i have made a view frustum from scratch in javascript. i have been having trouble with objects that the camera is place within and also facing away from.
an example of the problem is below
ive been stuck on this for months with little help, chatgpt recommended that i switch to a right handed corodinate system, so i did, but it didnt seem to fix the problem.
my proccess for putting pixels on the screen is described below
step 1 = cross product with camera matrix
step 2 = cross product with projection matrix
step 3 = divide co-ordinates by their own w co-ord (normalize w to 1)
step 3.5 = im currently skipping culling. culling would go here, but since my object is made of multiple vertices i cant cull a vertex just because its offscreen as it forms part of a whole object, and that would deform the rest of the object
step 4 = cross product with projection to screen matrix
below shows how the co-ordinates of 1 vertex changes with each step
co-ordinates of vertex before projection
[5.00,9.00,10.00,1.00]
good projection (tile is good)
step 1 = [5, 9, -4.799999999999979, 10]
step 2 = [-8.660254038143698, 15.588457268658656, 15.353535353535376, 4.799999999999979]
step 3 = [-1.8042195912799448, 3.2475952643039006, 3.198653198653217, 1]
step 4 = [-120.63293869199174, 637.1392896455851, 3.198653198653217, 1]
pixels = -120.63293869199174,637.1392896455851
#############################
bad projection from within the object (tile is deformed)
step 1 = [5, 9, 0.6000000000000014, 10]
step 2 = [-8.660254038143698, 15.588457268658656, 20.808080808080813, -0.6000000000000014]
step 3 = [14.433756730239462, -25.980762114431034, -34.68013468013461, 1]
step 4 = [2315.0635095359194, -3747.114317164655, -34.68013468013461, 1]
pixels = 2315.0635095359194,-3747.114317164655
###############################
bad projection from behind (tile appears on the ceiling, when A it should be on the floor and B it shouldn't be visible)
step 1 = [5, 9, 16.800000000000004, 10]
step 2 = [-8.660254038143698, 15.588457268658656, 37.17171717171718, -16.800000000000004]
step 3 = [0.5154913117942677, -0.9278843612296817, -2.2126022126022122, 1]
step 4 = [227.32369676914016, 10.817345815547753, -2.2126022126022122, 1]
pixels = 227.32369676914016, 10.817345815547753
does anyone know which step could be wrong or need changing in situation 2 and 3? and why?
below is a minimal (i know its 500 lines... but its about as minimal as i can get it) just open it in a browser and use wasd to control it.
<head>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.6.0/jquery.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjs/11.3.3/math.js"></script>
<script async src="https://unpkg.com/es-module-shims#1.3.6/dist/es-module-shims.js"></script>
</head>
<body>
<div id="canvas div" style = "position: relative; left: 0px; float:left; top: 0px;" >
<h1> first person below </h1>
<canvas id="mi_canvas" width="300" height="300" style="border-style: solid;"></canvas> <br>
<h1> radar below </h1>
<canvas id="radar_canvas" width="300" height="300" style="border-style: solid;"></canvas>
</div>
