記一次小學四年級數學問題(四個人過橋)的解決

看到一個小學四年級的數學題，說是一共4個人過橋，分別單獨過橋用時3,4,6,9分鐘，該橋每次只能過兩個人，且每次過去之後必須要一個人回去接人，問四個人全部過去的最短時間。

真實題目確實很長，我不知道小學生遇到這個問題能否耐心讀完讀懂該問題。

所以我覺得題目確實蠻有意思的，有點腦筋急轉彎的感覺。

如果靜下心來解決，用排除法也能很快得到答案。

另外用Javascript窮盡法也能得到答案，網上還有人問js怎麼寫。

能力有限，用的比較死板的解決辦法，應該有大神有更好的解決辦法。

/// <reference path="jquery-1.10.2.js" />
$(document).ready(function () {
    $('#CrossBridge').html();
    HowToCrossBridge(3, 4, 6, 9);
});

/**
//console.log("第一次過橋由" + firstGo1 + "和" + firstGo2 + "過,共計" + firstGo2 + "分鐘");
//document.writeln("第一次過橋由" + firstGo1 + "和" + firstGo2 + "過,共計" + firstGo2 + "分鐘");
    知識點:
    1.數組的copy 注意區分深拷貝和淺拷貝
        array.slice(0)以及array.concat()
    2.數組的remove和push以及sort   
**/
function HowToCrossBridge(a, b, c, d) {
    var totalTime1 = 0;
    var breakFlag = true;
    var str1 = "";
    var count = 0;
    var minTime = 0;
    var minStr = "";

    //while (breakFlag) {
    //totalTime1 = 0;
    var waitingCross = [a, b, c, d];
    var hadCrossed = new Array();
    waitingCross = waitingCross.sort(function (a, b) { return a - b });//按順序從小到大排序

    //第一次過橋(過去2人，剩餘2人)
    for (var i = 0; i < 4; i++) {
        for (var j = i + 1; j < 4; j++) {
            //count += 1;
            totalTime1 = 0;
            var hadCrossed1 = hadCrossed.concat();
            var waitingCross1 = waitingCross.concat();
            var firstGo1 = waitingCross1[i];
            var firstGo2 = waitingCross1[j];

            totalTime1 = totalTime1 + firstGo2;
            str1 = "<p>第一次過橋由" + firstGo1 + "和" + firstGo2 + "過,共計<fond style='color:red'>" + firstGo2 + "</fond>分鐘,合計<fond style='color:red'>" + totalTime1 + "</fond>分鐘</p>";

            //移除等待過橋人員
            waitingCross1.remove(firstGo1);
            waitingCross1.remove(firstGo2);
            waitingCross1.sort(function (a, b) { return a - b });
            //添加已過橋人員
            hadCrossed1 = [firstGo1, firstGo2];
            hadCrossed1.sort(function (a, b) { return a - b });

            str1 += "<p>第一次過橋後 hadCrossed=" + hadCrossed1.join() + " waitingCross=" + waitingCross1.join() + "</p>";

            //第二次返回(過去1人，剩餘3人)
            for (var k = 0; k < 2; k++) {
                //count += 1;
                var hadCrossed2 = hadCrossed1.concat();
                var waitingCross2 = waitingCross1.concat();
                var str2 = str1;
                var totalTime2 = totalTime1;
                var secondBack = hadCrossed2[k];

                totalTime2 = totalTime2 + secondBack;
                str2 += "<p>第二次返回由" + secondBack + "過,共計<fond style='color:red'>" + secondBack + "</fond>分鐘,合計<fond style='color:red'>" + totalTime2 + "</fond>分鐘</p>";

                //添加等待過橋人員
                waitingCross2.push(secondBack);
                waitingCross2.sort(function (a, b) { return a - b });
                //移除已過橋人員
                hadCrossed2.remove(secondBack);
                hadCrossed2.sort(function (a, b) { return a - b });

                str2 += "<p>第二次返回後 hadCrossed=" + hadCrossed2.join() + " waitingCross=" + waitingCross2.join() + "</p>";

                //第三次過橋(過去3人，剩餘1人)
                for (var m = 0; m < 3; m++) {
                    for (var n = m + 1; n < 3; n++) {
                        //count += 1;
                        var str3 = str2;
                        var hadCrossed3 = hadCrossed2.concat();
                        var waitingCross3 = waitingCross2.concat();
                        var totalTime3 = totalTime2;
                        var thirdGo1 = waitingCross3[m];
                        var thirdGo2 = waitingCross3[n];

