/// <summary>
/// 乘法巧算
/// </summary>
/// <param name="formulas">計算式作成</param>
/// <remarks>
/// 計算式構成樣例： 36 = (?) X 6 = (?) X 2 = 4 X (?)
/// 結果列：6, 18, 9
/// </remarks>
protected virtual void CleverWithMultiple(IList <CleverCalculationFormula> formulas)
{
CleverCalculationFormula cleverCalculation = new CleverCalculationFormula
{
Type = (int)TopicType.Multiple,
ConfixFormulas = new List <Formula>(),
Answer = new List <int>()
};
// 乘法算式序列（取得隨機數後執行Check回調預判其是否可用）
var list = GetMultipleSyntagmaticOrdering(formulas);
if (!list.Any())
{
return;
}
int seq = 1;
// 從乘法算式序列中隨機選擇3個算式（不重複）
while (seq <= 3)
{
var formula = CommonUtil.GetRandomNumber(list);
cleverCalculation.Answer.Add(formula.Gap == GapFilling.Left ? formula.LeftParameter : formula.RightParameter);
cleverCalculation.ConfixFormulas.Add(formula);
list.Remove(formula);
seq++;
}
formulas.Add(cleverCalculation);
}
/// <summary>
/// 減法巧算
/// </summary>
/// <param name="formulas">計算式作成</param>
protected virtual void CleverWithSubtraction(IList <CleverCalculationFormula> formulas)
{
CleverCalculationFormula cleverCalculation = new CleverCalculationFormula
{
Type = (int)TopicType.Plus,
ConfixFormulas = new List <Formula>(),
Answer = new List <int>()
};
// 獲取兩個隨機非整數
// 減數的個位是大於等於3的兩位數
var right = CommonUtil.GetRandomNumber(20, 60, condition: _ => _ % 10 != 0 && _ % 10 >= 3, getDefault: () => 23);
// 被減數需要滿足借位計算
var left = CommonUtil.GetRandomNumber(50, 99, condition: _ => _ % 10 != 0 && _ > right && _ % 10 < right % 10, getDefault: () => 51);
var answer = left - right;
cleverCalculation.ConfixFormulas.Add(new Formula(left, right, answer, SignOfOperation.Subtraction));
cleverCalculation.Answer.Add(answer);
// 數字按照位數分解
int[] lefts = new int[2] {
left / 10, left % 10
};
int[] rights = new int[2] {
right / 10, right % 10
};
// 距離整數的差異值
int leftDiff = lefts[1] >= 5 ? 10 - lefts[1] : lefts[1];
int rightDiff = rights[1] >= 5 ? 10 - rights[1] : rights[1];
// eg: 51 - 19 = 50 - 18 || 52 - 20
if (lefts[1] + rights[1] == 10)
{
cleverCalculation.ConfixFormulas.Add(new Formula(left - leftDiff, right - leftDiff, answer, SignOfOperation.Subtraction));
cleverCalculation.ConfixFormulas.Add(new Formula(left + rightDiff, right + rightDiff, answer, SignOfOperation.Subtraction));
}
// eg: 51 - 12 = 50 - 11
else if (leftDiff < rightDiff)
{
cleverCalculation.ConfixFormulas.Add(new Formula(left - leftDiff, right - leftDiff, answer, SignOfOperation.Subtraction));
}
// eg: 53 - 19 = 54 - 20
else if (leftDiff > rightDiff)
{
cleverCalculation.ConfixFormulas.Add(new Formula(left + rightDiff, right + rightDiff, answer, SignOfOperation.Subtraction));
}
formulas.Add(cleverCalculation);
}
/// <summary>
/// 加法巧算
/// </summary>
/// <param name="formula">計算式</param>
/// <returns></returns>
private string CleverWithPlus(CleverCalculationFormula formula)
{
StringBuilder html = new StringBuilder();
StringBuilder answer = new StringBuilder();
string flag = "topic";
int controlIndex = 0;
formula.ConfixFormulas.ToList().ForEach(d =>
{
if ("topic".Equals(flag))
{
html.AppendFormat(LABEL_HTML_FORMAT, d.LeftParameter);
html.AppendFormat(LABEL_HTML_FORMAT, d.Sign.ToOperationUnicode());