<div id="big info div" style = "position: relative; left: 310px; float:left; float:top; top: 0px; width:400px;" >
<div id = "info_1111"> </div><br>
</div>
<script>
var floor_y_pos = 9
canvas = document.getElementById("mi_canvas");
ctx = canvas.getContext("2d");
radar = document.getElementById("radar_canvas");
radar_ctx = radar.getContext("2d");
render_distance = 1000;
fov = math.pi / 2
class Projection{
constructor(){
var NEAR = player.near_plane
var FAR = player.far_plane
var RIGHT = Math.tan(player.h_fov/2)
var LEFT = - RIGHT
var TOP = Math.tan(player.v_fov /2)
var BOTTOM = -TOP
var m00 = 2*NEAR / (RIGHT - LEFT)
var m02 = (RIGHT + LEFT)/(RIGHT - LEFT)
var m11 = 2*NEAR / (TOP - BOTTOM)
var m12 = (TOP + BOTTOM) /(TOP - BOTTOM)
var m22 = (FAR * NEAR) / (FAR - NEAR)
var m23 = -2 * NEAR * FAR / (FAR-NEAR)
this.projection_matrix = [
[-m00,0,m02,0],
[0,m11,0,0],
[m02,m12,-m22,-1],
[0,0,m23,0]
]
var HW=player.H_WIDTH
var HH = player.H_HEIGHT
this.to_screen_matrix = [
[HW,0,0,0],
[0,HH,0,0],
[0,0,1,0],
[HW,HH,0,1]
]
}
}
function multiply(a, b) {
var aNumRows = a.length, aNumCols = a[0].length,
bNumRows = b.length, bNumCols = b[0].length,
m = new Array(aNumRows); // initialize array of rows
for (var r = 0; r < aNumRows; ++r) {
m[r] = new Array(bNumCols); // initialize the current row
for (var c = 0; c < bNumCols; ++c) {
m[r][c] = 0; // initialize the current cell
for (var i = 0; i < aNumCols; ++i) {
m[r][c] += a[r][i] * b[i][c];
}
}
}
return m;
}
function mi_position_matrix_multiplier(A, B)
{
var new_matrix = []
for (var new_num_ind = 0; new_num_ind < A.length; ++new_num_ind)
{
this_num = 0;
for (var a_ind = 0; a_ind < A.length; ++a_ind)
{
this_num += (A[a_ind] * B[a_ind][new_num_ind])
}
// console.log("just added this num to my new matrix = "+this_num.toString())
new_matrix.push(this_num)
}
return new_matrix;
}
function pythagoras(thing1, thing2)
{
dist = (((thing1[0]-thing2[0])**2)+((thing1[1]-thing2[1])**2))**0.5
return dist
}
class vertex{
constructor(x, y,z , id){
this.id = id
this.position = [x,y,z,1]
this.min_dist = 1.5 // minimum possible distance between player and object
}
is_this_object_behind_player(){
var arrow_length = 0.0001;
var pointing_position = [player.position[0]+(player.forward[0]*arrow_length) , player.position[2]-(player.forward[2]*arrow_length)]
var dist1 = pythagoras([this.position[0],this.position[2]], pointing_position)
var dist2 = pythagoras([this.position[0],this.position[2]], [player.position[0],player.position[2]])
if (dist1 < dist2){
return true;}
else if (dist1 > dist2){
return false;}
else{console.log(" else ");}
}
screen_projection(){
var position = mi_position_matrix_multiplier(this.position , player.camera_matrix())
console.log(position+" = position , which is a cross product of this.position"+this.position+" & "+ player.camera_matrix()+ " = player.camera_matrix()")
update_matrix_info_debug("camera_matrix",player.camera_matrix())
update_matrix_info_debug("position", position)
position = mi_position_matrix_multiplier(position , projection.projection_matrix) // does this just convert the position to cameras reference frame.
