java - 要打印的数组的非相邻元素的最大总和
问题描述
有一个整数数组{1,2,3,-1,-3,2,5},我的工作是打印导致子数组最大和的元素,得到的和是通过添加不相邻的元素在数组中。
我使用动态编程编写了代码以给出最大总和。但无法打印元素。
public static int maxSum(int arr[])
{
int excl = 0;
int incl = arr[0];
for (int i = 1; i < arr.length; i++)
{
int temp = incl;
incl = Math.max(Math.max(excl + arr[i], arr[i]), incl);
excl = temp;
}
return incl;
}
例子 :
{1,2,3,-1,-3,2,5}
应该返回{1,3,5}
最大总和为9{4,5,4,3}
有两个{4,4}
和{5,3}
,在对我们得到的两个数组进行排序时{4,4}
,{3,5}
由于 3<4 我们打印{3,5}
.(包含第一个最小元素的数组)。
解决方案
您可以保留一个数组来跟踪index of elements
用于add to the current element
.
我已经使用父数组修改了您的代码以跟踪它。另外,我更改了一些变量名称(根据我的理解)。
public static void maxSum(int[] arr){
int n = arr.length;
int[] parent = new int[n];
parent[0] = -1;
int lastSum = 0; // last sum encountered
int lastPos = -1; // position of that last sum
int currSum = arr[0]; // current sum
int currPos = 0; // position of the current sum
for (int i = 1; i < n; i++) {
parent[i] = lastPos; // save the last sum's position for this element
// below this it is mostly similar to what you have done;
// just keeping track of position too.
int probableSum = Integer.max(arr[i] + lastSum, arr[i]);
int tSum = currSum;
int tPos = currPos;
if(probableSum > currSum){
currSum = probableSum;
currPos = i;
}
lastSum = tSum;
lastPos = tPos;
}
System.out.println(currSum); // print sum
System.out.println(Arrays.toString(parent)); // print parent array; for debugging purposes.
// logic to print the elements
int p = parent[n - 1];
System.out.print(arr[n - 1] + " ");
while (p != -1) {
System.out.print(arr[p] + " ");
p = parent[p];
}
}
我相信代码可以清理很多,但这是以后的练习:)
输出:
{1,2,3,-1,-3,2,5} => 5 3 1
{4,5,4,3} => 3 5
更新。添加了一些代码解释
lastSum
&的值currSum
在循环执行期间发生变化。最好通过观察它们的值在循环内如何变化来理解它们。
i
在循环的第 th 次迭代开始期间,lastSum
保存可以添加到第i
th 个元素的最大值;i-2
所以基本上可以通过迭代到第一个元素
来获得最大值。保存通过迭代到第 th 个元素currSum
可以获得的最大值。i-1
在循环结束时lastSum
添加到第i
th 个元素并指定为currSum
。如果lastSum
小于 0,则将i
元素本身指定为currSum
。旧值currSum
现在称为lastSum
lastPos
&currPos
保存各自总和值的最新索引。
在下面显示的每次迭代的所有状态中,最右边的和表示currSum
迭代开始时。左侧的值currSum
表示lastSum
。它们的索引位置分别记录在currPos
&lastPos
中。
par[]
保存使用的最后一个索引的值lastSum
。该数组稍后用于构造形成最大非相邻和的实际元素集。
initially
idx = -1, 0, 1, 2, 3, 4, 5, 6
arr = 0, 1, 2, 3, -1, -3, 2, 5
sum = 0 1
par = -1
i=1 iteration state
idx = -1, 0, 1, 2, 3, 4, 5, 6
arr = 0, 1, 2, 3, -1, -3, 2, 5
sum = 0 1, ?
par = -1, !
// before update
currSum = 1, currPos = 0
lastSum = 0, lastPos = -1
// updating
par[1] = lastPos = -1
probableSum = max(2 + 0, 2) = 2 // max(arr[i] + lastSum, arr[i])
? = max(1, 2) = 2 // max(currSum, probableSum)
! = i = 1
// after update
lastSum = currSum = 1
lastPos = currPos = 0
currSum = ? = 2
currPos = ! = 1
i=2 iteration state
idx = -1, 0, 1, 2, 3, 4, 5, 6
arr = 0, 1, 2, 3, -1, -3, 2, 5
sum = 0 1, 2 ?
par = -1, -1 !
