一个机器人位于一个 m x n 网格的左上角 (起始点在下图中标记为“Start” )。机器人每次只能向下或者向右移动一步。机器人试图达到网格的右下角(在下图中标记为“Finish”)。问总共有多少条不同的路径?
/**
* Copyright (C), 2018-2020
* FileName: uniquePaths62
* Author: xjl
* Date: 2020/7/7 8:34
* Description: 62. 不同路径
*/
package DP;
import org.junit.Test;
public class uniquePaths62 {
public int uniquePaths(int m, int n) {
//d[i][j]: start->(i,j) 一共有多少个uniqueunique paths
//d[i][j]=dp[i-1][j]+d[i][j-1]
//d[0][0]=1
int[][] dp = new int[m][n];
dp[0][0] = 1;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i > 0) {
dp[i][j] += dp[i - 1][j];
}
if (j > 0) {
dp[i][j] += dp[i][j - 1];
}
}
}
return dp[m - 1][n - 1];
}
@Test
public void test() {
int i = uniquePaths(3, 4);
System.out.println(i);
}
}
一个机器人位于一个 m x n 网格的左上角 (起始点在下图中标记为“Start” )。机器人每次只能向下或者向右移动一步。机器人试图达到网格的右下角(在下图中标记为“Finish”)。现在考虑网格中有障碍物。那么从左上角到右下角将会有多少条不同的路径?
/**
* Copyright (C), 2018-2020
* FileName: uniquePathsWithObstacles63
* Author: xjl
* Date: 2020/7/7 9:05
* Description: 63. 不同路径 II
*/
package DP;
public class uniquePathsWithObstacles63 {
public int uniquePathsWithObstacles(int[][] obstacleGrid) {
int m = obstacleGrid.length;
int n = obstacleGrid[0].length;
int[][] dp = new int[m][n];
dp[0][0] = 1;
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (obstacleGrid[i][j] == 1) {
dp[i][j] = 0;
} else {
if (j > 0) {
dp[i][j] += dp[i][j - 1];
}
if (i > 0) {
dp[i][j] += dp[i - 1][j];
}
}
}
}
return dp[m - 1][n - 1];
}
}
/**
* Copyright (C), 2018-2020
* FileName: rob198
* Author: xjl
* Date: 2020/7/7 9:19
* Description: 198. 打家劫舍
*/
package DP;
import org.junit.Test;
public class rob198 {
public int subRob(int[] nums) {
if (nums == null || nums.length == 0) {
return 0;
}
int frist = 0;
int second = 0;
int maxMoney = 0;
for (int index = 0; index < nums.length; index++) {
maxMoney = Math.max(nums[index] + frist, second);
frist = second;
second = maxMoney;
}
return maxMoney;
}
public int rob(int[] nums) {
//输入数据的校验
if (nums.length < 1) {
return 0;
}
if (nums.length == 1) {
return nums[0];
}
if (nums.length == 2) {
return Math.max(nums[0], nums[1]);
}
//
int[] dp = new int[nums.length];
dp[0] = nums[0];
dp[1] = nums[1];
int max = Math.max(dp[0], dp[1]);
for (int i = 2; i < nums.length; i++) {
dp[i] = maxVal(dp, i - 1) + nums[i];
max = max < dp[i] ? dp[i] : max;
}
return max;
}
private int maxVal(int[] dp, int i) {
int max = -1;
for (int j = 0; j < i; j++) {
max = max < dp[j] ? dp[j] : max;
}
return max;
}
@Test
public void test(){
int[] array={1,2,3,1};
int i = subRob(array);
System.out.println(i);
}
}
/**
* Copyright (C), 2018-2020
* FileName: rob213
* Author: xjl
* Date: 2020/7/7 9:39
* Description: 213. 打家劫舍 II
*/
package DP;
import org.junit.Test;
public class rob213 {
public int rob(int[] nums) {
if (nums == null || nums.length == 0) {
return 0;
}
//判断一个特殊的情况
if (nums.length == 1) {
return nums[0];
}
return Math.max(subRob(nums, 0, nums.length - 1), subRob(nums, 1, nums.length));
}
public int subRob(int[] nums, int start, int end) {
if (nums == null || nums.length == 0) {
return 0;
}
int frist = 0;
int second = 0;
int maxMoney = 0;
for (int index = start; index < end; index++) {
maxMoney = Math.max(nums[index] + frist, second);
frist = second;
second = maxMoney;
}
return maxMoney;
}
@Test
public void test(){
int[] array={1,2,3,1};
int rob = rob(array);
System.out.println(rob);
}
}
/**
* Copyright (C), 2018-2020
* FileName: rob337
* Author: xjl
* Date: 2020/7/7 9:56
* Description: 337. 打家劫舍 III
*/
package DP;
public class rob337 {
public class TreeNode {
int val;
TreeNode left;
TreeNode right;
TreeNode(int x) {
val = x;
}
}
public int rob(TreeNode root) {
if (root == null) {
return 0;
}
int[] res = postRoot(root);
return Math.max(res[0],res[1]);
}
private int[] postRoot(TreeNode root) {
if (root == null) return new int[]{0, 0};
int[] l = postRoot(root.left);
int[] r = postRoot(root.right);
int[] res = new int[2];
res[0] = Math.max(l[0], l[1]) + Math.max(r[0], r[1]);
res[1] = l[0] + r[0] + root.val;
return res;
}
}