console.log(position+" = position , which is a cross product of position"+position+" & "+ projection.projection_matrix+ " = projection.projection_matrix")
update_matrix_info_debug("projection_matrix",projection.projection_matrix)
update_matrix_info_debug("position after being multiplied by proj matrix", position)
// if so then i image to screen matrix is insufficient
for (let i = 0; i < position.length; i++) {
position[i] = position[i]/position[3]
}
console.log(position+" = position after being normaslized")
for (let i = 0; i < position.length; i++) {
if (i != 9787781){
console.log(i+" =-= "+position[i])
if (this.is_this_object_behind_player()){for (let ii = 0; ii < position.length; ii++) {position[ii] = -999999999;} console.log("culling1")}
if (position[i] > 2){for (let ii = 0; ii < position.length; ii++) {position[ii] = -9999;} console.log("culling2")}
if (position[i] < -2){for (let ii = 0; ii < position.length; ii++) {position[ii] = -9999;} console.log("culling3")}
}
} // also all examples say set position = 0 if culling
console.log(position+" = position after being culled")
position = mi_position_matrix_multiplier(position , projection.to_screen_matrix)
console.log(position+" = position after being multiplied by "+projection.to_screen_matrix+ " = projection.to_screen_matrix")
update_matrix_info_debug("projection.to_screen_matrix",projection.to_screen_matrix)
update_matrix_info_debug("position after being multiplied by projection.to_screen_matrix", position)
ctx.beginPath();
var scale_multiplier = (render_distance / pythagoras([this.position[0],this.position[2]] , [player.position[0],player.position[2]]))*1.5
var arrow_size = 0.02 * scale_multiplier;
ctx.moveTo(position[0]-arrow_size ,position[1]+arrow_size);
ctx.lineTo(position[0]+arrow_size ,position[1]-arrow_size);
ctx.moveTo(position[0]+arrow_size ,position[1]+arrow_size);
ctx.lineTo(position[0]-arrow_size, position[1]-arrow_size);
ctx.stroke();
}
return_screen_projection(dont_cull = false){
var position = mi_position_matrix_multiplier(this.position , player.camera_matrix())
position = mi_position_matrix_multiplier(position , projection.projection_matrix) // does this just convert the position to cameras reference frame.
for (let i = 0; i < position.length; i++) {
position[i] = position[i]/position[3]
}
position = mi_position_matrix_multiplier(position , projection.to_screen_matrix)
return [position[0],position[1]]
}
}
class player{
constructor(){
this.position =[0,0,0,1.0]
this.forward = [0,0,1,1]
this.up = [0,1,0,1]
this.right =[1,0,0,1]
this.h_fov = 3.1415926535/3
this.v_fov = this.h_fov * (canvas.height / canvas.width)
this.near_plane = 1
this.far_plane = 100
this.moving_speed = 0.2
this.rotation_speed = 0.1
this.H_WIDTH = canvas.width/2
this.H_HEIGHT = canvas.height/2
this.anglePitch = 0
this.angleYaw = 0
}
set_camera_angle(){
var rotate = multiply(rotate_x(this.anglePitch) , rotate_y(this.angleYaw))
this.forward = [0, 0, 1, 1]
this.up = [0, 1, 0, 1]
this.right = [1, 0, 0, 1]
this.forward = mi_position_matrix_multiplier(this.forward , rotate)
this.right = mi_position_matrix_multiplier(this.right , rotate)
this.up = mi_position_matrix_multiplier(this.up , rotate)
}
camera_yaw(angle){
this.angleYaw += angle}
translate_matrix(self){
var x = this.position[0];
var y = this.position[1];
var z = this.position[2];
var w = this.position[3];
return [
[1,0,0,0],
[0,1,0,1],
[0,0,1,0],
[-x,-y,z, 1]
]}
rotate_matrix(){
var rx = this.right[0]
var ry = this.right[1]
var rz = this.right[2]
var w = this.right[3]
var fx = this.forward[0]
var fy = this.forward[1]
var fz = this.forward[2]
var w = this.forward[3]
var ux = this.up[0]
var uy = this.up[1]
var uz = this.up[2]
var w = this.up[3]
return [
[rx,ux,fx,0],
[ry,uy,fy,0],
[rz,uz,fz,0],
[0,0,0,1]
]
}
camera_matrix(){
return multiply(this.translate_matrix(), this.rotate_matrix());
}
check_min_distance_isnt_overcome_by_this_move(dx, dy){
var can_move = true;
