{"trustable":true,"prependHtml":"\u003cstyle\u003e.statText pre { font-size: 12px; }\ntable {display:block !important; width:100%; }\ntable tbody {display:block !important; width:100%; }\ntable tbody tr { width:100% !important;display: block;}\ntable tbody tr td.statText { margin-left: 5px; display: inline-block; width: fit-content; }\ntable tbody tr td.statText br { display: block; content: \" \";line-height: 12px;margin: 12px 0;}\ntable tbody tr td.statText table table pre {\n white-space: pre-wrap;\n text-overflow: ellipsis;\n word-break: break-all;\n}\ntd { padding: 0 !important; border: none !important; }\npre { line-height: normal; margin: 0; }\n\u003c/style\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\n \n \t\t\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u003ch3\u003eProblem Statement\u003c/h3\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003eFox Ciel is in college.\nShe still needs to take n courses before she can graduate.\nThose courses are numbered 0 through n-1.\n\u003cbr\u003eThere may be some dependencies between the courses.\nFor each valid i, Ciel must take course \u003cb\u003ea\u003c/b\u003e[i] before taking course \u003cb\u003eb\u003c/b\u003e[i].\nThe courses are numbered in such a way that for each valid i we have \u003cb\u003ea\u003c/b\u003e[i] \u0026lt; \u003cb\u003eb\u003c/b\u003e[i].\nNote that this means that Ciel can always finish all her courses: for example, she may take them in the order 0, 1, ..., n-1.\n\u003cbr\u003eMost colleges use GPA (grade point average) to grade their students, but Ciel\u0027s college is different.\nThey use a rating system similar to the one used at TopCoder.\nCiel\u0027s initial rating is 1200.\nFor each course, Ciel has estimated how well she will perform in the course and how this will influence her rating.\nThus, we know that for each i, taking course i will increase Ciel\u0027s rating by \u003cb\u003echange\u003c/b\u003e[i].\nNote that this amount remains the same regardless of when Ciel takes the course.\nAlso note that for some courses the value \u003cb\u003echange\u003c/b\u003e[i] may be negative.\nFor example, \u003cb\u003echange\u003c/b\u003e[7] \u003d -200 means that taking course 7 will reduce Ciel\u0027s rating by 200.\n\u003cbr\u003eThe college is going to give a Rating Progress Award to one of the students.\nThis award is given to the student who had the largest \u003ci\u003erating progress\u003c/i\u003e during their studies.\nThe \u003ci\u003erating progress\u003c/i\u003e of a student is defined as follows:\nLet r[0], r[1], ..., r[n] be the sequence of the student\u0027s ratings.\n(Here, r[i] is the rating the student had after finishing i courses.)\nThe student\u0027s rating progress is the value max { r[i] - r[j] | 0 \u0026lt;\u003d j \u0026lt;\u003d i \u0026lt;\u003d n}.\n\u003cbr\u003eCiel wants to win the Rating Progress Award.\nYou are given the int[] \u003cb\u003echange\u003c/b\u003e with n elements and the int[]s \u003cb\u003ea\u003c/b\u003e and \u003cb\u003eb\u003c/b\u003e that describe the dependencies between the courses.\nCompute and return the largest possible rating progress Ciel can have if she chooses the optimal order in which to take her n courses.\nRemember that she needs to choose an order that satisfies all the given dependencies.\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u003ch3\u003eDefinition\u003c/h3\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003eClass:\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003eRatingProgressAward\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003eMethod:\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003emaximalProgress\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003eParameters:\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003eint[], int[], int[]\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003eReturns:\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003eint\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003eMethod signature:\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003eint maximalProgress(int[] change, int[] a, int[] b)\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e(be sure your method is public)\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u003ch3\u003eConstraints\u003c/h3\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" valign\u003d\"top\" class\u003d\"statText\"\u003e-\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003en will be between 1 and 50, inclusive.\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" valign\u003d\"top\" class\u003d\"statText\"\u003e-\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003cb\u003echange\u003c/b\u003e will contain exactly n elements.\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" valign\u003d\"top\" class\u003d\"statText\"\u003e-\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003eEach element in \u003cb\u003echange\u003c/b\u003e will be between -1,000 and 1,000, inclusive.\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" valign\u003d\"top\" class\u003d\"statText\"\u003e-\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003cb\u003ea\u003c/b\u003e will contain between 0 and 1,000 elements, inclusive.\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" valign\u003d\"top\" class\u003d\"statText\"\u003e-\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003cb\u003ea\u003c/b\u003e and \u003cb\u003eb\u003c/b\u003e will contain the same number of elements.\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" valign\u003d\"top\" class\u003d\"statText\"\u003e-\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003eFor each i, 0 \u0026lt;\u003d \u003cb\u003ea\u003c/b\u003e[i] \u0026lt; \u003cb\u003eb\u003c/b\u003e[i] \u0026lt; n.\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u003ch3\u003eExamples\u003c/h3\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" nowrap\u003d\"true\" class\u003d\"statText\"\u003e0)\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{1,-1,10,-10,100,-100}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003eReturns: 111\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003eThere are no dependencies - Ciel can take the courses in any order she likes.\nThe optimal solution is to take all courses with a positive rating change consecutively.\nFor example, suppose she takes the courses in the order { 0, 2, 4, 1, 3, 5 }.\nThe sequence of her ratings will be {1200, 1201, 1211, 1311, 1310, 1300, 1200}.\nThus, her rating progress will be 1311 - 1200 \u003d 111.\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" nowrap\u003d\"true\" class\u003d\"statText\"\u003e1)\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{1,-1,10,-10,100,-100}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{0,1,2,3,4}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{1,2,3,4,5}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003eReturns: 100\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003eThis time the given dependencies mean that Ciel has no choice: she must take the courses in increasing order.\nWhen she does so, the sequence of her ratings will be {1200, 1201, 1200, 1210, 1200, 1300, 1200}.\nThus, in this case her rating progress is only 1300 - 1200 \u003d 100.\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" nowrap\u003d\"true\" class\u003d\"statText\"\u003e2)\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{8,-10,5,1,-3,6,-7,2,-1,-4,0,-2}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{0,1,2,4,5,6,8,9,10}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{1,2,3,5,6,7,9,10,11}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003eReturns: 14\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" nowrap\u003d\"true\" class\u003d\"statText\"\u003e3)\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{8,-10,5,1,-3,6,-7,2,-1,-4,0,-2}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{0,1,2,4,5,6,8,9,10,1}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{1,2,3,5,6,7,9,10,11,5}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003eReturns: 12\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" nowrap\u003d\"true\" class\u003d\"statText\"\u003e4)\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{1000,-1000,1000}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{0,0,0,1,1,1}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{1,1,1,2,2,2}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003eReturns: 1000\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align\u003d\"center\" nowrap\u003d\"true\" class\u003d\"statText\"\u003e5)\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u0026nbsp;\u0026nbsp;\u0026nbsp;\u0026nbsp;\u003c/td\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{-1000}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003e{}\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003cpre\u003eReturns: 0\u003c/pre\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd class\u003d\"statText\"\u003e\u003ctable\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd colspan\u003d\"2\" class\u003d\"statText\"\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003chr\u003e\u003cp\u003eThis problem statement is the exclusive and proprietary property of TopCoder, Inc. Any unauthorized use or reproduction of this information without the prior written consent of TopCoder, Inc. is strictly prohibited. (c)2024, TopCoder, Inc. All rights reserved. \u003c/p\u003e\n \n "}}]}