From 3548d2a957ed6c8998686f5e1124cd96dca15c1d Mon Sep 17 00:00:00 2001 From: Leo <582717189@qq.com> Date: Thu, 7 Jan 2021 17:53:36 +0800 Subject: [PATCH] 18 --- src/leo/class18/CardsInLine.java | 132 ++++++++++++++++++++- src/leo/class18/RobotWalk.java | 93 ++++++++++++++- src/leo/class19/ConvertToLetterString.java | 10 ++ src/leo/class19/Knapsack.java | 10 ++ src/leo/class19/StickersToSpellWord.java | 10 ++ 5 files changed, 248 insertions(+), 7 deletions(-) create mode 100644 src/leo/class19/ConvertToLetterString.java create mode 100644 src/leo/class19/Knapsack.java create mode 100644 src/leo/class19/StickersToSpellWord.java diff --git a/src/leo/class18/CardsInLine.java b/src/leo/class18/CardsInLine.java index 4e3525b..6e27a0b 100644 --- a/src/leo/class18/CardsInLine.java +++ b/src/leo/class18/CardsInLine.java @@ -45,6 +45,35 @@ public class CardsInLine { } } + static class Recursion1 { + public static int win(int[] arr) { + if (arr.length == 0 || arr == null) { + return 0; + } + int f = f(arr, 0, arr.length - 1); + int g = g(arr, 0, arr.length - 1); + return Math.max(g, f); + } + + private static int g(int[] arr, int l, int r) { + if (l == r) { + return 0; + } + int p1 = f(arr, l + 1, r); + int p2 = f(arr, l, r - 1); + return Math.min(p1, p2); + } + + private static int f(int[] arr, int l, int r) { + if (l == r) { + return arr[l]; + } + int p1 = arr[l] + g(arr, l + 1, r); + int p2 = arr[r] + g(arr, l, r - 1); + return Math.max(p1, p2); + } + } + static class RecursionDp { public static int win(int[] arr) { if (arr.length == 0 || arr == null) { @@ -94,6 +123,57 @@ public class CardsInLine { } } + static class RecursionDp1 { + public static int win(int[] arr) { + if (arr.length == 0 || arr == null) { + return 0; + } + int n = arr.length; + int[][] fDp = new int[n][n]; + int[][] gDp = new int[n][n]; + for (int i = 0; i < n; i++) { + for (int j = 0; j < n; j++) { + fDp[i][j] = -1; + gDp[i][j] = -1; + } + } + int f = f(arr, 0, n - 1, fDp, gDp); + int g = g(arr, 0, n - 1, fDp, gDp); + return Math.max(f, g); + } + + private static int g(int[] arr, int l, int r, int[][] fDp, int[][] gDp) { + if (gDp[l][r] != -1) { + return gDp[l][r]; + } + int ans = 0; + if (l != r) { + int p1 = f(arr, l + 1, r, fDp, gDp); + int p2 = f(arr, l, r - 1, fDp, gDp); + ans = Math.min(p1, p2); + } + gDp[l][r] = ans; + return ans; + + } + + private static int f(int[] arr, int l, int r, int[][] fDp, int[][] gDp) { + if (fDp[l][r] != -1) { + return fDp[l][r]; + } + int ans = 0; + if (l == r) { + ans = arr[l]; + }else{ + int p1 = arr[l] + g(arr, l + 1, r, fDp, gDp); + int p2 = arr[r] + g(arr, l, r - 1, fDp, gDp); + ans = Math.max(p1, p2); + } + fDp[l][r] = ans; + return ans; + } + } + static class DP { public static int win(int[] arr) { if (arr.length == 0 || arr == null) { @@ -116,12 +196,56 @@ public class CardsInLine { gDp[l][r] = Math.min(fDp[l + 1][r], fDp[l][r - 1]); l++; r++; + } } + for (int i = 0; i < n; i++) { + for (int j = 0; j < n; j++) { + System.out.print(fDp[i][j]); + System.out.print(","); + } + System.out.println(); + } + System.out.println("--------"); + for (int i = 0; i < n; i++) { + for (int j = 0; j < n; j++) { + System.out.print(gDp[i][j]); + System.out.print(","); + } + System.out.println(); + } + return Math.max(fDp[0][n - 1], gDp[0][n - 1]); } } + static class DP1 { + public static int win(int[] arr) { + if (arr.length == 0 || arr == null) { + return 0; + } + int n = arr.length; + + int[][] fDp = new int[n][n]; + int[][] gDp = new int[n][n]; + for (int i = 0; i < n; i++) { + fDp[i][i] = arr[i]; + } + for (int i = 1; i < n; i++) { + int row = 0; + int col = i; + while (col < n) { + fDp[row][col] = Math.max(arr[row] + gDp[row + 1][col], arr[col] + gDp[row][col - 1]); + gDp[row][col] = Math.min(fDp[row + 1][col], fDp[row][col - 1]); + row++; + col++; + } + } + return Math.max(fDp[0][n - 1], gDp[0][n - 1]); + + } + } + public static void main(String[] args){ @@ -129,10 +253,10 @@ public class CardsInLine { int range = 60; int[] arr = randomArray(maxSize, range); - - System.out.println(Recursion.win(arr)); - System.out.println(RecursionDp.win(arr)); - System.out.println(DP.win(arr)); +// arr = new int[]{9, 8, 3, 5, 2}; + System.out.println(Recursion1.win(arr)); + System.out.println(RecursionDp1.win(arr)); + System.out.println(DP1.win(arr)); } public static int[] randomArray(int maxSize, int range) { diff --git a/src/leo/class18/RobotWalk.java b/src/leo/class18/RobotWalk.java index 522791f..b19fa64 100644 --- a/src/leo/class18/RobotWalk.java +++ b/src/leo/class18/RobotWalk.java @@ -7,6 +7,18 @@ import java.awt.event.KeyEvent; * @ClassName RobotWalk * @DATE 2021/1/5 4:27 下午 * @Description + * 一个机器人, 从start出发, + * 走到aim,在走k步的情况下, + * 一共有多少种走法? + * + * + * 假设有排成一行的N个位置，记为1~N，N 一定大于或等于 2 + * 开始时机器人在其中的M位置上(M 一定是 1~N 中的一个) + * 如果机器人来到1位置，那么下一步只能往右来到2位置； + * 如果机器人来到N位置，那么下一步只能往左来到 N-1 位置； + * 如果机器人来到中间位置，那么下一步可以往左走或者往右走； + * 规定机器人必须走 K 步，最终能来到P位置(P也是1~N中的一个)的方法有多少种 + * 给定四个参数 N、M、K、P，返回方法数。 */ public class RobotWalk { @@ -58,6 +70,29 @@ public class RobotWalk { } + + static class Recursion1 { + public static int walk(int N, int start, int aim, int k) { + if (N < 2 || start > N || start < 1 || aim > N || aim < 1 || k < 1) { + return -1; + } + return process(start, k, aim, N); + } + + private static int process(int cur, int rest, int aim, int n) { + if (rest == 0) { + return aim == cur ? 1 : 0; + } + if (cur == 1) { + return process(2, rest - 1, aim, n); + } + if (cur == n) { + return process(n - 1, rest - 1, aim, n); + } + return process(cur - 1, rest - 1, aim, n) + process(cur + 1, rest - 1, aim, n); + + } + } /** * 从顶向下的动态规划(记忆化搜索) */ @@ -94,6 +129,40 @@ public class RobotWalk { } } + + static class RecursionDp1 { + public static int walk(int n,int start,int aim,int k) { + if (n < 2 || start > n || start < 2 || aim < 2 || aim > n || k < 1) { + return -1; + } + int[][] dp = new int[n + 1][k + 1]; + for (int i = 0; i < dp.length; i++) { + for (int j = 0; j < dp[i].length; j++) { + dp[i][j] = -1; + } + } + return process(start, k, aim, n, dp); + } + + private static int process(int cur, int rest, int aim, int n, int[][] dp) { + if (dp[cur][rest] != -1) { + return dp[cur][rest]; + } + int ans = 0; + if (rest == 0) { + ans = cur == aim ? 1 : 0; + } else if (cur == 0) { + ans = process(2, rest - 1, aim, n, dp); + } else if (cur == n) { + ans = process(n - 1, rest - 1, aim, n, dp); + } else { + ans = process(cur + 1, rest - 1, aim, n, dp) + process(cur - 1, rest - 1, aim, n, dp); + } + dp[cur][rest] = ans; + return ans; + + } + } /** * 状态转移 cur为行,rest为列 * 动态规划是结果,不是原因 @@ -117,6 +186,24 @@ public class RobotWalk { } } + static class DP1 { + public static int walk(int n, int start, int aim, int k) { + if (n < 2 || start > n || start < 1 || aim > n || aim < 1 || k < 1) { + return -1; + } + int[][] dp = new int[n + 1][k + 1]; + dp[aim][0] = 1; + for (int rest = 1; rest <= k; rest++) { + dp[1][rest] = dp[2][rest - 1]; + for (int cur = 2; cur < n; cur++) { + dp[cur][rest] = dp[cur - 1][rest - 1] + dp[cur + 1][rest - 1]; + } + dp[n][rest] = dp[n - 1][rest - 1]; + } + return dp[start][k]; + } + } + public static class walkMain { public static void main(String[] args){ @@ -124,9 +211,9 @@ public class RobotWalk { int start = 2; int aim = 4; int k = 6; - System.out.println(Recursion.walk(N, start, aim, k)); - System.out.println(RecursionDp.walk(N, start, aim, k)); - System.out.println(DP.walk(N, start, aim, k)); + System.out.println(Recursion1.walk(N, start, aim, k)); + System.out.println(RecursionDp1.walk(N, start, aim, k)); + System.out.println(DP1.walk(N, start, aim, k)); } diff --git a/src/leo/class19/ConvertToLetterString.java b/src/leo/class19/ConvertToLetterString.java new file mode 100644 index 0000000..c6d1a79 --- /dev/null +++ b/src/leo/class19/ConvertToLetterString.java @@ -0,0 +1,10 @@ +package leo.class19; + +/** + * @author Leo + * @ClassName ConvertToLetterString + * @DATE 2021/1/7 5:19 下午 + * @Description + */ +public class ConvertToLetterString { +} diff --git a/src/leo/class19/Knapsack.java b/src/leo/class19/Knapsack.java new file mode 100644 index 0000000..936a275 --- /dev/null +++ b/src/leo/class19/Knapsack.java @@ -0,0 +1,10 @@ +package leo.class19; + +/** + * @author Leo + * @ClassName Knapsack + * @DATE 2021/1/6 9:43 上午 + * @Description + */ +public class Knapsack { +} diff --git a/src/leo/class19/StickersToSpellWord.java b/src/leo/class19/StickersToSpellWord.java new file mode 100644 index 0000000..775462d --- /dev/null +++ b/src/leo/class19/StickersToSpellWord.java @@ -0,0 +1,10 @@ +package leo.class19; + +/** + * @author Leo + * @ClassName StickersToSpellWord + * @DATE 2021/1/7 5:52 下午 + * @Description + */ +public class StickersToSpellWord { +}