console.log(" zzzzzzzzzzzzz ")
for (let i = 0; i < objects.length; i++) {
var dist=Math.abs(pythagoras([objects[i].position[0], objects[i].position[2]] , [this.position[0], this.position[2]]))
var dist2=Math.abs(pythagoras([objects[i].position[0], objects[i].position[2]] , [this.position[0]+dx, this.position[2]+dy]))
console.log(dist +" ########################### " +dist2)
if ((dist2 < objects[i].min_dist)&(dist > dist2))
{can_move = false; console.log(objects[i].min_dist +" yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy")}
else{console.log(objects[i].min_dist+" can move this is bloody min dist xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx "+dist2);}
}
return can_move;
}
move(event)
{
var key_code = parseInt(event.keyCode)
if (key_code == 37 || key_code == 39 || key_code == 83 || key_code == 87 || key_code == 119|| key_code == 115)
{
var dx = Math.cos(this.angleYaw)*this.moving_speed
var dy = Math.sin(this.angleYaw)*this.moving_speed
console.log("that were moving = dx , dy = "+dx.toString()+" , "+dy.toString())
if ( key_code == 37 || key_code == 87 || key_code == 119) {
if (this.check_min_distance_isnt_overcome_by_this_move(dx, -dy)){
this.position[0] += -dy
this.position[2] += dx
}
}
if (key_code == 39 || key_code == 83 || key_code == 115) {
for (let i = 0; i < this.position.length; i++) {
if (this.check_min_distance_isnt_overcome_by_this_move(dx, dy)){
this.position[0] += dy
this.position[2] += -dx
}
}
}
}
else {
if ( key_code == 38 || key_code == 65 || key_code == 97) {
this.camera_yaw(-this.rotation_speed)
}
if (key_code == 40 || key_code == 68 || key_code == 100) {
this.camera_yaw(this.rotation_speed)
}
this.set_camera_angle()
}
}
}
function translate(pos){
tx,ty,tz=pos
return np.array([
[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[tx,ty,tz,1]
])}
function rotate_x(angle){
return [
[1,0,0,0],
[0,Math.cos(angle),Math.sin(angle),0],
[0,-Math.sin(angle),Math.cos(angle),0],
[0,0,0,1]
]
}
function rotate_y(a){
return [
[math.cos(a),0, -math.sin(a),0],
[0,1,0,0],
[math.sin(a), 0 , math.cos(a),0],
[0,0,0,1]
]
}
function update_radar(){
var arrow_length = 4;
var object_size = 6.5;
radar_ctx.beginPath();
var mid_screen = [radar.width/2,radar.height/2];
pointing_position = [mid_screen[0]+(player.forward[0]*arrow_length) , mid_screen[1]-(player.forward[2]*arrow_length)]
radar_ctx.moveTo(mid_screen[0], mid_screen[1]); // start of player pos on radar
radar_ctx.lineTo(pointing_position[0], pointing_position[1]);
radar_ctx.lineTo(pointing_position[0]-2, pointing_position[1]-2);
radar_ctx.lineTo(pointing_position[0]+2, pointing_position[1]+2);
radar_ctx.lineTo(pointing_position[0]-2, pointing_position[1]+2);
radar_ctx.moveTo(mid_screen[0], mid_screen[1]);
for (let i = 0; i < objects.length; i++) {
var dx = (player.position[0]-objects[i].position[0])
var dz = player.position[2]+objects[i].position[2]
var x = (dx*2) + mid_screen[0]
var z = (dz*2) + mid_screen[1]
x = x +(object_size/2)
z = z +(object_size/2)
radar_ctx.moveTo(x-object_size,z-object_size);
radar_ctx.lineTo(x+object_size,z+object_size);
radar_ctx.moveTo(x+object_size,z-object_size);
radar_ctx.lineTo(x-object_size,z+object_size);
}
radar_ctx.stroke();
}
function update_matrix_info_debug(matrix_name, matrix){
if (matrix[0].length > 1)
{
for (let x = 1; x < matrix.length+1; x++) {
for (let y = 1; y < matrix.length+1; y++) {
// console.log(matrix_name.toString()+"_"+x.toString()+y.toString());
document.getElementById(matrix_name.toString()+"_"+x.toString()+y.toString()).innerHTML = matrix[x-1][y-1]
}
}
}
else {
for (let x = 1; x < matrix.length+1; x++) {document.getElementById(matrix_name.toString()+"_"+"1"+x.toString()).innerHTML = matrix[x-1]}
}
}
class box{
constructor(x,z,size){
var low_y = 0.5
var high_y = low_y - size
this.position = [x+(size/2),0,z+(size/2)]
this.vertices = [new vertex(x,low_y,z,0),new vertex(x+size,low_y,z,1),new vertex(x,low_y,z+size,2),new vertex(x+size,low_y,z+size,3),
