假设字符串是＆＃34; anuja＆＃34;，输出应为2，因为如果我删除字符＆＃39; u＆＃39;并且＆＃39; n＆＃39;，给定的字符串变成回文。因此输出应该是最小删除次数。 更多例子：输入字符串：＆＃34; ababa＆＃34; 输出：0（无需移除） 输入字符串：＆＃34; abcdba＆＃34; 输出：1（删除＆＃39; c＆＃39;或＆＃39; d＆＃39;） 请解释算法。
答案 0 :(得分：13)
让dp[i, i] = 0 for all i (every single character is a palindrome)
。我们有：
dp[i, j]要查找a[i] == a[j]，请考虑使用随机字符串。我们有两种可能性：
第一个和最后一个字符相等：[i+1, j-1]。在这种情况下，我们可以减少问题，找到需要删除的最小字符数，以使子串a[i] != a[j]成为回文。
第一个和最后一个字符不相等：dp[i, j] = dp[i + 1, j - 1] # if a[i] == a[j]
min(dp[i + 1, j], dp[i, j - 1]) + 1 # otherwise
。在这种情况下，我们需要删除其中一个。我们将删除导致我们找到更好解决方案的内容。
所以我们有：
anuja以 | 1 2 3 4 5
-------------
1 | 0 1 2 2 2
2 | 0 1 2 3
3 | 0 1 2
4 | 0 1
5 | 0
为例。我们得到：
dp[1, n]请注意，矩阵从主对角线开始计算并按顺序继续向上，对角线平行于主对角线。答案是using System;
using System.Collections.Generic;
using System.Drawing;
using System.IO;
using System.Linq;
using System.Runtime.InteropServices;
using System.Text;
using System.Threading.Tasks;
namespace WindowsFormsApplication6 {
public class Helper {
private const uint ILD_TRANSPARENT = 0x00000001;
private const uint SHGFI_SYSICONINDEX = 0x000004000;
private const uint SHGFI_ICON = 0x000000100;
public static readonly int MaxEntitiesCount = 80;
public static void GetDirectories(string path, List<Image> col, IconSizeType sizeType, Size itemSize) {
DirectoryInfo dirInfo = new DirectoryInfo(path);
DirectoryInfo[] dirs = dirInfo.GetDirectories("*", SearchOption.TopDirectoryOnly);
for (int i = 0; i < dirs.Length && i < MaxEntitiesCount; i++) {
DirectoryInfo subDirInfo = dirs[i];
if (!CheckAccess(subDirInfo) || !MatchFilter(subDirInfo.Attributes)) {
continue;
}
col.Add(GetFileImage(subDirInfo.FullName, sizeType, itemSize));
}
}
public static bool CheckAccess(DirectoryInfo info) {
bool isOk = false;
try {
var secInfo = info.GetAccessControl();
isOk = true;
}
catch {
}
return isOk;
}
public static bool MatchFilter(FileAttributes attributes) {
return (attributes & (FileAttributes.Hidden | FileAttributes.System)) == 0;
}
public static Image GetFileImage(string path, IconSizeType sizeType, Size itemSize) {
return IconToBitmap(GetFileIcon(path, sizeType, itemSize), sizeType, itemSize);
}
public static Image IconToBitmap(Icon ico, IconSizeType sizeType, Size itemSize) {
if (ico == null) {
return new Bitmap(itemSize.Width, itemSize.Height);
}
return ico.ToBitmap();
}
public static Icon GetFileIcon(string path, IconSizeType sizeType, Size itemSize) {
SHFILEINFO shinfo = new SHFILEINFO();
IntPtr retVal = SHGetFileInfo(path, 0, ref shinfo, (uint)Marshal.SizeOf(shinfo), (int)(SHGFI_SYSICONINDEX | SHGFI_ICON));
int iconIndex = shinfo.iIcon;
IImageList iImageList = (IImageList)GetSystemImageListHandle(sizeType);
IntPtr hIcon = IntPtr.Zero;
if (iImageList != null) {
iImageList.GetIcon(iconIndex, (int)ILD_TRANSPARENT, ref hIcon);
}
Icon icon = null;
if (hIcon != IntPtr.Zero) {
icon = Icon.FromHandle(hIcon).Clone() as Icon;
DestroyIcon(shinfo.hIcon);
}
return icon;
}
private static IImageList GetSystemImageListHandle(IconSizeType sizeType) {
IImageList iImageList = null;
Guid imageListGuid = new Guid("46EB5926-582E-4017-9FDF-E8998DAA0950");
int ret = SHGetImageList((int)sizeType, ref imageListGuid, ref iImageList);
return iImageList;
}
[DllImport("shell32.dll", CharSet = CharSet.Auto)]
private static extern IntPtr SHGetFileInfo(string pszPath, uint dwFileAttributes, ref SHFILEINFO psfi, uint cbFileInfo, uint uFlags);
[DllImport("shell32.dll", EntryPoint = "#727")]
private static extern int SHGetImageList(int iImageList, ref Guid riid, ref IImageList ppv);
[DllImport("user32.dll", SetLastError = true)]
private static extern bool DestroyIcon(IntPtr hIcon);
public enum IconSizeType {
Medium = 0x0,
Small = 0x1,
Large = 0x2,
ExtraLarge = 0x4
}
[StructLayout(LayoutKind.Sequential, CharSet = CharSet.Auto)]
private struct SHFILEINFO {
public IntPtr hIcon;
public int iIcon;
public uint dwAttributes;
[MarshalAs(UnmanagedType.ByValTStr, SizeConst = 260)]
public string szDisplayName;
[MarshalAs(UnmanagedType.ByValTStr, SizeConst = 80)]
