[問題追加] Count Points in Triangle

geo/count_points_in_triangle/checker.cpp

@@ -0,0 +1,62 @@
+// https://github.com/MikeMirzayanov/testlib/blob/master/checkers/wcmp.cpp
+
+// The MIT License (MIT)
+
+// Copyright (c) 2015 Mike Mirzayanov
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "testlib.h"
+
+using namespace std;
+
+int main(int argc, char * argv[])
+{
+    setName("compare sequences of tokens");
+    registerTestlibCmd(argc, argv);
+
+    int n = 0;
+    string j, p;
+
+    while (!ans.seekEof() && !ouf.seekEof()) 
+    {
+        n++;
+
+        ans.readWordTo(j);
+        ouf.readWordTo(p);
+
+        if (j != p)
+            quitf(_wa, "%d%s words differ - expected: '%s', found: '%s'", n, englishEnding(n).c_str(), compress(j).c_str(), compress(p).c_str());
+    }
+
+    if (ans.seekEof() && ouf.seekEof())
+    {
+        if (n == 1)
+            quitf(_ok, "\"%s\"", compress(j).c_str());
+        else
+            quitf(_ok, "%d tokens", n);
+    }
+    else
+    {
+        if (ans.seekEof())
+            quitf(_wa, "Participant output contains extra tokens");
+        else
+            quitf(_wa, "Unexpected EOF in the participants output");
+    }
+}

geo/count_points_in_triangle/gen/dense.cpp

@@ -0,0 +1,35 @@
+#include <cstdio>
+#include <vector>
+
+#include "../params.h"
+#include "random.h"
+using namespace std;
+
+int main(int, char* argv[]) {
+    long long seed = atoll(argv[1]);
+    auto gen = Random(seed);
+
+    int n = N_MAX;
+    int m = M_MAX;
+    int q = Q_MAX;
+    printf("%d\n", n);
+    for (int i=0; i<n; i++) {
+        long long a = gen.uniform(-12, 12);
+        long long b = gen.uniform(-12, 12);
+        printf("%lld %lld\n", a, b);
+    }
+    printf("%d\n", m);
+    for (int i=0; i<m; i++) {
+        long long a = gen.uniform(-9, 9);
+        long long b = gen.uniform(-9, 9);
+        printf("%lld %lld\n", a, b);
+    }
+    printf("%d\n", q);
+    for (int i=0; i<q; i++) {
+        int a = gen.uniform(0, n-1);
+        int b = gen.uniform(0, n-1);
+        int c = gen.uniform(0, n-1);
+        printf("%d %d %d\n", a, b, c);
+    }
+    return 0;
+}

geo/count_points_in_triangle/gen/example_00.in

@@ -0,0 +1,17 @@
+5
+-1 -1
+-1 2
+2 -1
+2 2
+5 5
+5
+0 0
+0 1
+1 0
+1 1
+1 1
+4
+0 1 2
+3 3 3
+0 3 4
+1 4 2

geo/count_points_in_triangle/gen/max_random.cpp

@@ -0,0 +1,35 @@
+#include <cstdio>
+#include <vector>
+
+#include "../params.h"
+#include "random.h"
+using namespace std;
+
+int main(int, char* argv[]) {
+    long long seed = atoll(argv[1]);
+    auto gen = Random(seed);
+
+    int n = N_MAX;
+    int m = M_MAX;
+    int q = Q_MAX;
+    printf("%d\n", n);
+    for (int i=0; i<n; i++) {
+        long long a = gen.uniform(-X_AND_Y_ABS_MAX, X_AND_Y_ABS_MAX);
+        long long b = gen.uniform(-X_AND_Y_ABS_MAX, X_AND_Y_ABS_MAX);
+        printf("%lld %lld\n", a, b);
+    }
+    printf("%d\n", m);
+    for (int i=0; i<m; i++) {
+        long long a = gen.uniform(-X_AND_Y_ABS_MAX, X_AND_Y_ABS_MAX);
+        long long b = gen.uniform(-X_AND_Y_ABS_MAX, X_AND_Y_ABS_MAX);
+        printf("%lld %lld\n", a, b);
+    }
+    printf("%d\n", q);
+    for (int i=0; i<q; i++) {
+        int a = gen.uniform(0, n-1);
+        int b = gen.uniform(0, n-1);
+        int c = gen.uniform(0, n-1);
+        printf("%d %d %d\n", a, b, c);
+    }
+    return 0;
+}