new vertex(x,high_y,z,4),new vertex(x+size,high_y,z,5),new vertex(x,high_y,z+size,6),new vertex(x+size,high_y,z+size,7)
]
this.faces=[ [0,1,3,2,0], [0,1,5,4,0] , [1,3,7,5,1] , [4,5,7,6,4] , [2,6,7,3,2] , [0,4,6,2,0]]
// this.faces=[ [0,4,6,2,0]]
}
draw_all_vertices(){
for (let i = 0; i < this.vertices.length; i++) {
this.vertices[i].screen_projection()
}
}
draw_all_faces(){
var each_point = []
for (let i = 0; i < this.vertices.length; i++) {
each_point.push(this.vertices[i].return_screen_projection())
}
var skip_drawing = if_most_of_these_numbers_are_off_screen(each_point)
if (skip_drawing){console.log(" skipp drawing any faces init ");return;}
ctx.fillStyle = '#f00';
var moved_to_first_yet = false
for (let face = 0; face < this.faces.length; face++) {
ctx.beginPath();
console.log("%%%%%%%%%%%%%%%%%%%%%%%%%");
console.log(this.faces);
console.log(this.faces[face]);
for (let vertex = 0; vertex < this.faces[face].length; vertex++)
{
console.log(vertex+" vertex bef dddddddddddddddddddddddddddddd")
var vertex2 = this.faces[face][vertex]
console.log(vertex2+" vertex aft ddddddddd ")
if (moved_to_first_yet == false)
{
moved_to_first_yet = true
ctx.moveTo( each_point[this.vertices[vertex2].id][0],each_point[this.vertices[vertex2].id][1]);
}
else{ctx.lineTo( each_point[this.vertices[vertex2].id][0],each_point[this.vertices[vertex2].id][1]);}
}
ctx.closePath();
ctx.fill();
}
}
}
class two_d_surdace {
constructor(verex1,verex2,verex3,verex4 , colour){
this.vertices = [verex1,verex2,verex3,verex4]
this.colour = colour
}
draw_all_faces(){
var each_point = []
for (let i = 0; i < this.vertices.length; i++) {
each_point.push(this.vertices[i].return_screen_projection(true))
}
ctx.fillStyle = this.colour;
var moved_to_first_yet = false
for (let vertex = 0; vertex < this.vertices.length; vertex++)
{
console.log(each_point[vertex][0]+" , "+each_point[vertex][1]+ " actual x y points on screen for this vertex of corner of floor ")
if (moved_to_first_yet == false)
{
moved_to_first_yet = true
ctx.moveTo( each_point[vertex][0],each_point[vertex][1]);
}
else{ctx.lineTo( each_point[vertex][0],each_point[vertex][1]);}
}
ctx.closePath();
ctx.fill();
}
}
function if_off_screen(x, y)
{
if (x> canvas.width || x < 0){console.log(x +" x = off screen "); return true;}
if (y > canvas.height || y < 0){console.log(y +" y = off screen "); return true;}
console.log(x +" , "+y + " =x,y = not off screen ");
return false;
}
function if_most_of_these_numbers_are_off_screen(numbers){
var threshold = 1; //Math.floor(numbers.length*0.49)
var counter = 0
console.log(numbers + " xxxx numbers as they come in ")
for (let i = 0; i < numbers.length; i++) { if (if_off_screen(numbers[i][0], numbers[i][1])){console.log(numbers[i]+" , "+numbers[i+1]+ " = numbers[i] are off screen"); counter +=1} else{console.log(numbers[i]+" , "+numbers[i+1]+ " = numbers[i] not off screen")} }
console.log("quuin quoirs of raptor");
if (counter >= threshold){console.log(threshold+" < " + counter);return true}
console.log(threshold+" > " + counter);
return false;
}
player = new player();
projection = new Projection()
objects = [] //
floor = new two_d_surdace(new vertex(50,floor_y_pos,50) , new vertex(-50,floor_y_pos,50) , new vertex(-50,floor_y_pos,-50) , new vertex(50,floor_y_pos,-50) , '#F90' )
update_radar()
$(document).on("keypress", function (event) {
player.move(event)
ctx.beginPath();
radar_ctx.beginPath();
radar_ctx.clearRect(0, 0, canvas.width, canvas.height);
ctx.clearRect(0, 0, canvas.width, canvas.height);
for (let i = 0; i < objects.length; i++) {
objects[i].draw_all_faces()
objects[i].draw_all_vertices()
}
floor.draw_all_faces()
update_radar()
});
</script>
</body>
I'm trying to solve this problem from Google's Code Jam 2008:
The problem is called Train Timetable and you can find the full explanation here:
Code Jam - Train Timetable
Note: I've decided to solve the problem with Node.js.