html.AppendFormat(LABEL_HTML_FORMAT, d.RightParameter);
}
if ("result".Equals(flag))
{
html.AppendLine(string.Format(LABEL_HTML_FORMAT, SignOfCompare.Equal.ToSignOfCompareUnicode()));
html.AppendLine(GetHtml(GapFilling.Left, d.LeftParameter, GapFilling.Left, _parentIndex, controlIndex++));
html.AppendLine(string.Format(LABEL_HTML_FORMAT, d.Sign.ToOperationUnicode()));
html.AppendLine(GetHtml(GapFilling.Right, d.RightParameter, GapFilling.Right, _parentIndex, controlIndex++));
answer.AppendFormat("{0};", d.LeftParameter);
answer.AppendFormat("{0};", d.RightParameter);
}
flag = "result";
});
html.AppendLine(string.Format(LABEL_HTML_FORMAT, SignOfCompare.Equal.ToSignOfCompareUnicode()));
html.AppendLine(GetHtml(GapFilling.Answer, formula.Answer[0], GapFilling.Answer, _parentIndex, controlIndex++));
answer.AppendFormat("{0}", formula.Answer[0]);
// 用於結果驗證
html.AppendFormat(ANSWER_HTML_FORMAT, _parentIndex.ToString().PadLeft(2, '0'), Base64.EncodeBase64(answer.ToString()));
return(html.ToString());
}
/// <summary>
/// 綜合題型巧算（拆解）
/// </summary>
/// <param name="formula">計算式</param>
/// <returns></returns>
private string CleverWithSyntheticUnknit(CleverCalculationFormula formula)
{
StringBuilder html = new StringBuilder();
StringBuilder answer = new StringBuilder();
html.AppendFormat(LABEL_HTML_FORMAT, formula.ConfixFormulas[0].LeftParameter).AppendLine();
html.AppendFormat(LABEL_HTML_FORMAT, formula.ConfixFormulas[0].Sign.ToOperationUnicode()).AppendLine();
html.AppendFormat(LABEL_HTML_FORMAT, formula.ConfixFormulas[0].RightParameter).AppendLine();
int controlIndex = 0;
html.AppendLine(string.Format(LABEL_HTML_FORMAT, SignOfCompare.Equal.ToSignOfCompareUnicode()));
html.AppendLine(GetHtml(GapFilling.Left, formula.ConfixFormulas[1].LeftParameter, GapFilling.Left, _parentIndex, controlIndex++));
html.AppendLine(string.Format(LABEL_HTML_FORMAT, formula.ConfixFormulas[1].Sign.ToOperationUnicode()));
html.AppendLine(GetHtml(GapFilling.Right, formula.ConfixFormulas[1].RightParameter, GapFilling.Right, _parentIndex, controlIndex++));
html.AppendLine(string.Format(LABEL_HTML_FORMAT, formula.ConfixFormulas[3].Sign.ToOperationUnicode()));
html.AppendLine(GetHtml(GapFilling.Left, formula.ConfixFormulas[2].LeftParameter, GapFilling.Left, _parentIndex, controlIndex++));
html.AppendLine(string.Format(LABEL_HTML_FORMAT, formula.ConfixFormulas[2].Sign.ToOperationUnicode()));
html.AppendLine(GetHtml(GapFilling.Right, formula.ConfixFormulas[2].RightParameter, GapFilling.Right, _parentIndex, controlIndex++));
html.AppendLine(string.Format(LABEL_HTML_FORMAT, SignOfCompare.Equal.ToSignOfCompareUnicode()));
html.AppendLine(GetHtml(GapFilling.Answer, formula.Answer[0], GapFilling.Answer, _parentIndex, controlIndex++));
answer.AppendFormat("{0};", formula.ConfixFormulas[1].LeftParameter);
answer.AppendFormat("{0};", formula.ConfixFormulas[1].RightParameter);
answer.AppendFormat("{0};", formula.ConfixFormulas[2].LeftParameter);
answer.AppendFormat("{0};", formula.ConfixFormulas[2].RightParameter);
answer.AppendFormat("{0}", formula.Answer[0]);
// 用於結果驗證
html.AppendFormat(ANSWER_HTML_FORMAT, _parentIndex.ToString().PadLeft(2, '0'), Base64.EncodeBase64(answer.ToString()));
