import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } string COLOR(string s = "") { return "\x1b[" ~ s ~ "m"; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } void main() { /* const N = 2; const W = 3; const V = [3, 4]; const X = [1, 2]; */ /* V[1, N] V[x] > V[1] + V[x-1] (x >= 3) V[1]/1 > V[x]/x V[x] = a x + b (x >= 3) */ const N = 1000; const W = 1000; int[] V, X; V ~= W; X ~= 1; { const a = W + 1; const b = W + 1; foreach_reverse (x; 2 .. W + 1) { V ~= a * x - b; X ~= x; } } writeln(N, " ", W); foreach (i; 0 .. N) { writeln(V[i], " ", X[i]); } foreach (i; 0 .. N - 1) { const det = V[i] * X[i + 1] - V[i + 1] * X[i]; assert(det > 0 || (det == 0 && X[i] >= X[i + 1])); } auto fs = new int[W + 1]; foreach (i; 0 .. N) { foreach_reverse (x; 0 .. W - X[i] + 1) chmax(fs[x + X[i]], fs[x] + V[i]); } auto gs = new int[W + 1]; foreach (x; 0 .. W + 1) { int xx = x; foreach (i; 0 .. N) { if (xx >= X[i]) { xx -= X[i]; gs[x] += V[i]; } } } debug { writeln("fs = ", fs); writeln("gs = ", gs); foreach (x; 1 .. W + 1) { assert(fs[x] >= gs[x]); if (fs[x] == gs[x]) { writeln("match x = ", x); } } } }