public string szTypeName;
}
[ComImport,
Guid("46EB5926-582E-4017-9FDF-E8998DAA0950"),
InterfaceType(ComInterfaceType.InterfaceIsIUnknown)]
private interface IImageList {
[PreserveSig]
int Add(IntPtr hbmImage, IntPtr hbmMask, ref int pi);
[PreserveSig]
int ReplaceIcon(int i, IntPtr hicon, ref int pi);
[PreserveSig]
int SetOverlayImage(int iImage, int iOverlay);
[PreserveSig]
int Replace(int i, IntPtr hbmImage, IntPtr hbmMask);
[PreserveSig]
int AddMasked(IntPtr hbmImage, int crMask, ref int pi);
[PreserveSig]
int Draw(ref IMAGELISTDRAWPARAMS pimldp);
[PreserveSig]
int Remove(int i);
[PreserveSig]
int GetIcon(int i, int flags, ref IntPtr picon);
[PreserveSig]
int GetImageInfo(int i, ref IMAGEINFO pImageInfo);
[PreserveSig]
int Copy(int iDst, IImageList punkSrc, int iSrc, int uFlags);
[PreserveSig]
int Merge(int i1, IImageList punk2, int i2, int dx, int dy, ref Guid riid, ref IntPtr ppv);
[PreserveSig]
int Clone(ref Guid riid, ref IntPtr ppv);
[PreserveSig]
int GetImageRect(int i, ref RECT prc);
[PreserveSig]
int GetIconSize(ref int cx, ref int cy);
[PreserveSig]
int SetIconSize(int cx, int cy);
[PreserveSig]
int GetImageCount(ref int pi);
[PreserveSig]
int SetImageCount(int uNewCount);
[PreserveSig]
int SetBkColor(int clrBk, ref int pclr);
[PreserveSig]
int GetBkColor(ref int pclr);
[PreserveSig]
int BeginDrag(int iTrack, int dxHotspot, int dyHotspot);
[PreserveSig]
int EndDrag();
[PreserveSig]
int DragEnter(IntPtr hwndLock, int x, int y);
[PreserveSig]
int DragLeave(IntPtr hwndLock);
[PreserveSig]
int DragMove(int x, int y);
[PreserveSig]
int SetDragCursorImage(ref IImageList punk, int iDrag, int dxHotspot, int dyHotspot);
[PreserveSig]
int DragShowNolock(int fShow);
[PreserveSig]
int GetDragImage(ref POINT ppt, ref POINT pptHotspot, ref Guid riid, ref IntPtr ppv);
[PreserveSig]
int GetItemFlags(int i, ref int dwFlags);
[PreserveSig]
int GetOverlayImage(int iOverlay, ref int piIndex);
}
;
[StructLayout(LayoutKind.Sequential)]
private struct IMAGELISTDRAWPARAMS {
public int cbSize;
public IntPtr himl;
public int i;
public IntPtr hdcDst;
public int x;
public int y;
public int cx;
public int cy;
public int xBitmap;
public int yBitmap;
public int rgbBk;
public int rgbFg;
public int fStyle;
public int dwRop;
public int fState;
public int Frame;
public int crEffect;
}
[StructLayout(LayoutKind.Sequential)]
private struct IMAGEINFO {
public IntPtr hbmImage;
public IntPtr hbmMask;
public int Unused1;
public int Unused2;
public RECT rcImage;
}
[StructLayout(LayoutKind.Sequential)]
public struct RECT {
public int Left, Top, Right, Bottom;
public RECT(int l, int t, int r, int b) {
Left = l;
Top = t;
Right = r;
Bottom = b;
}
public RECT(Rectangle r) {
Left = r.Left;
Top = r.Top;
Right = r.Right;
Bottom = r.Bottom;
}
public Rectangle ToRectangle() {
return Rectangle.FromLTRB(Left, Top, Right, Bottom);
}
public void Inflate(int width, int height) {
Left -= width;
Top -= height;
Right += width;
Bottom += height;
}
public override string ToString() {
return string.Format("x:{0},y:{1},width:{2},height:{3}", Left, Top, Right - Left, Bottom - Top);
}
}
[System.Runtime.InteropServices.StructLayout(System.Runtime.InteropServices.LayoutKind.Sequential)]
public struct POINT {
public int X, Y;
public POINT(int x, int y) {
this.X = x;
this.Y = y;
}
public POINT(Point pt) {
this.X = pt.X;
this.Y = pt.Y;
}
public Point ToPoint() {
return new Point(X, Y);
}
}
}
}
。
这类似于Levenshtein distance，但它只考虑删除。
答案 1 :(得分：1)
您可以测量从字符串到其反向的编辑距离（levenshtein距离）（忽略替换）。期望的值将是该值的一半。
此问题与UVA 10739类似。这是一个example implementation。
示例实现（适合您的情况）可以是：
string P, Q;
getline(cin, P);
Q = string(P.rbegin(), P.rend());
int p = P.size(), q = Q.size();
for(int i=0; i<=p; i++) { T[i][0] = i; }
for(int i=0; i<=q; i++) { T[0][i] = i; }
for(int i=1; i<=p; i++) {
for(int j=1; j<=q; j++) {
if (P[i-1] == Q[j-1])
T[i][j] = T[i-1][j-1];
else
T[i][j] = min(T[i-1][j], T[i][j-1]) + 1;
}
}
cout << "Case " << tt << ": " << T[p][q]/2 << endl;