return(html.ToString());
}
/// <summary>
/// 乘法巧算
/// </summary>
/// <param name="formula">計算式</param>
/// <returns></returns>
private string CleverWithMultiple(CleverCalculationFormula formula)
{
StringBuilder html = new StringBuilder();
StringBuilder answer = new StringBuilder();
html.AppendFormat(LABEL_HTML_FORMAT, formula.ConfixFormulas[0].Answer);
int controlIndex = 0;
formula.ConfixFormulas.ToList().ForEach(d =>
{
html.AppendLine(string.Format(LABEL_HTML_FORMAT, SignOfCompare.Equal.ToSignOfCompareUnicode()));
html.AppendLine(GetHtml(d.Gap, d.LeftParameter, GapFilling.Left, _parentIndex, controlIndex++));
html.AppendLine(string.Format(LABEL_HTML_FORMAT, SignOfOperation.Multiple.ToOperationUnicode()));
html.AppendLine(GetHtml(d.Gap, d.RightParameter, GapFilling.Right, _parentIndex, controlIndex++));
});
formula.Answer.ForEach(d => answer.AppendFormat("{0};", d));
answer.Length -= 1;
// 用於結果驗證
html.AppendFormat(ANSWER_HTML_FORMAT, _parentIndex.ToString().PadLeft(2, '0'), Base64.EncodeBase64(answer.ToString()));
return(html.ToString());
}
/// <summary>
/// 減法巧算
/// </summary>
/// <param name="formula">計算式</param>
/// <returns></returns>
private string CleverWithSubtraction(CleverCalculationFormula formula)
{
return(CleverWithPlus(formula));
}
/// <summary>
/// 綜合題型巧算（合併）
/// </summary>
/// <param name="formulas">計算式作成</param>
protected virtual void CleverWithSyntheticCombine(IList <CleverCalculationFormula> formulas)
{
// 當前反推判定次數（一次推算內次數累加）
int defeated = 0;
CleverCalculationFormula cleverCalculation = new CleverCalculationFormula
{
Type = (int)Synthetic.Combine,
ConfixFormulas = new List <Formula>(),
Answer = new List <int>()
};
while (1 == 1)
{
// 如果大於三次則認為此題無法作成繼續下一題
if (defeated == INVERSE_NUMBER)
{
cleverCalculation = null;
break;
}
cleverCalculation.ConfixFormulas.Clear();
cleverCalculation.Answer.Clear();
var answer = 0;
// 獲取一個10以內的共有因數
int factorShare = CommonUtil.GetRandomNumber(3, 9);
// 合併方法(加法或者减法)
SignOfOperation combine = CommonUtil.GetRandomNumber(SignOfOperation.Plus, SignOfOperation.Subtraction);
StringBuilder express = new StringBuilder();
// 加法合併
if (combine == SignOfOperation.Plus)
{
int factor1 = CommonUtil.GetRandomNumber(1, 9);
// 加法合併的兩種情況：
// 1.相加之和是整十數
int factor2 = CommonUtil.GetRandomNumber(1, 50, condition: _ => (_ % 10 == 0 || _ + factor1 <= 10) && _ != factor1, getDefault: () => 30);
// 2.相加之和是十
if (factor2 > 10)
{
factor2 -= factor1;
}
// 隨機排列計算式各參數（打亂參數位置）
SetNewGuidFactors(out List <int> factors1, factorShare, factor1);
SetNewGuidFactors(out List <int> factors2, factorShare, factor2);
// eg: 8 * 5 + 2 * 5 = (8 + 2) * 5 = 10 * 5
express.AppendFormat(CultureInfo.CurrentCulture, "{0}*{1}+{2}*{3}", factors1[0], factors1[1], factors2[0], factors2[1]);
answer = (factor1 + factor2) * factorShare;
cleverCalculation.ConfixFormulas.Add(new Formula(factor1 + factor2, factorShare, answer, SignOfOperation.Multiple));
cleverCalculation.Answer.Add(answer);
}
// 減法合併
else
{
int factor1 = CommonUtil.GetRandomNumber(11, 19);
int factor2 = CommonUtil.GetRandomNumber(5, 9, condition: _ => factor1 - _ <= 10, getDefault: () => 5);
// 隨機排列計算式各參數（打亂參數位置）
SetNewGuidFactors(out List <int> factors1, factorShare, factor1);
