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LC198_house_robber.java
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52 lines (43 loc) · 1.46 KB
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package Week06;
public class LC198_house_robber {
/*
思路：
1. 状态数组定义： a[i]: 0..i 能偷到max value : a[n-1]
2. DP方程 : a[i] = a[i-1] + nums[i], 这里有问题，不知道i-1是否偷。没办法递推
3. 升维：a[i][0,1]: 0表示 i不偷； 1表示 i偷
4. DP方程：
a[i][0] = Max(a[i-1][0], a[i-1][1])
a[i][1] = Max(a[i-1][0], 0) + nums[i] => a[i-1][0] + nums[i]
* */
public int rob(int[] nums) {
if (nums == null || nums.length==0) return 0;
int n = nums.length;
int[][] dp = new int[n][2];
dp[0][0] = 0; //不偷
dp[0][1] = nums[0]; //偷
for (int i=2;i<n; i++){
dp[i][0] = Math.max(dp[i-1][0], dp[i-1][1]);
dp[i][1] = dp[i-1][0] + nums[i];
}
return Math.max(dp[n-1][0], dp[n-1][1]);
}
/*
重新定义状态数组，降维
状态数组: a[i]: 0..i天，且nums[i]必偷的最大值， 能偷到max value : max(a)
DP方程 : a[i] = Max(a[i-1], a[i-2] + nums[i]);
* */
public int rob_2(int[] nums) {
if (nums == null || nums.length==0) return 0;
if (nums.length==1) return nums[0];
int n = nums.length;
int[] dp = new int[n];
dp[0] = nums[0];
dp[1] = Math.max(nums[0],nums[1]);
int res = Math.max(dp[0], dp[1]);
for (int i=2;i<n; i++){
dp[i] = Math.max(dp[i-1], dp[i-2] + nums[i]);
res = Math.max(res, dp[i]);
}
return res;
}
}