geo/count_points_in_triangle/gen/middle_random.cpp

@@ -0,0 +1,42 @@
+
+/*
+
+An easier solution ( O( N + M Q ) time ) can pass this testcase.
+
+*/
+
+#include <cstdio>
+#include <vector>
+
+#include "../params.h"
+#include "random.h"
+using namespace std;
+
+int main(int, char* argv[]) {
+    long long seed = atoll(argv[1]);
+    auto gen = Random(seed);
+
+    int n = N_MAX;
+    int m = M_MAX;
+    int q = min<long long>(Q_MAX, 4000'0000 / m);
+    printf("%d\n", n);
+    for (int i=0; i<n; i++) {
+        long long a = gen.uniform(-X_AND_Y_ABS_MAX, X_AND_Y_ABS_MAX);
+        long long b = gen.uniform(-X_AND_Y_ABS_MAX, X_AND_Y_ABS_MAX);
+        printf("%lld %lld\n", a, b);
+    }
+    printf("%d\n", m);
+    for (int i=0; i<m; i++) {
+        long long a = gen.uniform(-X_AND_Y_ABS_MAX, X_AND_Y_ABS_MAX);
+        long long b = gen.uniform(-X_AND_Y_ABS_MAX, X_AND_Y_ABS_MAX);
+        printf("%lld %lld\n", a, b);
+    }
+    printf("%d\n", q);
+    for (int i=0; i<q; i++) {
+        int a = gen.uniform(0, n-1);
+        int b = gen.uniform(0, n-1);
+        int c = gen.uniform(0, n-1);
+        printf("%d %d %d\n", a, b, c);
+    }
+    return 0;
+}

geo/count_points_in_triangle/hash.json

@@ -0,0 +1,22 @@
+{
+  "dense_00.in": "036f55e2799522e6368dc78fbef79e2822b4bb70ecc8541702f1fe5cb712a09f",
+  "dense_00.out": "464ed740e3d66104017ab38cb686f86b9958a1bbc8a8a0fd68496b1047c2075b",
+  "dense_01.in": "922fc5c5ca06f32d650f7164ba045641fd036b4b0c4725b767c6d4849dff3ef5",
+  "dense_01.out": "a7e3f7722d143d68eb9642fa64b030e1d46a7726b03dea96735298aea5c1211b",
+  "example_00.in": "1c1694bc76fbc885dc663f31749118c55f44de16e2c55694e6b716f9f72d409a",
+  "example_00.out": "49f044318460c78482da423fe4ce239bace57b06a491ad9b3e3a4d0714677955",
+  "max_random_00.in": "d2a0b5d592650f276a858f20eacc2046aa7ae6393dbe72e61a95305771c2adcc",
+  "max_random_00.out": "0dc84b413514d605a519a8d1ec04294d6f0625885a0c04fca6d1d2f1eada4eb5",
+  "max_random_01.in": "247830f28271610bc44722d51ed7fcf68ce5d3cdeae8058db8fa0652db6d10c0",
+  "max_random_01.out": "4031253445c3116e20f9e268ece2bcb8853cb51dcf8b689afd68076403d3d3ca",
+  "middle_random_00.in": "ec976e9a05c375faac0df26e48f28e126051196b76a069e9a6a0e41333d4c2d9",
+  "middle_random_00.out": "f88de1179fdfeafad2f55ee99d9f4e8abc586a3b3516884e77b5014051981a81",
+  "middle_random_01.in": "840dc205732fc0d926b9b4ea68964c6072351ae10e0708d65d97f8355e276b21",
+  "middle_random_01.out": "126b89028d49cb542bf6afa7c9b3344373176b700cbc30311078209fe6733509",
+  "middle_random_02.in": "254c810f18356b5205a6e620dcf2a605a7c8a319be1131122d5501df1317aff2",
+  "middle_random_02.out": "4411360df1cb335f27ff23481d2e70a7889034bc94cdfde512394590914db6de",
+  "middle_random_03.in": "b1a7a4d9106d7fd0ed0787941203ce0eb689367e058517a0067db82274bc4778",
+  "middle_random_03.out": "1a3fdb542543d1d159d4640fd3b2c03af7239ddd26d3e3b6473ca08f408283c7",
+  "middle_random_04.in": "b3914b4927f1f6ebcefe7336b322806a18f2381d795d59caf8eb5554d97c0993",
+  "middle_random_04.out": "edd0d6403ec3ba37c3796b689c2a7c0044a9587545428446535e5acfd2f5c7a7"
+}

geo/count_points_in_triangle/info.toml

@@ -0,0 +1,29 @@
+title = 'Count Points in Triangles'
+timelimit = 5.0
+forum = "https://github.com/yosupo06/library-checker-problems/issues/908"
+
+[[tests]]
+    name = "example.in"
+    number = 1
+[[tests]]
+    name = "middle_random.cpp"
+    number = 5
+[[tests]]
+    name = "max_random.cpp"
+    number = 2
+[[tests]]
+    name = "dense.cpp"
+    number = 2
+
+[[solutions]]
+    name = "naive.cpp"
+    allow_tle = true
+[[solutions]]
+    name = "fast.cpp"
+
+
+[params]
+    N_MAX = 500
+    M_MAX = 500
+    Q_MAX = 1_000_000
+    X_AND_Y_ABS_MAX = 1_000_000_000