SetNewGuidFactors(out List <int> factors2, factorShare, factor2);
// eg: 18 * 5 - 9 * 5 = (18 - 9) * 5 = 20
express.AppendFormat(CultureInfo.CurrentCulture, "{0}*{1}-{2}*{3}", factors1[0], factors1[1], factors2[0], factors2[1]);
answer = (factor1 - factor2) * factorShare;
cleverCalculation.ConfixFormulas.Add(new Formula(factor1 - factor2, factorShare, answer, SignOfOperation.Multiple));
cleverCalculation.Answer.Add(answer);
}
// 計算式推導
var calc = new ExpressArithmeticUtil();
if (!calc.IsResult(express.ToString(), out int result))
{
defeated++;
continue;
}
if (result != answer)
{
defeated++;
continue;
}
// 加入推導出計算式集合
calc.Formulas.ToList().ForEach(f => cleverCalculation.ConfixFormulas.Add(f));
defeated = 0;
break;
}
if (cleverCalculation != null)
{
formulas.Add(cleverCalculation);
}
}
/// <summary>
/// 綜合題型巧算（拆解）
/// </summary>
/// <param name="formulas">計算式作成</param>
protected virtual void CleverWithSyntheticUnknit(IList <CleverCalculationFormula> formulas)
{
// 當前反推判定次數（一次推算內次數累加）
int defeated = 0;
CleverCalculationFormula cleverCalculation = new CleverCalculationFormula
{
Type = (int)Synthetic.Unknit,
ConfixFormulas = new List <Formula>(),
Answer = new List <int>()
};
while (1 == 1)
{
// 如果大於三次則認為此題無法作成繼續下一題
if (defeated == INVERSE_NUMBER)
{
cleverCalculation = null;
break;
}
cleverCalculation.ConfixFormulas.Clear();
cleverCalculation.Answer.Clear();
// 獲取一個待拆解的非整數(不包含各位為5的數)
int unknitValue = CommonUtil.GetRandomNumber(10, 60, condition: _ => _ % 10 != 0 && _ % 10 != 5, getDefault: () => 46);
// 獲取一個10以內的因數
int factor = CommonUtil.GetRandomNumber(3, 9, condition: _ => _ != unknitValue % 10, getDefault: () => 5);
// 數字按照位數分解
int[] unknits = new int[2] {
unknitValue / 10, unknitValue % 10
};
// 距離整數的差異值
int unknitDiff = unknits[1] >= 5 ? 10 - unknits[1] : unknits[1];
// 結果值
int answer = unknitValue * factor;
// 用於設定待拆解因數的位置
LeftOrRight leftOrRight = CommonUtil.GetRandomNumber(LeftOrRight.Left, LeftOrRight.Right);
cleverCalculation.Answer.Add(answer);
if (leftOrRight == LeftOrRight.Left)
{
cleverCalculation.ConfixFormulas.Add(new Formula(unknitValue, factor, answer, SignOfOperation.Multiple));
}
else
{
cleverCalculation.ConfixFormulas.Add(new Formula(factor, unknitValue, answer, SignOfOperation.Multiple));
}
StringBuilder express = new StringBuilder();
// 加法拆解
if (unknits[1] < 5)
{
// eg: 12 * 5 = 10 * 5 + 2 * 5
express.AppendFormat(CultureInfo.CurrentCulture, "{0}*{1}+{2}*{3}", unknitValue - unknitDiff, factor, unknits[1], factor);
}
// 減法拆解
else
{
// eg: 18 * 5 = 20 * 5 - 2 * 5
express.AppendFormat(CultureInfo.CurrentCulture, "{0}*{1}-{2}*{3}", unknitValue + unknitDiff, factor, unknitDiff, factor);
}
// 計算式推導
var calc = new ExpressArithmeticUtil();
if (!calc.IsResult(express.ToString(), out int result))
{
defeated++;
continue;
}
if (result != answer)
{
defeated++;
continue;
}
// 加入推導出計算式集合
calc.Formulas.ToList().ForEach(f => cleverCalculation.ConfixFormulas.Add(f));
defeated = 0;
break;
}
if (cleverCalculation != null)
{
formulas.Add(cleverCalculation);
}
}
/// <summary>
/// 加法巧算
/// </summary>
/// <param name="formulas">計算式作成</param>
/// <remarks>
/// 計算式構成樣例： 57 + 78 = (?) + (?) = (?)