// before update
currSum = 2, currPos = 1
lastSum = 1, lastPos = 0
// updating
par[2] = lastPos = 0
probableSum = max(3 + 1, 3) = 4 // max(arr[i] + lastSum, arr[i])
? = max(2, 4) = 4 // max(currSum, probableSum)
! = i = 2
// after update
lastSum = currSum = 2
lastPos = currPos = 1
currSum = ? = 4
currPos = ! = 2
i = 3 iteration state
idx = -1, 0, 1, 2, 3, 4, 5, 6
arr = 0, 1, 2, 3, -1, -3, 2, 5
sum = 0 1, 2 4 ?
par = -1, -1 0 !
// before update
currSum = 4, currPos = 2
lastSum = 2, lastPos = 1
//updating
par[3] = lastpos = 1
probableSum = max(-1 + 2, -1) = 1 // max(arr[i] + lastSum, arr[i])
? = max(4, 1) = 4 // max(currSum, probableSum) ; no update in ?'s value
! = currPos = 2 // as ?'s value didn't update
// after update
lastSum = currSum = 4
lastPos = currPos = 2
currSum = ? = 4
currPos = ! = 2
i = 4 iteration
idx = -1, 0, 1, 2, 3, 4, 5, 6
arr = 0, 1, 2, 3, -1, -3, 2, 5
sum = 0 1, 2 4 4 ?
par = -1, -1 0 1 !
// before update
currSum = 4, currPos = 2
lastSum = 4, lastPos = 2
// updating
par[4] = lastPos = 2
probableSum = max(-3 + 4, -3) = 1 // max(arr[i] + lastSum, arr[i])
? = max(4, 1) = 4 // max(currSum, probableSum) ; no update in ?'s value
! = currPos = 2 // as ?'s value didn't update
// after update
lastSum = currSum = 4
lastPos = currPos = 2
currPos = ? = 4
currPos = ! = 2
i = 5 iteration
idx = -1, 0, 1, 2, 3, 4, 5, 6
arr = 0, 1, 2, 3, -1, -3, 2, 5
sum = 0 1, 2 4 4 4 ?
par = -1, -1 0 1 2 !
// before update
currSum = 4, currPos = 2
lastSum = 4, lastPos = 2
// updating
par[5] = lastPos = 2
probableSum = max(2 + 4, 2) = 6 // max(arr[i] + lastSum, arr[i])
? = max(4, 6) = 6 // max(currSum, probableSum)
! = i = 5
// after update
lastSum = currSum = 4
lastPos = currPos = 2
currPos = ? = 6
currPos = ! = 5
i = 6 iteration state
idx = -1, 0, 1, 2, 3, 4, 5, 6
arr = 0, 1, 2, 3, -1, -3, 2, 5
sum = 0 1, 2 4 4 4 6 ?
par = -1, -1 0 1 2 2 !
// before update
currSum = 6, currPos = 5
lastSum = 4, lastPos = 2
// updating
par[6] = lastPos = 2
probableSum = max(5 + 4, 5) = 9 // max(arr[i] + lastSum, arr[i])
? = max(6, 9) = 9 // max(currSum, probableSum)
! = i = 6
// after update
lastSum = currSum = 6
lastPos = currPos = 5
currPos = ? = 9
currPos = ! = 6
after all iteration state
idx = -1, 0, 1, 2, 3, 4, 5, 6
arr = 0, 1, 2, 3, -1, -3, 2, 5
sum = 0 1, 2 4 4 4 6 9
par = -1, -1 0 1 2 2 2
通过使用 par[] 并循环直到 par[p] != -1 我们可以获得元素的索引,它实际上形成了一组实际需要的元素。直接查看代码。
例如
p = last = 6
arr[p] = arr[6] = 5 // element
p = par[p] = par[6] = 2
arr[p] = arr[2] = 3 // element
p = par[p] = par[2] = 0
arr[p] = arr[0] = 1 // element
p = par[p] = par[0] = -1 // stop
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