geo/count_points_in_triangle/sol/correct.cpp

@@ -0,0 +1,107 @@
+/*
+
+O( N^2 M + Q ) time solution
+
+too slow at N,M = 1000
+
+*/
+
+#include "fastio.hpp"
+#include <vector>
+#include <algorithm>
+#include <cassert>
+
+template<class Int = long long, class Int2 = long long>
+struct VecI2 {
+    Int x, y;
+    VecI2() : x(0), y(0) {}
+    VecI2(Int _x, Int _y) : x(_x), y(_y) {}
+    VecI2 operator+(VecI2 r) const { return VecI2(x+r.x, y+r.y); }
+    VecI2 operator-(VecI2 r) const { return VecI2(x-r.x, y-r.y); }
+    VecI2 operator-() const { return VecI2(-x, -y); }
+    Int2 operator*(VecI2 r) const { return Int2(x) * Int2(r.x) + Int2(y) * Int2(r.y); }
+    Int2 operator^(VecI2 r) const { return Int2(x) * Int2(r.y) - Int2(y) * Int2(r.x); }
+    static bool compareYX(VecI2 a, VecI2 b){ return a.y < b.y || (!(b.y < a.y) && a.x < b.x); }
+    static bool compareXY(VecI2 a, VecI2 b){ return a.x < b.x || (!(b.x < a.x) && a.y < b.y); }
+};
+
+
+using i64 = long long;
+using namespace std;
+using Vec = VecI2<i64>;
+#define rep(i,n) for(int i=0; i<(int)(n); i++)
+
+int main(){
+    using nachia::cin;
+    using nachia::cout;
+    int N; cin >> N;
+    vector<Vec> A(N);
+    rep(i,N) cin >> A[i].x >> A[i].y;
+    int M; cin >> M;
+    vector<Vec> B(M);
+    rep(i,M) cin >> B[i].x >> B[i].y;
+
+    auto pointL = vector<int>(N); // bx < Ax
+    auto pointM = vector<int>(N); // bx = Ax
+    rep(i,N) rep(j,M) if(A[i].y == B[j].y){
+        if(B[j].x < A[i].x) pointL[i]++;
+        if(B[j].x == A[i].x) pointM[i]++;
+    }
+
+    auto edgeL = vector<vector<int>>(N, vector<int>(N)); // bx < lerp(Ax, Bx)
+    auto edgeM = vector<vector<int>>(N, vector<int>(N)); // bx = lerp(Ax, Bx)
+    rep(a,N) rep(b,N) if(A[a].y < A[b].y){
+        rep(i,M) if(A[a].y < B[i].y && B[i].y < A[b].y){
+            auto det = (A[a] - A[b]) ^ (B[i] - A[b]);
+            if(det < 0) edgeL[a][b]++;
+            if(det == 0) edgeM[a][b]++;
+        }
+    }
+
+    int Q; cin >> Q;
+    rep(qi, Q){
+        int a,b,c; cin >> a >> b >> c;
+        if(Vec::compareYX(A[b], A[a])) swap(a, b);
+        if(Vec::compareYX(A[c], A[b])) swap(b, c);
+        if(Vec::compareYX(A[b], A[a])) swap(a, b);
+        // c   ^y
+        // b   |
+        // a   +---> x
+
+        //      c
+        // nega |
+        //      v posi
+        //      a
+        auto det = (A[a] - A[c]) ^ (A[b] - A[c]);
+        int ans = 0;
+        if(det != 0){
+            if(A[a].y == A[b].y){ // A[a].x < A[b].x
+                //   c
+                // a   b
+                ans = edgeL[b][c] - (edgeL[a][c] + edgeM[a][c]);
+            } else if(A[b].y == A[c].y){ // A[b].x < A[c].x
+                // b   c
+                //   a
+                ans = edgeL[a][c] - (edgeL[a][b] + edgeM[a][b]);
+            } else if(det < 0){
+                //    c
+                // b
+                //    a
+                ans += edgeL[a][c];
+                ans -= edgeL[b][c] + edgeM[b][c];
+                ans -= edgeL[a][b] + edgeM[a][b];
+                ans -= pointL[b] + pointM[b];
+            } else {
+                // c
+                //    b
+                // a
+                ans += edgeL[a][b];
+                ans += edgeL[b][c];
+                ans += pointL[b];
+                ans -= edgeL[a][c] + edgeM[a][c];
+            }
+        }
+        cout << ans << '\n';
+    }
+    return 0;
+}