                        totalTime3 = totalTime3 + thirdGo2;
                        str3 += "<p>第三次過橋由" + thirdGo1 + "和" + thirdGo2 + "過,共計<fond style='color:red'>" + thirdGo2 + "</fond>分鐘,合計<fond style='color:red'>" + totalTime3 + "</fond>分鐘</p>";

                        //移除
                        waitingCross3.remove(thirdGo1);
                        waitingCross3.remove(thirdGo2);
                        waitingCross3.sort(function (a, b) { return a - b });

                        hadCrossed3.push(thirdGo1);
                        hadCrossed3.push(thirdGo2);
                        hadCrossed3.sort(function (a, b) { return a - b });

                        str3 += "<p>第三次過橋後 hadCrossed=" + hadCrossed3.join() + " waitingCross=" + waitingCross3.join() + "</p>";

                        //第四次返回(過去2人，剩餘2人)
                        for (var l = 0; l < 2; l++) {
                            count += 1;
                            var hadCrossed4 = hadCrossed3.concat();
                            var waitingCross4 = waitingCross3.concat();
                            var str4 = str3;
                            var totalTime4 = totalTime3;
                            var fouthBack = hadCrossed4[l];

                            totalTime4 = totalTime4 + fouthBack;
                            str4 += "<p>第四次返回由" + fouthBack + "過,共計<fond style='color:red'>" + fouthBack + "</fond>分鐘,合計<fond style='color:red'>" + totalTime4 + "</fond>分鐘</p>";
                            //添加
                            waitingCross4.push(fouthBack);
                            waitingCross4.sort(function (a, b) { return a - b });
                            //移除
                            hadCrossed4.remove(fouthBack);
                            hadCrossed4.sort(function (a, b) { return a - b });

                            str4 += "<p>第四次返回後 hadCrossed=" + hadCrossed4.join() + " waitingCross=" + waitingCross4.join() + "</p>";

                            //第五次過橋（全部通過）
                            var hadCrossed5 = hadCrossed4.concat();
                            var waitingCross5 = waitingCross4.concat();
                            var totalTime5 = totalTime4;
                            var fifthGo1 = waitingCross5[0];
                            var fifthGo2 = waitingCross5[1];

                            totalTime5 = totalTime5 + fifthGo2;
                            str4 += "<p>第五次過橋由" + fifthGo1 + "和" + fifthGo2 + "過,共計<fond style='color:red'>" + fifthGo2 + "</fond>分鐘,合計<fond style='color:red'>" + totalTime5 + "</fond>分鐘</p>";
                            //添加
                            waitingCross5.remove(fifthGo1);
                            waitingCross5.remove(fifthGo2);
                            waitingCross5.sort(function (a, b) { return a - b });
                            //移除
                            hadCrossed5.push(fifthGo1);
                            hadCrossed5.push(fifthGo2);
                            hadCrossed5.sort(function (a, b) { return a - b });

                            str4 += "<p>第五次過橋後 hadCrossed=" + hadCrossed5.join() + " waitingCross=" + waitingCross5.join() + "</p>";
                            str4 += "<p><fond style='color:red'>本方案共計" + totalTime5 + "分鐘</fond></p>";

                            var str5 = "方案" + count + str4;
                            str5 += "<p>==================================================================</p>";
                            $('#CrossBridge').append(str5);

                            if (minTime > 0) {
                                if (totalTime5 < minTime) {
                                    minStr = str5;
                                }
                            }
                            else {
                                minTime = totalTime5;
                                minStr = str5;
                            }
                        }
                    }
                }
            }
        }
    }
    //}

    $('#CrossBridge').append("<p>/********************************************最短時間方案爲**************************************************************/</p>");
    $('#CrossBridge').append(minStr);
}

/*
數組中隨機取幾個元素
var items = ['1','2','4','5','6','7','8','9','10'];
console.log( getRandomArrayElements(items, 4) );
數組中隨機獲取一個元素
var item = items[Math.floor(Math.random()*items.length)];
*/
function getRandomArrayElements(arr, count) {
    var shuffled = arr.slice(0), i = arr.length, min = i - count, temp, index;
    while (i-- > min) {
        index = Math.floor((i + 1) * Math.random());
        temp = shuffled[index];
        shuffled[index] = shuffled[i];
        shuffled[i] = temp;
    }
    return shuffled.slice(min);
}

Array.prototype.indexOf = function (val) {
    for (var i = 0; i < this.length; i++) {
        if (this[i] == val)
            return i;
    }
    return -1;
}

Array.prototype.remove = function (val) {
    var index = this.indexOf(val);
    if (index > -1) {
        this.splice(index, 1);
    }
}