动态规划的一些程序

1、最长公共子串

public class sf_dp_LongestCommenSubString {

public static void main(String[] args) {
// TODO Auto-generated method stub
String str1="abcdepoiopswegsdjgnegh";
String str2="bcdefpoiqwnsuiguwnenwgenwuengiewugnwebignb";
int max = 0;
int[][] dp = new int[str1.length()+1][str2.length()+1];
for(int i=1;i<dp.length;i++){
char c1 = str1.charAt(i-1);
for(int j=1;j<dp[0].length;j++){
char c2 = str2.charAt(j-1);
if(c1==c2){
dp[i][j] = dp[i-1][j-1]+1;
}else{
dp[i][j] = 0;
}
max = Math.max(max, dp[i][j]);
}
}
System.out.println(max);
}

}

2、最长递增子序列

public class sf_dp_LIS {

public static void main(String[] args) {
// TODO Auto-generated method stub
int[] nums = {3,5,6,2,5,4,19,5,6,8,12};
int len = 1;
int[] max = new int[nums.length];
int[] maxindex = new int[nums.length];
max[0] = nums[0];
maxindex[0] = 0;
for(int i=1;i<nums.length;i++){
if(nums[i] > max[len-1]){
max[len] = nums[i];
maxindex[len] = i;
len++;
}else{
int pos = binarysearch(max,0,len-1,nums[i]);
max[pos] = nums[i];
maxindex[pos] = i;
}
}
for(int i=0;i<len;i++){
System.out.print(nums[maxindex[i]]+" ");
}
System.out.println();
System.out.println(len);
}
public static int binarysearch(int[] max,int left,int right,int key){
while(left<=right){
int mid = (right - left) / 2 + left;
if(max[mid] == key){
return mid;
}
else if(max[mid]<key){
left = mid+1;
}else{
right = mid-1;
}
}
return left;
}

}

3、最大子序列和

public class sf_dp_MaxSum {

public static void main(String[] args) {
// TODO Auto-generated method stub
int[] nums = {-3,-4,-2,-6};
int len = nums.length;
int maxsum = nums[0];
int cursum = nums[0];
for(int i=1;i<len;i++){
if(cursum<0){
cursum = nums[i];
}
else{
cursum += nums[i];
}
maxsum = Math.max(cursum, maxsum);
}
System.out.println(maxsum);
}

}

4、合唱队

public class Main{
public static void main(String[] args){
Scanner in = new Scanner(System.in);
while(in.hasNext()){
int n = in.nextInt();
int[] nums = new int
;
for(int i=0;i<n;i++){
nums[i] = in.nextInt();
}
System.out.println(fun(nums,n));
}
}
public static int fun(int[] nums,int n){
int[] len1 = new int
; //从左到右
int[] len2 = new int
; //从右到左
for(int k=0;k<n;k++){ //初始化2个数组
len1[k] = 1;
len2[k] = 1;
}
for(int i=1;i<n;i++){  //求最长递增子序列的方法
for(int j=0;j<i;j++){
if(nums[i]>nums[j]&&len1[i]<len1[j]+1)
len1[i] = len1[j]+1;
}
}
for(int i=n-2;i>=0;i--){ //求最长递减子序列(其实就是反向求最长递增子序列)
for(int j=n-1;j>i;j--){
if(nums[i]>nums[j]&&len2[i]<len2[j]+1)
len2[i] = len2[j]+1;
}
}
int max = 0;
for(int k=0;k<n;k++){
if(max<len1[k]+len2[k]-1)  //还要减一，因为中间的数算了2次
max = len1[k]+len2[k]-1;
}
return n-max;
}
}

5、最长回文子串长度

public class LongestPalindromic {

public static void main(String[] args) {
// TODO Auto-generated method stub
String str = "abcdcbaaweewdd";
int len = str.length();
int max = 0;
int left = 0;
int right = 0;
boolean[][] c = new boolean[len][len];
for(int i=0;i<len;i++){
for(int j=0;j<len;j++){
if(i>=j)
c[i][j] = true;
else
c[i][j] = false;
}
}
for(int j=1;j<len;j++){
for(int i=0;i<j;i++){
if(str.charAt(i)==str.charAt(j)&&c[i+1][j-1]){
c[i][j] = true;
if(j-i+1>max){
max = j-i+1;
left = i;
right = j;
}
}
else{
c[i][j] = false;
}
}
}
System.out.println(max);
}

}