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LeetCode300.java
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97 lines (92 loc) · 2.52 KB
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package problems;
import java.util.Arrays;
/**
* dp[i]为考虑前i个元素，以第i个数字结尾的最长上升子序列的长度。
* 在计算dp[i]之前，我们已经计算出dp[0...i-1]的值，则状态转移方程为：
* dp[i] = max(dp[j])+1, 其中 0<=j<i 且 num[j] < num[i]
* 最后数组的最大上升子序列即所有dp[i]中的最大值
* LIS_length = max(dp[i]),其中0<=i<n
*/
public class LeetCode300 {
public int lengthOfLIS(int[] nums) {
if(nums.length == 0){
return 0;
}
int[] dp = new int[nums.length];
dp[0] = 1;
int maxAns = 1;
for (int i = 1; i < nums.length; i++) {
dp[i] = 1;
for (int j = 0; j < i; j++) {
if(nums[i] > nums[j]){
dp[i] = Math.max(dp[i], dp[j] + 1);
}
}
maxAns = Math.max(dp[i], maxAns);
}
return maxAns;
}
}
/**
* 最长上升子序列
*/
class LeetCode300_1 {
public int lengthOfLIS(int[] nums) {
int n = nums.length;
int[] dp = new int[n];
dp[0] = 1;
int maxans = 1;
for (int i = 1; i < n; i++) {
dp[i] = 1;
for (int j = 0; j < i; j++) {
if(nums[i] > nums[j]) {
dp[i] = Math.max(dp[j] + 1, dp[i]);
}
}
maxans = Math.max(maxans, dp[i]);
}
return maxans;
}
}
class LeetCode300_2 {
public int lengthOfLIS(int[] nums) {
if(nums.length == 0) {
return 0;
}
int[] dp = new int[nums.length];
int res = 1;
Arrays.fill(dp, 1);
for (int i = 1; i < nums.length; i++) {
for (int j = 0; j < i; j++) {
if(nums[i] > nums[j]) {
dp[i] = Math.max(dp[j] + 1, dp[i]);
}
}
res = Math.max(res, dp[i]);
}
return res;
}
public int lengthOfLIS1(int[] nums) {
if(nums.length == 0){
return 0;
}
int[] tails = new int[nums.length];
int res = 0;
for (int num : nums) {
int i = 0, j = res;
while (i < j) {
int mid = (i + j) / 2;
if(tails[mid] < num) {
i = mid + 1;
} else {
j = mid;
}
}
tails[i] = num;
if(res == j){
res ++;
}
}
return res;
}
}