面試手撕代碼(五)-動態規劃
1.揹包問題
public class Main {
public static int backPack(int[] w, int[] v, int m){
int[][] dp = new int[v.length+1][m+1];
int[] items = new int[v.length+1];
for (int i = 1; i <= v.length; i++) {
for (int j = 1; j <= m; j++) {
if(w[i-1]>j){
dp[i][j] = dp[i-1][j];
}else{
dp[i][j] = Math.max(dp[i-1][j],dp[i-1][j-w[i-1]]+v[i-1]);
}
}
}
return dp[v.length][m];
}
public static void main(String[] args) throws Exception{
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
int n = Integer.parseInt(br.readLine());
int m = Integer.parseInt(br.readLine());
String[] strings = br.readLine().split(" ");
int[] w = new int[n];
int[] v = new int[n];
for (int i = 0; i < w.length; i++) {
w[i] = Integer.parseInt(strings[i]);
}
strings = br.readLine().split(" ");
for (int i = 0; i < v.length; i++) {
v[i] = Integer.parseInt(strings[i]);
}
System.out.println(backPack(w,v,m));
}
}
2.機器人行走
/**
*一個機器人從左上角出發,每次可以向下或向右走一步,求幾種方式走到右下角
* @author
*
*/
public class Mian {
public static int uniquePaths(int m,int n){
int[][] f=new int[m][n];
for (int i = 0; i < m; i++) {//行
for (int j = 0; j < n; j++) {//列
if (i==0||j==0) {
f[i][j]=1;
}else {
f[i][j]=f[i-1][j]+f[i][j-1];
}
}
}
return f[m-1][n-1];
}
}
3.青蛙跳
/**
*在n塊石頭分別在x軸的0,1........n-1位置,一直青蛙從0跳到n-1,如果青蛙在第i塊石頭上,他最多可以右跳距離a,問青蛙是否跳到石頭n-1
* @author
*
*/
public class Main{
public static boolean conJump(int[] A){
int n=A.length;
boolean[] f=new boolean[n];
f[0]=true;
for (int j = 0; j < n; j++) {
f[j]=false;
for (int i = 0; i < j; i++) {
if (f[i]&&i+A[i]>=i) {
f[j]=true;
break;
}
}
}
return f[n-1];
}
}
4.最小數
/**
* 如果有三種硬幣2 5 7,用這三種硬幣湊出最少的硬幣數,使得總數爲27。
* @author
*
*/
public class Main {
public static void main(String[] args) {
int[] A={500,1};
int M=1000;
System.out.println(coinChange(A,M));
}
// {2 5 7} 27
public static int coinChange(int[] A,int M){
int[] f=new int[M+1];
int n=A.length;
f[0]=0;
//f[1],f[2],......,f[27]
for (int i = 1; i <=M; i++) {
f[i]=Integer.MAX_VALUE;
//f[i]=min{f[i-A[0]]+1,.....,f[i-A[n-1]]+1}
for (int j = 0; j < n; j++) {
//避免i-A[j]是負數,並且避免f[i-A[j]]是無窮大
if (i>=A[j]&&f[i-A[j]]!=Integer.MAX_VALUE) {
f[i]=Math.min(f[i-A[j]]+1, f[i]);
}
}
}
if (f[M]==Integer.MAX_VALUE) {
f[M]=-1;
}
return f[M];
}
}