|
|
package class04;
|
|
|
|
|
|
// 测试链接 : https://leetcode.com/problems/candy/
|
|
|
public class Code05_CandyProblem {
|
|
|
|
|
|
// 这是原问题的优良解
|
|
|
// 时间复杂度O(N)，额外空间复杂度O(N)
|
|
|
public static int candy1(int[] arr) {
|
|
|
if (arr == null || arr.length == 0) {
|
|
|
return 0;
|
|
|
}
|
|
|
int N = arr.length;
|
|
|
int[] left = new int[N];
|
|
|
for (int i = 1; i < N; i++) {
|
|
|
if (arr[i - 1] < arr[i]) {
|
|
|
left[i] = left[i - 1] + 1;
|
|
|
}
|
|
|
}
|
|
|
int[] right = new int[N];
|
|
|
for (int i = N - 2; i >= 0; i--) {
|
|
|
if (arr[i] > arr[i + 1]) {
|
|
|
right[i] = right[i + 1] + 1;
|
|
|
}
|
|
|
}
|
|
|
int ans = 0;
|
|
|
for (int i = 0; i < N; i++) {
|
|
|
ans += Math.max(left[i], right[i]);
|
|
|
}
|
|
|
return ans + N;
|
|
|
}
|
|
|
|
|
|
// 这是原问题空间优化后的解
|
|
|
// 时间复杂度O(N)，额外空间复杂度O(1)
|
|
|
public static int candy2(int[] arr) {
|
|
|
if (arr == null || arr.length == 0) {
|
|
|
return 0;
|
|
|
}
|
|
|
int index = nextMinIndex2(arr, 0);
|
|
|
int res = rightCands(arr, 0, index++);
|
|
|
int lbase = 1;
|
|
|
int next = 0;
|
|
|
int rcands = 0;
|
|
|
int rbase = 0;
|
|
|
while (index != arr.length) {
|
|
|
if (arr[index] > arr[index - 1]) {
|
|
|
res += ++lbase;
|
|
|
index++;
|
|
|
} else if (arr[index] < arr[index - 1]) {
|
|
|
next = nextMinIndex2(arr, index - 1);
|
|
|
rcands = rightCands(arr, index - 1, next++);
|
|
|
rbase = next - index + 1;
|
|
|
res += rcands + (rbase > lbase ? -lbase : -rbase);
|
|
|
lbase = 1;
|
|
|
index = next;
|
|
|
} else {
|
|
|
res += 1;
|
|
|
lbase = 1;
|
|
|
index++;
|
|
|
}
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
|
|
|
public static int nextMinIndex2(int[] arr, int start) {
|
|
|
for (int i = start; i != arr.length - 1; i++) {
|
|
|
if (arr[i] <= arr[i + 1]) {
|
|
|
return i;
|
|
|
}
|
|
|
}
|
|
|
return arr.length - 1;
|
|
|
}
|
|
|
|
|
|
public static int rightCands(int[] arr, int left, int right) {
|
|
|
int n = right - left + 1;
|
|
|
return n + n * (n - 1) / 2;
|
|
|
}
|
|
|
|
|
|
// 这是进阶问题的最优解，不要提交这个
|
|
|
// 时间复杂度O(N), 额外空间复杂度O(1)
|
|
|
public static int candy3(int[] arr) {
|
|
|
if (arr == null || arr.length == 0) {
|
|
|
return 0;
|
|
|
}
|
|
|
int index = nextMinIndex3(arr, 0);
|
|
|
int[] data = rightCandsAndBase(arr, 0, index++);
|
|
|
int res = data[0];
|
|
|
int lbase = 1;
|
|
|
int same = 1;
|
|
|
int next = 0;
|
|
|
while (index != arr.length) {
|
|
|
if (arr[index] > arr[index - 1]) {
|
|
|
res += ++lbase;
|
|
|
same = 1;
|
|
|
index++;
|
|
|
} else if (arr[index] < arr[index - 1]) {
|
|
|
next = nextMinIndex3(arr, index - 1);
|
|
|
data = rightCandsAndBase(arr, index - 1, next++);
|
|
|
if (data[1] <= lbase) {
|
|
|
res += data[0] - data[1];
|
|
|
} else {
|
|
|
res += -lbase * same + data[0] - data[1] + data[1] * same;
|
|
|
}
|
|
|
index = next;
|
|
|
lbase = 1;
|
|
|
same = 1;
|
|
|
} else {
|
|
|
res += lbase;
|
|
|
same++;
|
|
|
index++;
|
|
|
}
|
|
|
}
|
|
|
return res;
|
|
|
}
|
|
|
|
|
|
public static int nextMinIndex3(int[] arr, int start) {
|
|
|
for (int i = start; i != arr.length - 1; i++) {
|
|
|
if (arr[i] < arr[i + 1]) {
|
|
|
return i;
|
|
|
}
|
|
|
}
|
|
|
return arr.length - 1;
|
|
|
}
|
|
|
|
|
|
public static int[] rightCandsAndBase(int[] arr, int left, int right) {
|
|
|
int base = 1;
|
|
|
int cands = 1;
|
|
|
for (int i = right - 1; i >= left; i--) {
|
|
|
if (arr[i] == arr[i + 1]) {
|
|
|
cands += base;
|
|
|
} else {
|
|
|
cands += ++base;
|
|
|
}
|
|
|
}
|
|
|
return new int[] { cands, base };
|
|
|
}
|
|
|
|
|
|
public static void main(String[] args) {
|
|
|
int[] test1 = { 3, 0, 5, 5, 4, 4, 0 };
|
|
|
System.out.println(candy2(test1));
|
|
|
|
|
|
int[] test2 = { 3, 0, 5, 5, 4, 4, 0 };
|
|
|
System.out.println(candy3(test2));
|
|
|
}
|
|
|
|
|
|
}
|