/// 結果列：135
/// </remarks>
protected virtual void CleverWithPlus(IList <CleverCalculationFormula> formulas)
{
CleverCalculationFormula cleverCalculation = new CleverCalculationFormula
{
Type = (int)TopicType.Plus,
ConfixFormulas = new List <Formula>(),
Answer = new List <int>()
};
// 獲取兩個隨機非整數
var left = CommonUtil.GetRandomNumber(10, 99, _ => _ % 10 != 0, () => 11);
var right = CommonUtil.GetRandomNumber(10, 99, _ => _ % 10 != 0 && _ != left, () => 12);
var answer = left + right;
cleverCalculation.ConfixFormulas.Add(new Formula(left, right, answer, SignOfOperation.Plus));
cleverCalculation.Answer.Add(answer);
// 數字按照位數分解
int[] lefts = new int[2] {
left / 10, left % 10
};
int[] rights = new int[2] {
right / 10, right % 10
};
// 距離整數的差異值
int leftDiff = lefts[1] >= 5 ? 10 - lefts[1] : lefts[1];
int rightDiff = rights[1] >= 5 ? 10 - rights[1] : rights[1];
// eg: 58 + 57 => 60 + 59
// eg: 58 + 12 => 60 + 10
// eg: 55 + 25 => 60 + 20 || 50 + 30
if (lefts[1] >= 5 && (leftDiff < rightDiff || lefts[1] + rights[1] == 10))
{
// 左邊的值向上化整
cleverCalculation.ConfixFormulas.Add(new Formula(left + leftDiff, right - leftDiff, answer, SignOfOperation.Plus));
// 左右兩邊的值向上化整
if (lefts[1] == 5 && rights[1] == 5)
{
cleverCalculation.ConfixFormulas.Add(new Formula(left - leftDiff, right + leftDiff, answer, SignOfOperation.Plus));
}
}
// eg: 58 + 48 => 60 + 46 || 56 + 50
else if (lefts[1] > 5 && lefts[1] == rights[1])
{
// 左右兩邊的值向上化整
cleverCalculation.ConfixFormulas.Add(new Formula(left + leftDiff, right - leftDiff, answer, SignOfOperation.Plus));
cleverCalculation.ConfixFormulas.Add(new Formula(left - rightDiff, right + rightDiff, answer, SignOfOperation.Plus));
}
// eg: 57 + 69 => 56 + 70
// eg: 57 + 61 => 58 + 60
// eg: 55 + 21 => 56 + 20
// eg: 55 + 28 => 57 + 30
else if (lefts[1] >= 5 && leftDiff > rightDiff)
{
if (rights[1] >= 5)
{
// 右邊的值向上化整
cleverCalculation.ConfixFormulas.Add(new Formula(left - rightDiff, right + rightDiff, answer, SignOfOperation.Plus));
}
else
{
// 右邊的值向下化整
cleverCalculation.ConfixFormulas.Add(new Formula(left + rightDiff, right - rightDiff, answer, SignOfOperation.Plus));
}
}
// eg: 51 + 52 => 50 + 53
// eg: 51 + 59 => 50 + 60
// eg: 55 + 59 => 54 + 60
else if (lefts[1] <= 5 && (leftDiff < rightDiff || lefts[1] + rights[1] == 10))
{
// 左邊的值向下化整
cleverCalculation.ConfixFormulas.Add(new Formula(left - lefts[1], right + lefts[1], answer, SignOfOperation.Plus));
}
// eg: 51 + 41 => 50 + 42 || 52 + 40
else if (lefts[1] < 5 && lefts[1] == rights[1])
{
// 左右兩邊的值向下化整
cleverCalculation.ConfixFormulas.Add(new Formula(left - lefts[1], right + lefts[1], answer, SignOfOperation.Plus));
cleverCalculation.ConfixFormulas.Add(new Formula(left + lefts[1], right - rights[1], answer, SignOfOperation.Plus));
}
// eg: 54 + 61 => 55 + 60
// eg: 54 + 69 => 53 + 70
// eg: 55 + 33 => 58 + 30
else if (lefts[1] <= 5 && leftDiff > rightDiff)
{
if (rights[1] >= 5)
{
// 右邊的值向上化整
cleverCalculation.ConfixFormulas.Add(new Formula(left - rightDiff, right + rightDiff, answer, SignOfOperation.Plus));
}
else
{
// 右邊的值向下化整
cleverCalculation.ConfixFormulas.Add(new Formula(left + rights[1], right - rights[1], answer, SignOfOperation.Plus));
}
}
// eg: 55 + 25 => 50 + 30 || 60 + 20
else if (lefts[1] == 5 && rights[1] == 5)
{
// 左右兩邊的值均可向下或者向下化整
cleverCalculation.ConfixFormulas.Add(new Formula(left - 5, right + 5, answer, SignOfOperation.Plus));
cleverCalculation.ConfixFormulas.Add(new Formula(left + 5, right - 5, answer, SignOfOperation.Plus));
}
formulas.Add(cleverCalculation);
}