My code is the next:
function timeToMinutes(time) {
const timeArray = time.split(":");
const hours = parseInt(timeArray[0]);
const minutes = parseInt(timeArray[1]);
const hoursInMinutes = hours * 60;
const total = hoursInMinutes + minutes;
return total;
}
function timetableFiller(NAB, NBA, array) {
let timetable = {
departuresFromA: [],
arrivalsToB: [],
departuresFromB: [],
arrivalsToA: [],
};
for (let i = 0; i < NAB + NBA; i++) {
let tempArr = [];
tempArr = array[i].split(" ");
if (i < NAB) {
timetable.departuresFromA.push(tempArr[0]);
timetable.arrivalsToB.push(tempArr[1]);
} else {
timetable.departuresFromB.push(tempArr[0]);
timetable.arrivalsToA.push(tempArr[1]);
}
}
return timetable;
}
function timetableToMinutes(timetable) {
let timetableMinutes = {
departuresFromA: [],
arrivalsToB: [],
departuresFromB: [],
arrivalsToA: [],
};
for (const property in timetable) {
timetable[property].map((element) =>
timetableMinutes[property].push(timeToMinutes(element))
);
}
return timetableMinutes;
}
function trainsNeededCounter(arrivalsFromDestiny, departuresFromOrigin, tat) {
let trainsNeeded = departuresFromOrigin.length;
for (let i = 0; i < arrivalsFromDestiny.length; i++) {
for (let j = 0; j < departuresFromOrigin.length; j++) {
if (arrivalsFromDestiny[i] + tat <= departuresFromOrigin[j]) {
trainsNeeded = trainsNeeded - 1;
departuresFromOrigin.splice(j, 1);
}
}
}
return trainsNeeded;
}
function responseGenerator(inputA, inputB, caseNumber) {
return `Case #${caseNumber}: ${inputA} ${inputB}`;
}
function problemSolution(input) {
const numberOfCases = parseInt(input[0]);
input.shift();
let response = [];
let caseNumber = 0;
let NAB;
let NBA;
for (let i = 0; i < input.length; i = i + NAB + NBA + 2) {
caseNumber = caseNumber + 1;
const tat = parseInt(input[i]);
const arrayNTrips = input[i + 1].split(" ");
NAB = parseInt(arrayNTrips[0]);
NBA = parseInt(arrayNTrips[1]);
const arraySchedule = input.slice(i + 2, i + 2 + NAB + NBA);
const timetable = timetableFiller(NAB, NBA, arraySchedule);
const timetableMinutes = timetableToMinutes(timetable);
const trainsNeededAB = trainsNeededCounter(
timetableMinutes.arrivalsToA,
timetableMinutes.departuresFromA,
tat
);
const trainsNeededBA = trainsNeededCounter(
timetableMinutes.arrivalsToB,
timetableMinutes.departuresFromB,
tat
);
response.push(
responseGenerator(trainsNeededAB, trainsNeededBA, caseNumber)
);
}
return response;
}
function readInput() {
const readline = require("readline");
const rl = readline.createInterface({
input: process.stdin,
output: process.stdout,
terminal: false,
});
let problem = [];
rl.on("line", (line) => {
problem.push(line);
}).on("close", () => {
const solution = problemSolution(problem);
solution.map((response) => console.log(response));
});
}
readInput();
How to replicate the issue
You should login into Code Jam with your Google account.
