dp[i] += dp[i - num];}}}return dp[target];}
}

整数拆分

343. 整数拆分

方法一：动态规划

class Solution {public int integerBreak(int n) {int[] dp = new int[n + 1];dp[1] = 1;for (int i = 2; i <= n; i++) {for (int j = i - 1; j >= 1; j--) {dp[i] = Math.max(dp[i], Math.max(dp[j] * (i - j), j * (i - j)));}}return dp[n];}
}

方法二：最佳因子是e，所以整数首选3，后选2

class Solution {public int integerBreak(int n) {//首选3，后选2if (n <= 3) return n - 1;if (n % 3 == 0) {return (int)(Math.pow(3, n / 3));} else if (n % 3 == 1) {return (int)(Math.pow(3, n / 3 - 1)) * 4;} else {return (int)(Math.pow(3, n / 3)) * 2; }}
}

完全平方数

279. 完全平方数

class Solution {public int numSquares(int n) {int[] dp = new int[n + 1];int e = (int)Math.sqrt(n);Arrays.fill(dp, n);dp[0] = 0;for (int i = 0; i < n; i++) {for (int j = 1; j * j <= n; j++) {if (i + j * j <= n) {dp[i + j * j] = Math.min(dp[i + j * j], dp[i] + 1);}}}return dp[n];}
}

---

21天的煎熬，终于结束啦！

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