Paste into the code area on the right side and activate the Test run mode.
As input you can copy paste the sample input provided in the problem and you can see that the output is exactly as the sample output.
I've tried with my own variations of the input and the responses seems correct but when I run the real attempt the platform says WA or Wrong Answer.
Thank you so much for your help!
I made a video about this recently. You should check it out.
I think you can understand the logic flow from it. We are both doing the same thing basically.
https://youtu.be/_Cp51vMDZAs
-check this out
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;
void solve(int t)
{
int NA, NB;
float T;
cin >> T >> NA >> NB;
cin.ignore();
vector<string> ASchedule, BSchedule;
if (NA > 0)
for (int i = 0; i < NA; i++)
{
string s;
getline(cin, s);
ASchedule.push_back(s);
}
if (NB > 0)
for (int i = 0; i < NB; i++)
{
string s;
getline(cin, s);
BSchedule.push_back(s);
}
int alength, blength;
alength = (int)ASchedule.size();
blength = (int)BSchedule.size();
if (alength == 0 || blength == 0)
{
cout << "Case #" << t << ": " << alength << " " << blength << endl;
return;
}
float TT = T / 10;
string val, value;
int d;
float ADH, ADM, AAH, AAM, BDH, BDM, BAH, BAM;
vector<float> AD, AA, BD, BA;
for (int i = 0; i < alength; i++)
{
val = ASchedule[i];
ADH = stof(val.substr(0, 2));
AAH = stof(val.substr(6, 2));
ADM = stof(val.substr(3, 2));
AAM = stof(val.substr(9, 2));
if (val.at(9) == '0')
{
AAM /= 10;
AAM += TT;
AAM *= 10;
}
else
AAM += T;
if (AAM > 59)
{
d = -1;
while (AAM != 59)
{
AAM -= 1;
d++;
}
AAH++;
AAM = 0;
AAM += d;
}
// if (ADH > 23)
// ADH = 0;
// if (AAH > 23)
// AAH = 0;
ADM /= 100;
ADH += ADM;
AAM /= 100;
AAH += AAM;
AD.push_back(ADH);
AA.push_back(AAH);
}
for (int j = 0; j < blength; j++)
{
value = BSchedule[j];
BDH = stof(value.substr(0, 2));
BDM = stof(value.substr(3, 2));
BAH = stof(value.substr(6, 2));
BAM = stof(value.substr(9, 2));
if (value.at(9) == '0')
{
BAM /= 10;
BAM += TT;
BAM *= 10;
}
else
BAM += T;
if (BAM > 59)
{
d = -1;
while (BAM != 59)
{
BAM -= 1;
d++;
}
BAH++;
BAM = 0;
BAM += d;
}
// if (BDH > 23)
// BDH = 0;
// if (BAH > 23)
// BAH = 0;
BDM /= 100;
BDH += BDM;
BAM /= 100;
BAH += BAM;
BA.push_back(BAH);
BD.push_back(BDH);
}
int no1 = alength, no2 = blength;
sort(BD.begin(), BD.end());
sort(BA.begin(), BA.end());
sort(AA.begin(), AA.end());
sort(AD.begin(), AD.end());
for (int i = 0; i < alength; i++)
for (int j = 0; j < blength; j++)
if (AD[i] >= BA[j])
{
no1--;
BA[j] = 50;
break;
}
for (int i = 0; i < blength; i++)
for (int j = 0; j < alength; j++)
if (AA[j] <= BD[i])
{
no2--;
AA[j] = 50;
break;
}
cout << "Case #" << t << ": " << no1 << " " << no2 << endl;
}
int main()
{
int N;
cin >> N;
cin.ignore();
for (int t = 1; t <= N; t++)
solve(t);
}